diccionario de geofisica d

1. D
DÕA: Digital-to-Analog ͑q.v.͒.
D & A: Dry and Abandoned; refers to an abandoned well.
daisy chain: A method of propagating signals along a bus,
often used in applications in which devices not request-
ing a signal respond by simply passing the signal on.
The first device requesting the signal breaks the daisy-
chain continuity. A daisy-chain scheme assigns priori-
ties based on the electrical position of a device along
the bus.
damped error multipliers: The ratio of damping factors
to the spectral value, indicating the change of param-
eters during successive iterations. See Raiche et al.
͑1985͒.
damping: 1. A slowing down or opposition to oscillation
caused by dissipation of the oscillation energy. „a…
Critical damping, ␮c, is the minimum damping that
will prevent oscillation from taking place. „b… The
damping factor ␮ is the ratio of the system friction to
that necessary for critical damping, or the quotient of
the logarithm of the ratio of two successive oscillations
if the system is underdamped. The damping factor is
one for critical damping, less than one for an under-
damped system ͑which will oscillate͒, and greater than
one for an overdamped system. See Figure D-1. „c…
Most geophones are slightly underdamped, often hav-
ing optimum damping that is 0.66 ␮c, which provides
the most rapid convergence. 2. Site damping is con-
cerned with natural resonances and the response to
standing-waves. Site damping can be thought of as
either the rate of amplitude decrease after cessation of
excitation or as the decrease in amplitude response as
the excitation frequency differs from the resonant fre-
quency. Measuring damping and Q generally requires
the use of controlled vibrators.
Daniell window: ͑dan’ y‫ץ‬l͒ See Figure W-12.
darcy: ͑dar’ se¯͒ A unit of permeability; the permeability
that will allow a fluid flow of one milliliter per second
of one centipoise viscosity fluid through one square
centimeter under a pressure gradient of one atmosphere
per centimeter. The unit commonly used is the milli-
darcy.
Darcy’s law: A relationship for 1D fluid flow rate q:
qϭ͑kA/␮͒⌬p/⌬x,
where kϭpermeability, Aϭcross-sectional area, ␮
ϭviscosity, and ⌬pϭpressure differential across the
thickness ⌬x. For radial flow into a cylindrical bore-
hole,
qϭ͑k/␮͒2␲rh͑‫ץ‬␳/‫ץ‬r͒,
where rϭradial distance and hϭheight of the cylinder.
dar Zarrouk: ͑dar zar ruk’͒ The name given by Maillet to
resistivity parameters or curves that deal with layered
anisotropic materials. The dar Zarrouk variable is the
transversal unit resistance (␳T), the depth integral of
the transverse resistivity perpendicular to the strata; the
dar Zarrouk function is the longitudinal unit con-
ductance (1/␳L), the depth integral of the conductivity
parallel to the strata; and the dar Zarrouk curve is a
plot of the mean resistivity (␳T) of the formation down
to the depth z, plotted versus the anisotropy coefficient
times z(␳T␳L)1/2
:
␳Tϭ⌺␳izi and 1/␳Lϭ⌺zi/␳i,
where zi are layer thicknesses. See Maillet ͑1947͒.
DAS: Deconvolution After Stack.
data bank: A database ͑q.v.͒.
database: 1. Computerized record-keeping system with
the purpose of maintaining information and making it
available on demand. 2. A collection of data organized
and managed by a central facility, not necessarily digi-
tal or computer based. A database management sys-
tem „DBMS… is a centralized computer facility to man-
age and provide consistent and secure access to a
database.
data compression: A scheme for packing data into a
smaller space.
data dimensionality: The smallest number of variables
that could be used to represent the data in a set.
data fusion: Merging data, often at different scales.
data harvesting: 1. Retrieving data that has been stored
temporarily at a geophone or ocean-bottom seismom-
FIG. D-1. Damping. (a) Effect of damping on an impulsive
input. (b) Effect of damping on the amplitude of a periodic
input.
78

2. eter or other type of station. 2. Collection of data from
a storage unit.
data influence matrix: See Jacobian.
data link: A comunication channel for transforming data
between two points.
data mining: Algorithms to search existing data sets to
locate data with certain attributes of interest.
data model: A description of data and data relationships.
data preparation: Translating data into machine-readable
form.
data reduction: Transforming experimental data into a
useful, ordered form, e.g., by correcting for known
effects such as elevation differences, measurement sys-
tem characteristics, etc.
data set: 1. A set of data. 2. A device for converting
signals from a terminal into a form suitable for trans-
mission and vice-versa. 3. A named collection of data
on a computer storage medium.
data storage capacities: Liner ͑1999͒ lists current data
storage capacities ͑using B for bytes͒ as: 9-track tape,
200-700 MB; CD-ROM disk, 650 MB; optical disk, 2
GB; digital audio tape, 2-5 GB; DVD disk, 5 GB;
digital linear tape, 10-15 GB; magnetic hard disk, 50
GB.
datum: ͑da¯’ d‫ץ‬m͒ 1. An arbitrary reference surface, the
reduction to which minimizes local topographic and
near-surface effects. 2. Elevation datum, the reference
level for elevation measurements, often sea level. 3.
Seismic datum, an arbitrary reference surface, the
reduction to which minimizes local topographic and
near-surface effects. Seismic times and velocity deter-
minations are referred to the datum plane ͑usually but
not necessarily horizontal and planar͒ as if sources and
geophones had been located on the datum plane and as
if no low-velocity layer existed. 4. A paleo-datum is
used in an attempt to restore strata or reflections to the
structural positions held at some ancient time.
datum correction: A calculation of the time required for a
seismic pulse to travel from the source to the datum
plane and from the datum plane to the geophone. This
value is subtracted from observed reflection times to
give the arrival time as if sources and geophones had
been located on the datum surface without any low or
irregular velocities below the datum. See static correc-
tion ͑q.v.͒.
datum correction velocity: The velocity assumed
beneath the datum surface, often the subweathering
velocity.
datum elevation: See datum.
datuming: ͑da¯’ t‫ץ‬m ‫ץ‬ng͒ 1. The arbitrary flattening and
straightening of a particular reflection for use as a
reference on a cross-section, i.e., using a paleo-datum;
flattening ͑see Figure F-12͒ thereby assuming that
everything was horizontal at the time of the paleo-
datum. The result emphasizes differences between this
and other reflections. 2. Changing the reference plane
of a wavefield.
datumized section: See flattened section.
datum plane: See datum.
daughter: An isotope formed by radioactive decay of a
parent isotope.
day number: The number of a day within a calendar year,
referred to Greenwich.
dB: DeciBel ͑q.v.͒ and see Figure D-3.
dBASE: A file format and data-management software
dBm: Decibels less than 1 milliwatt of power. Used, for
example, in specifying sensitivity for a certain input
impedance, such as ‘‘50 dBm at 5000 ohms.’’
DBMS, DBS: Acronym for DataBase Management Sys-
tem. See database.
dBÕoctave: Unit for expressing the slopes of filter curves.
dc: Direct Current
dc component: The amplitude of the Fourier analysis
component at zero frequency.
dc coupling: See coupling.
dc exponent: A quantity used in overpressure studies.
dc pulse method: See pulse method.
DDH: Diamond Drill Hole.
dead: 1. Not electrically connected, as a geophone whose
connection to the cable has pulled loose. 2. Having no
signal, as a dead trace. 3. Said of an area that has no
economical value. 4. Dead oil contains no dissolved
gas.
dead man: A buried anchor to which guy wires are
attached.
dead oil: Crude oil containing very little dissolved gas.
dead reckoning: Determining position by extrapolation of
the track and direction from a previously known point.
Inertial navigation and Doppler sonar are sophisticated
versions of dead reckoning. See positioning.
debris flow: ͑d‫’ץ‬ bre¯͒ A mass of fragments that are larger
than sand size that flowed into place. Similar to a
mudflow or turbidite except for larger particle size.
debug: To search for and remedy malfunctions or errors,
as with instruments or computer programs.
decade: A factor of 10 ͑or 1/10͒, used, for example, in
comparing two frequencies.
decade-normalized PFE: See percent frequency effect.
decay constant: The time for an exponentially changing
voltage to vary by 1/e ͑or to change 63%͒ from its
initial value. Also called time constant.
decay curve: 1. A graph of the decay of a quantity as a
function of time. An IP ͑induced potential͒ voltage
decay curve may be characteristic of a particular mate-
rial. In theory it can be transformed to a resistivity
spectrum. See Figure D-2. 2. The return of spinning
nuclei to their prior state after a superimposed magnetic
FIG. D-2. Decay curve for material containing two radio-
nucleides. The decay curve can be decomposed into the
two component curves and the slopes of a and b give their
respective half-lives.
data influence matrix 79 decay curve

3. field has been removed, as in nuclear magnetic reso-
nance logging ͑q.v.͒. Related to relaxation time.
decay lifetime: See pulsed neutron-capture log.
Decca: One of several radio positioning systems available
from Decca Survey Ltd.
decibel „dB…: ͑des’ ‫ץ‬ b‫ץ‬l͒ A unit used in expressing power
or intensity ratios: 10 log10 of the power ratio. An
amplitude ratio of 2 ͑which represents a power ratio of
4͒ is equivalent to 6 dB. Also expressed as 20 log10 of
the amplitude ratio. See also Figure D-3. 1 dB
ϭ0.1151 neper. Named for Alexander Graham Bell
͑1847–1922͒, American inventor.
decibelÕoctave: The change in response between frequen-
cies that are an octave apart, i.e., between frequencies
having the ratio either 1/2 or 2. Used to describe filter
slopes.
decile: Partitioning into tenths, e.g., values between 90%
and 100% are the tenth decile. In a distribution, P90
would include 90% of the elements, i.e., all except the
highest 10%.
decimate: ͑des’ ‫ץ‬ ma¯t͒ To resample systematically to
reduce the number of samples used to represent data.
decision rule: The criterion used to establish discriminate
functions, developed during the learning ͑training͒
stage of a supervised classification.
declination: ͑dek l‫’ץ‬ na¯ shun͒ 1. The angle between geo-
graphic north and magnetic north. Angles east of geo-
graphic north are considered positive, west of north
negative. 2. The angle between the celestial equator and
a celestial body. Differs from celestial latitude.
decoder: A logic device that converts data from one num-
ber system to another ͑e.g., an octal-to-decimal
decoder͒. Decoders are also used to recognize unique
addresses ͑such as a device address͒ and bit patterns.
de´collement: ͑da¯’ kol ma or da¯ kol’ ma͒ A detachment
surface across which structural deformation styles dif-
fer. Usually involves slippage along a bedding-plane
͑thrust faulting͒ and/or plastic flow.
decomposition: Separating into components. 1. Separat-
ing effects of different kinds or attributable to different
causes. 2. Separating a potential ͑e.g., gravity͒ map into
regional and residual; residualizing ͑q.v.͒. 3. Removing
the effects of filtering from a filtered waveform; decon-
volution ͑q.v.͒. 4. Deriving resistivity stratification from
a kernel function.
deconvolution: ͑de kon vo¯’ lu¯ sh‫ץ‬n͒ 1. A process designed
to restore a waveshape to the form it had before it
underwent a linear filtering action ͑convolution͒;
inverse filtering. The objective of deconvolution is to
nullify objectionable effects of an earlier filter action
and thus improve the recognizability and resolution of
reflected events. May mean „a… system deconvolution
to remove the filtering effect of the recording system;
„b… dereverberation or deringing to remove the filter-
ing action of a water layer; see also Backus filter and
gapped deconvolution; „c… predictive deconvolution to
attenuate multiples that involve the surface or near-
surface reflectors; „d… deghosting to remove the effects
of energy that leaves the source in the upward direction;
„e… whitening or equalizing to make all frequency
components within a band-pass equal in amplitude; „f…
shaping the amplitude-frequency and/or phase
response to match that of adjacent channels; or „g…
wavelet processing ͑q.v.͒. Deconvolution results may
vary markedly with different phase assumptions, gate
locations or widths, or operator lengths. Often involves
Wiener filtering ͑q.v.͒. Also called decomposition. See
Sheriff and Geldart ͑1995, 285 and 292–303͒. 2. Poten-
tial maps, well logs, and other data sets besides time
series may be deconvolved.
decorrugation: Removing herringbone effects ͑see her-
ringbone͒ that result from mislocation or datum-shifts
in acquisition, such as may be employed in aeromag-
netic data reduction.
decoupling: With respect to vibrators, when the pad loses
contact with the ground. Generally peak ground force is
set to not exceed 90% of the hold-down weight.
dedicated: Devoted exclusively to; for example, a ‘‘dedi-
cated’’ power generator might supply the power for a
seismic recording system only, another dedicated gen-
erator might power the navigation equipment, both
being separate from a ship’s normal power supply.
deep porosity density: Density farther away from the
borehole as measured with a borehole gravimeter ͑q.v.͒
rather than with a density log.
Deep Sea Drilling Program „DSDP…: An international
program from 1963 to 1983, which resulted in drilling
624 boreholes in the deep ocean floor from the drill ship
Glomar Challenger. See also JOIDES. The Ocean Drill-
ing Program (ODP) ͑q.v.͒ succeeded it.
deep seismic sounding „DSS…: A seismic profile ͑usually
refraction͒ that has the objective of studying the crust,
Moho, and upper mantle.
DeepStar: A consortium of oil and service companies
͑begun 1992͒ that tries to develop production technol-
ogy for use in deep marine areas.
deep tow: A sensor towed by a boat at larger-than-usual
depth, so as to be closer to features being imaged.
deep water: Water over a depth of 600 ft.
default: A specific action or value to be taken in case an
instruction or value is omitted.
deflagration: ͑def’ l‫ץ‬a gra¯, sh‫ץ‬n͒ An oxidation that pro-
ceeds at less than shock-wave velocity, often Ͻ1000
m/s. When it travels at shock wave velocity it is called
detonation.
Amplitude Energy
dB ratio ratio
Ϫ120 10Ϫ6
10Ϫ12
Ϫ80 10Ϫ4
10Ϫ8
Ϫ40 0.01 10Ϫ4
Ϫ20 0.1 0.01
Ϫ10 0.316 0.1
Ϫ6 0.501 0.251
Ϫ3 0.708 0.501
0 1 1
ϩ3 1.413 1.997
ϩ6 1.995 3.980
ϩ10 3.162 10
ϩ20 10 100
ϩ80 104
108
FIG. D-3 Decibel conversion.
decay lifetime 80 deflagration

4. deflection angle: See angles (surveying) and Figure A-13.
deflection of the vertical: The angular difference between
a plumb line ͑the vertical͒ and a perpendicular to the
geodetic ellipsoid. Produced by irregularities in the
Earth’s mass distribution. See Figure G-1.
deformation coefficient: A measure of rock deformation
based on the ratio of its in-situ resistivity, velocity, or
fracture porosity to that when undeformed.
degaussing: ͑de¯ gous’ ‫ץ‬ng͒ Demagnetization ͑q.v.͒.
degeneracy: ͑de¯ jen’ ‫ץ‬r ‫ץ‬ se¯͒ The situation where more
than one eigenfunction is associated with the same
eigenvalue, as where two vibration modes have the
same frequency. S-waves have a degeneracy of two
͑SH- and SV-waves͒ in isotropic media.
deghosting: See deconvolution.
degree: The highest power that a variable assumes in a
polynomial expression, such as yϭAϩBxϩCx2
ϩ...
For a differential equation, the power of the highest
derivative. Linear implies that the degree is one and
that all terms beyond Bx are zero; quadratic, that it is
two and terms beyond Cx2
are zero; cubic, three;
quartic, four; etc.
degrees of freedom: The minimum number of indepen-
dent variables that must be specified to define a system.
del „ٌ…: The vector gradient operator. In rectangular coor-
dinates,
ٌϭi ‫ץ/ץ‬xϩj ‫ץ/ץ‬yϩk ‫ץ/ץ‬z,
where i, j, k are unit vectors in the x, y, z directions. ٌU
is the gradient of the scalar field U. The operator ٌ2
,
the Laplacian, appears frequently:
ٌ2
ϭٌ•ٌϭ‫ץ‬2
/‫ץ‬x2
ϩ‫ץ‬2
/‫ץ‬y2
ϩ‫ץ‬2
/‫ץ‬z2
.
As an operator on a vector field V, ٌ•V is called the
divergence, and ٌϫV is called the curl. Del is also
called nabla and the vector operator. See also Figure
C-14 for expressions using del in cylindrical and
spherical coordinates.
delay cap: A cap that detonates a fixed time after an
electrical current is applied.
delay filter: See linear-phase filter.
delay line: A device capable of retarding a signal by a
fixed time interval. Electrical delay lines may use
capacitive and inductive elements. Coaxial cables and
transmission lines delay signals by the transit time
through the lines.
delay lock: A technique whereby a received code is com-
pared with an internally generated code and is time
shifted until the two match.
delay time: 1. In refraction work, the additional time
required to traverse a raypath over the time that would
be required to traverse the horizontal component at the
highest velocity encountered on the raypath. Compare
intercept time. See Sheriff and Geldart ͑1995, 439͒. The
concept implies that the refractor is nearly horizontal
under both source point and detectors. Delay time is
often assigned separately to the source and geophone
ends of a raypath. See Figure D-4. 2. Delay produced
by a filter; see filter correction. 3. Time lag introduced
by a delay cap. 4. In induced-polarization work, the
time interval between the ‘‘off’’ instant of the charging
current and the instant a measuring voltmeter oscillo-
graph is turned ‘‘on.’’ Delay times up to 500 or 1000 ms
may be necessary to allow dissipation of transient volt-
ages that are not related directly to the polarization
decay voltage.
delimiter: A special character in a string used to denote
units of various kinds ͑e.g., blanks delimit words, peri-
ods, commas, delimit sentences, delimit parameters,
etc.͒.
delineation well: Appraisal well ͑q.v.͒.
delta ␦, ␦ *: ␦ * is one of the Thomsen anisotropic
parameters ͑q.v.͒:
␦ *͑delta*͒ϭ͑1/2c2
33͓͒2͑c13ϩc14͒2
Ϫ͑c33Ϫc44͒͑c11ϩc33Ϫ2c44͔͒,
where cij indicate elements in the elastic constants
matrix. Another Thomsen anisotropic parameter is ␧,
and with weak anisotropy, ␦, which is independent of ␧,
is generally used instead of ␦*; it is the most critical
factor for transverse isotropy:
␦͑delta͒ϭ͑1/2͓͒␧ϩ␦ */͑1Ϫ␤2
/␣2
͔͒
ϭ͓͑c13ϩc14͒2
Ϫ͑c33Ϫc44͒2
͔/
͓2C33͑c33Ϫc44͔͒.
Several seismic expressions involve ␦, such as the
short-offset moveout correction to the vertical velocity,
VNMOϭ␣ʈ(1ϩ␦). For long offsets, another anisotropy
parameter, ␩ ͑eta͒ captures the deviation of long-offset
P-wave moveout from what it would have been for
isotropicity:
␩ϭ͑␧Ϫ␦͒/͑1ϩ2␦͒.
delta function: 1. An impulse ͑q.v.͒. 2. Kronecker delta
͑q.v.͒.
FIG. D-4. Refraction delay time. At the critical angle: source delay timeϭSB/V1ϪAB/V2ϭSE/V1; geophone delay
timeϭCG/V1ϪCD/V2ϭFG/V1. Source delay timeϩgeophone delay timeϭhead-wave intercept time.
deflection angle 81 delta function

5. delta t „⌬t͒: Moveout or stepout. 1. The time difference
between the arrival times at different geophone groups.
See dip moveout and dip calculation. ⌬t ordinarily
does not imply normal moveout unless specifically
stated. 2. Interval transit time, as used with the sonic
log.
demagnetization: 1. A method for determining the stable
component of remanent magnetization by partial
demagnetization and removal of components with low
coercive force. The specimen is placed in a space with
nulled field ͑such as produced with Helmholz coils͒ and
then subjected to an alternating magnetic field that is
reduced gradually by decreasing the current of the field
coil or by removing the specimen from the coil. 2.
Reducing the magnetic field to zero to effect complete
demagnetization to clean a magnetic tape ͑remove the
data stored on it͒ so that the tape can be reused. A tape
may be rotated during the demagnetization to remove
the effect of the Earth’s magnetic field. Also called
alternating-field demagnetization and degaussing.
demigration: 1. Creating a zero-offset synthetic seismic
section from a structural model. 2. Inverting the seismic
migration process, e.g., to enable use of a different
velocity model.
demodulation: The process of retrieving an original sig-
nal from a modulated signal.
Demoivre’s theorem: ͑de mauv’͒ The relationship,
eir␪
ϭ͑cos ␪ϩi sin ␪͒r
ϭcos r␪ϩi sin r␪,
where iϭ͌(Ϫ1). Named for Abraham Demoivre
͑1667–1754͒, English mathematician. Also spelled De
Moivre.
deMorgan’s theorems: See Boolean algebra. Named for
Augustus deMorgan ͑1806–1871͒, English mathemati-
cian.
demulsifier: A chemical used to break down oil/water
emulsions by reducing the surface tension of the oil
film surrounding water droplets.
demultiplex: To separate the individual component chan-
nels that have been multiplexed. See multiplexed for-
mat.
dendrite: One of the branching fibers of a neuron that
conveys impulses. Used with neural networks.
Densilog: A density log ͑q.v.͒. Densilog is a Dresser Atlas
tradename.
densimeter: ͑den sim’ i t‫ץ‬r͒ An instrument for measuring
intensity of electromagnetic ͑usually light͒ radiation, as
in determining albedo from remote sensing images.
densitometer: A device to measure the optical density of
a small area of an image.
density: 1. Mass per unit volume. Commonly measured in
g/cm3
or kg/m3
, often without the units being expressed
explicitly. Bulk rock densities vary mainly because of
porosity and are generally in the range 1.9–2.8 g/cm3
.
The ratio of density to that of water is called specific
gravity and is dimensionless. 2. Frequency of occur-
rence. 3. The equivalent position of a color on a gray
scale. See Figure C-7a. 4. A measure of the degree of
blackening of an exposed photograph after develop-
ment.
FIG. D-5. Density log. (a) Schematic of compensated density logging sonde. (b) Log showing the density ␳b and the
correction for mudcake, etc., ⌬␳. (Courtesy Schlumberger.)
delta t „⌬t… 82 density

6. density basement: Where a very large density contrast
exists so that anomalies resulting from deeper contrasts
are lost in the noise.
density contrast: The difference in density between two
formations or rock units. Lateral density contrasts are
responsible for lateral changes in the Earth’s gravity.
density log: A well log that records formation density. The
logging tool consists of a gamma-ray source ͑e.g.,
Cs137
͒ and a detector so shielded that it records back-
scattered gamma rays from the formation. This second-
ary radiation depends on the density of electrons, which
is roughly proportional to the bulk density. The com-
pensated density-logging tool ͑FDC͒ includes a second
detector that responds more to the mud cake and small
borehole irregularities; its response is used to correct
the readings of the main detector. See Figure D-5.
Sometimes called gamma-gamma log. Compare
nuclear cement log and photon log.
density profile: A line of gravity readings taken over a
topographic feature having appreciable relief that is not
associated with density variations or structure, the
object being to determine the best density factor for
elevation corrections; Nettleton’s method. The most
appropriate density is the one that minimizes the cor-
relation of gravity values with elevation. Method
devised by L. L. Nettleton. See triplets and Telford et
al. ͑1990, 18͒.
density slicing: Converting the grey tones of an analog
image into a series of discrete tonal ranges.
dep: DEParture ͑q.v.͒.
departure „dep.…: The east or west component of a line
expressed in linear units; the difference of the longi-
tudes of the ends of the line measured at a given
latitude. For a line directed toward the northeast or
southeast quadrant, the departure is positive or easting;
it is negative or westing for a line directed toward the
southwest or northwest quadrant.
departure curve: A graph that allows one to correct for
FIG. D-6. Depositional patterns resulting from the combination of relative sea level changes and depositional influx.
These patterns are sometimes resolvable in seismic data. The progradational patterns are called clinoforms. (From
Emery and Myers, 1996, 25.)
density basement 83 departure curve

7. measuring conditions or situations that differ from
‘‘standard.’’ Such curves, for example, might correct
well logs for differences in temperature, hole diameter,
mud type, adjacent beds, invasion, etc.
dephasing: Converting to zero phase.
depletion drive: Production that relies on the natural
fluid-pressure energy to move reservoir fluids to pro-
duction wells.
depocenter: Area of maximum deposition indicated by
the maximum thickness of a stratigraphic unit. The
location of a depocenter generally varies with geologic
time.
depositional energy: See energy.
depositional patterns: See Figures D-6, C-6, and S-32.
depositional remanent magnetism „DRM…: See rema-
nent magnetism.
depositional sequence: A stratigraphic unit composed of
a relatively conformable succession of genetically
related strata, bounded at top and base by unconformi-
ties or their correlative conformities.
depositional system: A 3D assemblage of lithofacies that
are genetically linked. See system tract.
depropagation: Conceptually, seismic energy moved
backward into the earth from the line of observation.
Inversion using a wave-equation algorithm; downward
continuation.
depth controller: A device with moveable wings that
fastens to a marine streamer to maintain it at a prede-
termined depth; see Figure D-7. Often includes a mag-
netic compass. Also called a bird.
depth gather: 1. A collection of the seismic traces that all
reflect from the same point, often corrected for normal
moveout ͑velocity͒. After correcting for various pos-
sible velocities, events on the gather are horizontal
when the velocities are correct. Same as common-
reflecting-point gather or common-depth-point gather.
2. The same sort of collection for converted-wave data
except for a common conversion point.
depth imaging: Depth migration ͑q.v.͒.
depthing: Conversion from time to depth.
depth map: A seismic structure map that shows the ver-
tical distance from a datum to a stratigraphic horizon,
usually in feet or meters.
depth migration: Any migration that properly handles
both vertical and lateral velocity variations although
most programs are limited in dip. Depth migration
outputs an accurate image relative to the subsurface,
usually in depth, occasionally in vertical two-way trav-
eltime.
depth of compensation: The assumed depth at which the
pressure caused by overlying crustal elements is con-
stant and below which lateral density variations are
assumed to disappear. Involved in isostatic correction.
Sometimes taken as the top of the asthenosphere. See
also isostasy.
depth of invasion: See invaded zone.
depth of investigation: 1. The depth beyond the surface
to which an exploration system can effectively explore.
Depends on array design, spacing, property contrast,
body geometry, and signal-to-noise ratio. The maxi-
mum depth at which interfaces or the sources of anoma-
lies are resolvable considering the signal-to-noise ratio
and other measurement considerations. Also see skin
depth. 2. The radius of a cylinder about a logging sonde
within which 50% of the signal comes for electrical
tools, 90% for nuclear tools, a loosely defined standard.
See Figure D-8 and Spies ͑1989͒.
depth of penetration: 1. Depth of investigation ͑q.v.͒. 2.
Skin depth ͑q.v.͒.
depth phases: Waves from earthquakes that begin by trav-
eling upward, such as indicated by lower-case initial
letters: pP, pS, sP, sS; ghosts.
depth point: 1. In reflection seismic work as a property of
a set of data, the position midway between source point
and geophone ͑the midpoint͒, under which the point of
reflection is located if the reflector is horizontal and if
velocity layering is also horizontal, and if wave conver-
sion is not involved. Earlier called the ‘‘reflection
point.’’ 2. Sometimes used for reflecting points in the
subsurface, in which case its location may be different
for every event, depending on the reflector’s dip and
depth and the velocity distribution. 3. In refraction
work, the point for which the depth to a horizon has
been calculated, usually the point where the headwave
energy leaves the refractor to travel to the geophone.
See Figure D-9. See also conversion point.
depth probe: A group of profiles for which the measuring
system dimensions are successively increased, designed
to obtain information on the layering pattern in an area.
Also called sounding, expander, and depth profile. 1.
A refraction depth probe determines approximate
depths and velocities of refraction markers; also called
refraction test. 2. An electrical-surveying technique of
exploring vertically down into the earth by employing
an orderly horizontal expansion of the interelectrode
interval or by changing the frequencies. Data from a
depth probe are interpreted to give the depth to a
resistivity contrast or anomalous IP material if horizon-
tal layering exists. Also called vertical electrical
sounding ͑VES͒. See two-dimensional plot.
depth rule: A rule relating the depth of a body to a feature
of anomaly shape. Depth rules apply to specific
anomaly source-body shapes; see Figure D-10. 1. Rules
used in gravity interpretation include ͑a͒ half-width
rules ͑the half-width being half the width at half the
anomaly amplitude͒: for point masses: depthϭ1.3
half-width, and for horizontal line masses: depth
ϭhalf-width. ͑b͒ For thin semi-infinite slabs and
FIG. D-7. Depth controller is clamped around (or other-
wise fastened to) streamer. When hydrostatic pressure is
less than the controller setting, the vane tilts so as to
cause the controller to sink as it is pulled through the
water. When pressure is greater than the setting, the vane
tilts the other way, causing the controller to rise. (Courtesy
Conoco.)
dephasing 84 depth rule

8. faults: half the width between points where the anomaly
is one-quarter and three-quarters amplitude ͑see Figure
H-1͒. 2. Rules used in magnetic interpretation include
͑a͒ the straight-slope-measurement rule ͑q.v.͒; ͑b͒ the
Peters’ rule for dikes: depthϭ5/8 of the horizontal
distance between points where the slope is half the
maximum slope; ͑c͒ the Tiburg rule for magnetic
poles: depthϭ2/3 of the horizontal distance at half the
maximum amplitude; ͑d͒ the Hannel rule for magnetic
poles: depthϭhalf of the horizontal distance at a third
the maximum amplitude; ͑e͒ the Thalen rule: the depth
of a magnetic source is 0.7 the horizontal distance
between maxima and minima; and other such rules. See
also automated depth estimation and radial power
spectrum.
depth sampling interval: 1. The interval ⌬z for sampling
a sonic log to make a synthetic seismogram. Generally
⌬zрVmin⌬t/2,
where Vminϭminimum velocity and ⌬tϭtime sam-
pling interval. 2. Time sampling interval ͑q.v.͒ except
after conversion from time to depth. 3. In depth migra-
tion, the interval for sample outputs.
depth section: A seismic cross-section or record section
where the vertical scale is linear with depth. Usually
͑but not necessarily͒ the data have been migrated so
that their horizontal and vertical locations represent as
nearly as possible the true positions of features.
depth slices: 1. Horizontal slices through a 3D depth-
migrated volume, sometimes a 3D time-migrated vol-
ume where arrival time has been converted to depth
assuming no lateral velocity changes. 2. The result of
applying a wavelength filter to potential field data to
emphasize anomalies around some depth.
depth slicing: A filtering technique used to emphasize
gravity and magnetic features with a particular apparent
depth. Based on power-spectrum slopes. Also called
pseudodepth slicing. See Ruder ͑1997͒.
depth sounder: Fathometer ͑q.v.͒.
depth sounding: Sounding ͑q.v.͒.
depth stretched: Changing a seismic section from evenly
sampled in time to evenly sampled in depth, i.e., from
linear with arrival time to linear with depth assuming
no lateral changes in velocity. A processing step
employed before frequency-domain migration.
depth-velocity ambiguity: Conversion from a time sec-
tion to a depth section requires better knowledge of the
velocity than is usually available, so that uncertainties
in depth result from the uncertainties in velocity. Depth
migration ͑q.v.͒ attempts to remove this ambiguity by
adjusting the velocity model to achieve the sharpest
image.
Deregowski loop: ͑der e¯ gow’ sky͒ A technique used
where the velocity varies slowly in the lateral direction.
Depth-migrated gathers are corrected with a local
velocity function and then reanalyzed for velocity to
update the velocity field.
dereverberation: ͑de¯ ri vur, b‫ץ‬ ra¯’ sh‫ץ‬n͒ Deconvolution
͑q.v.͒ to attenuate seismic energy that bounces back-
and-forth in a surface water layer or other near-surface
layer. Also called deringing. See also Backus filter.
deringing: See dereverberation.
FIG. D-8. Depth of investigation and resolution for logging tools. Reflection seismic resolution is of the order of
10–100 m. (From Bourke et al., 1989, 31.)
depth sampling interval 85 deringing

9. derivative map: A map of one of the derivatives of a field
of values such as gravity, magnetics, time structure, etc.
The objective of a derivative map is to emphasize short
wavelength ͑high-frequency͒ anomalies. 1. Dip and
azimuth maps generally involve the first horizontal
derivative. 2. With potential fields the second vertical
derivative ͓based on Laplace’s equation, ‫ץ‬2
␾/‫ץ‬z2
ϭ
Ϫ(‫ץ‬2
␾/␾x2
ϩ‫ץ‬2
␾/‫ץ‬y2
)͔ was once used widely, but it
has largely been replaced by the total gradient or total
horizontal derivative. The horizontal derivatives,
‫ץ‬2
␾/‫ץ‬x2
and ‫ץ‬2
␾/‫ץ‬y2
, are usually estimated by finite-
difference methods from values measured at gridded
points on a map, often using a residualizing template
based on polar representation of the Laplacian or by 2D
convolution with such a template. See Cordell and
Grauch ͑1985͒.
derrick: See drill rig.
Descartes’ law: ͑da¯ kartz’͒ Snell’s law ͑q.v.͒. Named for
Rene´ Descartes ͑1596-1650͒, French philosopher and
scientist.
designature: Deconvolution to remove the embedded
wavelet ͑or a measured or modeled wavelet͒, i.e., to
FIG. D-9. Depth point. „a… Midpoint, „b… reflecting point, and „c… refraction depth point. Where reflector dips, the
reflecting point is not under the midpoint and the subsurface coverage on the reflector is not exactly the difference
between midpoints.
FIG. D-10. Depth rules showing where various measurements are made on an anomaly curve. Sokolov distance
ϭhorizontal distance between intersections of maximum-slope line with the regional and with the line parallel to the
regional through the maximum. Peters distanceϭhorizontal distance between half the maximum slope points. Maxi-
mum-slope distanceϭhorizontal distance over which the curve is approximately a straight line with the maximum
slope. Hannel distanceϭhorizontal distance between points having the maximum amplitude and 1/3 of that amplitude.
Half-width distanceϭhorizontal distance between points having the maximum amplitude and 1/2 of that amplitude
[sometimes half width (q.v.) is defined differently].
derivative map 86 designature

10. estimate what would have resulted from an impulsive
source with broad bandwidth.
design gate: The aperture or window that contains the
data from which parameters are to be determined.
desk accessory: A small computer program, usually a
utility program, that is usable while running another
program.
despiking: Removing spikes that are attributed to noise.
destripping: 1. Eliminating stripes caused by a mismatch
of the sensors in Landsat’s simultaneous scan lines. 2.
Suppressing amplitude stripes caused by acquisition
variations.
destructive interference: See interference.
det: 1 DETonator; an explosive cap ͑q.v.͒. 2. DETermi-
nant ͑q.v.͒.
detachment zone: See de´collement.
detail survey: A survey run after a prospect has been
located, the objective of which is to define details of the
prospect.
detectable limit: The minimum thickness for a bed to
give a reflection that stands out above the background.
Often of the order of 1/25 of the dominant wavelength.
Also called the limit of visibility. Compare resolvable
limit.
detection: In general, signal-processing procedure for
making choices about competitive decisions. Detection
often involves nonlinear signal processing. Binary
detection requires a choice between two decisions.
detector: 1. A device that senses or measures a phenom-
enon; a sensor. 2. A geophone ͑q.v.͒.
determinant: A scalar function of a square matrix ͑A͒:
det Aϭ͚i
aikAikϭ͚k
aikAik,
where Aik is the cofactor of the element aik. The
cofactor is (Ϫ1)iϩk
times the matrix found by deleting
the ith row and the kth column.
determinant resistivity: A term used with magnetotellu-
ric methods ͑q.v.͒ for the apparent resistivity ␳a based
on the magnetotelluric impedance tensor, Z:
␳aϭ͑1/␻␮0͒det͑Z͒,
where ␻ϭangular frequency and ␮0ϭpermeability of
free space. This parameter is rotationally invariant and
thus independent of the choice of coordinate axes, as
contrasted with other apparent resistivity definitions
based upon individual components of Z. See Ber-
dichevsky and Dimitriev ͑1976͒.
deterministic: From a certain set of causes, a unique
situation will develop. As opposed to probabilistic,
which leads only to the probability that certain situa-
tions will follow.
deterministic deconvolution: Deconvolution where the
particulars of the filter whose effects are to be removed
are known ͑or assumed͒. See Sheriff and Geldart ͑1995,
292͒
detonating cord: An explosive rope. A detonation at one
end starts an explosion wave traveling down the cord,
detonating other explosives that may be attached to the
cord.
detonator: Cap ͑q.v.͒.
detrending: Removing the average or a linear trend from
a data set prior to Fourier analysis.
detrital remanent magnetism „DRM…: See remanent
magnetism.
detuning: Adjusting amplitudes to remove variations
caused by the tuning effect ͑q.v.͒ in the vicinity of a
quarter wavelength thickness.
development well: A well drilled within an area believed
to be productive of oil, gas or other economic resource
previously discovered by an exploratory well. Compare
wildcat well, appraisal well.
deviation: 1. In drilling, departure of a borehole from
vertical. See drift, directional survey, and rectify. 2.
Angle with the vertical.
deviation of mean: Standard deviation ͑q.v.͒.
deviatoric stress: ͑de¯v, e¯ ‫ץ‬ tor ik’͒ The stress tensor can
be considered the sum of an isotropic part plus a
deviatoric part ͑deviatorix͒. See Bullen and Bolt
͑1985͒.
Devilish: An early method of accomplishing DMO pro-
cessing ͑q.v.͒. A Digicon tradename.
dextral: ͑dek’ str‫ץ‬l͒ Rotation to the right or clockwise. A
dextral strike-slip fault is also called right lateral.
Opposite is sinistral. See Figure F-4.
DFN: Delayed Fission Neutron log.
DFS: Digital ͑seismic͒ Field System. Texas Instruments
tradename.
DGPS: Differential Global Positioning System ͑q.v.͒.
DHD, DHI: Direct Hydrocarbon Detection/Indicator, a
misnomer because it is not ‘‘direct.’’ See hydrocarbon
indicators. DHI has also been called a ‘‘dry-hole indi-
cator’’ because of applying it inappropriately without
completely understanding it.
diachronous: ͑dı¯ ak’ r‫ץ‬ n‫ץ‬s͒ A rock type that in different
areas is of different age; time-transgressive.
diagenesis: Any chemical, physical, or biological change
that a sediment has undergone after it is deposited
͑except for weathering and metamorphism͒. It
embraces processes such as compaction, cementation,
leaching, hydration, recrystalization, replacement, dolo-
mitization, reworking, authigenesis, bacterial action,
and concretion formation. Diagenesis may destroy or
create porosity ͑secondary porosity͒ or permeability.
diagenetic magnetite: A magnetic mineral formed as a
replacement mineral by sedimentary diagenetic pro-
cesses including hydrothermal alteration, temperature,
pressure, change in EH/pH, dolomitization, and other
mineralization changes. Sometimes formed by hydro-
carbon seepage.
diagnostic check: A routine designed to locate malfunc-
tions.
dialog box: A pop-up on a computer screen that asks for
information or a decision.
diagonal matrix: A matrix that has zeros for all elements
not on the principal diagonal.
dialogue mode: See interactive.
diamagnetic: ͑dı¯, ‫ץ‬ mag net’ ik͒ Having net negative
magnetic susceptibility and a permeability less than that
of free space ͑less than unity in the cgs system͒. The
motion of an electron about a nucleus produces a min-
iature circular current whose magnetic-moment vector
precesses around an applied external field. This addi-
tional periodic motion produces a magnetic moment
opposite in direction to the applied field. Diamagnetic
effects rarely exceed one nanotesla, the most evident
diamagnetic anomalies caused by salt domes generally
design gate 87 diamagnetic

11. are evident only because other magnetic sources are so
far away. Compare paramagnetic and ferromagnetic.
diamond array: A type of geophone or source point array
in which the elements are laid out on a grid of lines at
about 45° to the seismic line, the pattern having the
general shape of a diamond. See Figure A-20.
diapir: ͑dı¯’ ‫ץ‬ per͒ A flow structure whose mobile core has
pierced overlying rocks. Salt and shale are the most
common sedimentary rocks involved in diapirs. Intru-
sive rocks can also form diapir-like features but ‘‘dia-
piric’’ is usually restricted to plastic flow.
dichroic: ͑dı¯ kro¯’ ik͒ A beam-splitting mirror that effi-
ciently reflects certain wavelengths while transmitting
others.
dictionary: A database in which identifiers are structured
and regulated. Identifiers have persistent meaning in all
logical files in which they occur.
die-away: See pulsed neutron-capture log.
dielectric constant „␧…: ͑dı¯, ‫ץ‬ lek’ trik͒ A measure of the
capacity of a material to store charge when an electric
field is applied. It is the dimensionless ratio of the
capacitivity or permittivity, the ratio of the electrical
displacement D to the electric field strength E, of the
material to that of free space:
Dϭ␧E.
Also called specific inductive capacity. It is frequency
and temperature dependent. Typical values are 1.0 for
air, 80 for water, 5-20 for granite, 3-100 for dry-to-
moist sand. A complex relative permittivity ␧* is
sometimes used:
␧*ϭ␧Ϫj␧Љ,
where ␧Љ is the dielectric loss factor, a measure of the
loss of energy through conductivity, polarization cur-
rents, etc.
dielectric log: A class of high-frequency, electric-logging
sondes that operate at a single frequency in the MHz to
low GHz range to measure formation effects of phase-
shift, amplitude, and attenuation on a transmitted elec-
tromagnetic wave. Phase shift, related to dielectric per-
mittivity, is treated as propagation time, tp, a quantity
virtually independent of salinity for water but signifi-
cantly lower than for oil, gas, or rock materials. If the
lithology is known, tp ͑corrected for attenuation͒ may
allow porosity determination. The dielectric log offers a
means to calculate residual hydrocarbon saturation in
the shallow flushed zone.
dielectric loss: The energy loss per cycle in a dielectric
material resulting from conduction and slow polariza-
tion currents or other dissipative effects.
dielectric permittivity: Dielectric constant ͑q.v.͒.
dielectric polarization: The response of a dielectric mate-
rial to an electric field, producing an induced dipole-
moment per unit volume. In an insulating dielectric
material, no net electric charge need be transferred by
the exciting field. By some definitions, induced polar-
ization is a lossy type of dielectric polarization with a
long time constant.
dielectric susceptibility: See electric susceptibility.
difference section, difference map, difference volume:
The result of subtracting one section, map, or volume
from another. 1. Where two maps/sections/volumes
were acquired at different times, the difference ͑time-
lapse mapÕsection͒ shows the changes that have
occurred. 2. Where the two maps are of different hori-
zons, the difference ͑isotime or isopach map͒ repre-
sents the thickness of the intervening interval. Thick-
ness changes may suggest changes in deposition or
removal subsequent to deposition.
differential: 1. A difference between quantities. Thus, a
differential voltmeter measures the difference between
voltages. 2. A differential input on a voltmeter helps
reject noise that originates from the ground. See
common-mode rejection.
differential compaction: Uneven settling of sediments as
a result of loss of porosity. Differences in the irrevers-
ible volume change that rocks suffer when put under
pressure, as by the weight of sediments deposited on
top of them. Reefs, for example, are often less com-
pactable than surrounding shales; the greater compac-
tion of the shales thus produces a drape structure over
the reef, and the amount of the vertical expression of
the drape features becomes smaller gradually with
height above the reef.
differential curvature: For a gravitational equipotential
surface, this is the difference between the curvature of
the surface in the direction in which it curves the most
and the curvature at right angles to this direction, mul-
tiplied by the gravitational constant. Measured by the
torsion balance. Also called horizontal directive ten-
dency „HDT….
differential Global Positioning System „DGPS…: A Glo-
bal Positioning System ͑q.v.͒ method for locating a
mobile station that employs a nearby fixed reference
station at a known location to remove unaccounted-for
deviations in a satellite’s location or in the travel path of
its signal through the atmosphere.
differential normal moveout: 1. The difference between
the normal moveouts of adjacent channels within a
gather. 2. Sometimes refers to residual normal moveout
͑q.v.͒, the normal moveout that remains after an incor-
rectly assumed amount is removed. 3. Also, may refer
to the difference between the normal moveout for pri-
mary events and that for multiples.
differential pressure: 1. The effective stress on a rock,
the difference between the pressure of a rock’s pore
fluid and that produced by the weight of the overbur-
den. It is important in drilling boreholes, controlling
compaction, and determining seismic velocity. Also
called Terzaghi effective stress. See normal pressure.
2. What drillers mean by differential pressure is usually
the difference in fluid pressures across the borehole
wall, the difference between the pressure induced by
the mud column and that of the formation fluid.
differential weathering correction: The difference
between the weathering corrections at two locations, for
example, at two nearby geophone groups.
differentiation: 1. A mathematical operation giving the
rate of change ͑slope͒ of a function with respect to
some variable. The equivalent operation for discrete
series is convolution with the operator ͓Ϫ1, ϩ1͔. 2.
Separation according to some criteria, such as particle
size. 3. Separation of a magma into fractions of differ-
ent bulk composition.
differentiator: Convolution with ͓ϩ1,Ϫ1͔, which thereby
diamond array 88 differentiator

12. determines the slope between adjacent samples for a
sample interval of unity.
diffracted reflection: The diffraction resulting from
reflected energy striking a diffracting point; its curva-
ture is appropriate to the diffracting point depth, not to
the arrival time.
diffraction: ͑di frak’ sh‫ץ‬n or dif frak’ sh‫ץ‬n͒ A redistribu-
tion in space of the intensity of waves resulting from
the presence of an object. 1. Penetration of wave energy
into areas forbidden by geometrical optics, e.g., the
bending of wave energy around obstacles without obey-
ing Snell’s law, as explained by Huygens’ principle.
The phenomenon by which energy is transmitted later-
ally along a wave crest. When a portion of a wavetrain
is interrupted by a barrier, diffraction allows waves to
propagate into the region of the barrier’s geometric
shadow. See Figure D-11. 2. An event observed on
seismic data produced by diffracted energy; see Figure
D-12. Such events result at the termination of reflectors
͑as at faults͒ and are characterized on seismic records
and sections by a distinctive curved alignment. A
simple diffraction lies along a diffraction curve ͑whose
curvature depends on the velocity distribution above
the diffracting point͒. Phantom diffractions involve
energy that reaches the diffracting point by a longer
route than the direct one ͑as with a diffracted reflec-
tion͒; they have more curvature than appropriate for
their arrival time. Diffractions generated by a line
source that is not at right angles to the line appear to
have less curvature, becoming flatter as the line gener-
ating the diffraction becomes parallel to the line of
observation. A reflection can be thought of as the
interference result of diffractions from points lying on
the reflector. When correctly migrated, a simple diffrac-
tion collapses at the location of the diffracting point.
See Sheriff and Geldart ͑1995, 63-8 and 159-161͒.
diffraction curve: A curve of maximum convexity, the
relation between the arrival time and observer position
for primary energy that has been diffracted from a
point. See Figure D-13. ͓One should speak of a diffrac-
tion ‘‘surface’’ to emphasize the 3D aspect.͔ The cur-
vature of reflected energy cannot exceed this curvature
͑except for reverse branches and certain situations such
as diffracted reflections͒. Diffraction curves are specific
for a particular velocity function, like the wavefront
chart to which they are related and from which they can
be constructed. Diffraction curves are used in identify-
ing simple diffractions, locating the diffracting points
͑see Figure M-11͒, in determining velocity from the
diffraction curvature, and as migration operators in
Kirchhoff migration ͑q.v.͒. Errors in interpreting dif-
fractions can result if the diffracting point lies to the
side of the seismic line, if the diffraction event results
from a line diffractor that is not normal to the seismic
line, or if the diffraction is not simple. See Hagedoorn
͑1954͒.
diffraction function: The function (sin ␲x)/␲x
ϭsinc ␲x; a sinc function.
diffraction knot: Where diffraction ͑q.v.͒ energy is
approximated by straight line segments and migrated
properly, the migrated segments cluster in an asterisk-
like ‘‘knot.’’
diffraction overlays: A set of diffraction curves such as
shown in Figure D-13, constructed for a specific veloc-
ity function, used to identify diffraction events on
unmigrated seismic sections.
diffraction stack: A weighted stack of all the elements
along a diffraction curve, which yields a migrated sec-
tion ͑to the extent that the data were 2D͒; the Kirchhoff
method of migration of reflection seismic data.
diffraction tomography: Tomography ͑q.v.͒ that relaxes
the assumption that energy propagates as a ray, using
wave-equation propagation for finding the physical
properties under investigation. 1. A technique for cross-
hole tomography ͑q.v.͒ based on analysis of the scat-
tered wavefield. 2. An inverse scattering technique that
images diffracted and scattered data. See Devaney
͑1982͒.
diffuse layer: The outer, more mobile ions of an
electrolyte-solid interface that together with the fixed
layer constitutes a double layer. Also called diffuse
zone, diffuse double layer, or outer Helmholtz
double layer.
diffuse reflector: A surface that reflects incident rays in
many directions.
diffusion: 1. The motion of ions or molecules in a solution
resulting from the presence of a concentration gradient.
2. A method of heat conduction resulting from the
motion of molecules.
diffusion distance: The time-domain equivalent of skin
depth ͑q.v.͒.
diffusion equation: 1. A simplification of the wave equa-
tion for EM-waves in a good conductor:
ٌ2
EϷj␻␮␴E or ٌ2
Hϭj␻␮␴H.
where ␻ϭangular frequency, ␮ϭmagnetic perme-
ability, and ␴ϭelectric conductivity. 2. An equation for
the rate of temperature change as a consequence of heat
diffusion:
‫ץ‬T/‫ץ‬tϭ͑k/␳cpٌ͒2
T,
where Tϭtemperature, tϭtime, kϭthermal diffusiv-
ity, ␳ϭdensity, and cpϭspecific heat at constant pres-
sure. See Fowler ͑1990, 222–223͒.
diffusion impedance: See Warburg impedance.
diffusion potential: Liquid junction potential ͑q.v.͒.
diffusion rate law: See Fick’s law.
Digihem: ͑dig’‫ץ‬ hem,͒ A helicopter-mounted electromag-
netic method; see electromagnetic.
digital: Representation of quantities in discrete ͑quan-
tized͒ units. A digital system is one in which the infor-
mation is contained and manipulated as a series of
discrete numbers, as opposed to an analog ͑q.v.͒ sys-
tem, in which the information is represented by a con-
tinuous flow of the quantity constituting the signal.
digital clipping: Loss of the most significant bit of a
number, such as that produced by overflow. Produces a
different result from ordinary clipping and generates
spurious high frequencies. See Figure C-5.
digital computer: See computer.
digital filter box: A special-purpose computer to carry out
convolution ͑q.v.͒.
digital geophone: A seismic sensor where signals are
digitized at the sensor rather than subsequently.
digital recording: Any method of recording data in digital
form, such as a series of magnetized or nonmagnetized
spots coded to represent numbers.
diffracted reflection 89 digital recording

13. digital-to-analog „DÕA…: Conversion of a digital ͑usually
binary͒ number into a corresponding voltage.
digitize: To quantize. 1. To sample a continuous voltage at
discrete regular time intervals, quantize the measure-
ments, and record the values as a sequence of numbers
in bit combinations on magnetic tape. 2. To sample a
function regularly. Equivalent to multiplying the func-
tion by a comb ͑q.v.͒. 3. To convert coordinates and
other parameters to a form that can be read by a digital
computer, as with an X-Y reader ͑q.v.͒.
digitizer: Equipment for sampling curves, seismic traces,
or other data recorded in analog form.
dihedral angle: ͑dı¯ he¯d’ r‫ץ‬l͒ The angle between two inter-
secting planes.
dike: 1. A tabular body that is longer vertically than in
other dimensions ͑as opposed to a slab͒; a prism.
FIG. D-11. Diffraction of a plane wave from a semi-infinite barrier. Schematic diagram showing the amplitude at time
t after the onset of the wave struck the tip of the barrier. Shown is the reflected wavefront, the wavefront that missed the
reflector, and diffractions from the reflector termination. Arrows point in the raypath directions. (Courtesy Chevron Oil
Co.)
digital-to-analog „DÕA… 90 dike

14. FIG. D-12. Diffractions generated by the termination of three horizontal reflectors. The diffraction curvature becomes
smaller as depth increases. The diffractions under the reflector (the backward branch) have reversed polarity to the
branches that extend beyond the reflection (forward branch). The crest of a diffraction curve locates the diffracting point
and its curvature depends on the depth and the velocity above the diffracting point. Reflection amplitude decreases to
one-half at the point where the reflection is tangent to the diffraction curve and the diffraction-curve amplitude is
antisymmetric about this point of tangency. Amplitudes and waveshapes are continuous at the point of tangency. The
diffraction curve is hyperbolic if the velocity above the diffracting point is constant. (Courtesy Chevron Oil Co.)
dike 91 dike

15. Vertical and dipping dike models are used commonly in
potential-field calculations. 2. Igneous rock that cuts
across adjacent rock. Also spelled dyke. See Figure
M-15.
DIL: Dual Induction resistivity Log.
dilatancy: ͑dı¯ la¯t’ ‫ץ‬n se¯͒ Volume increase caused by a
crack opening when a rock is under triaxial loading.
dilatancy theory: A hypothesis for the changes in rock
volume near a fault as the result of microfracturing
preceding an earthquake and consequent changes in the
ratio of the velocities of P- and S-waves, which are
used as earthquake predictors.
dilatation: 1. Volumetric strain, change in volume per unit
of volume. 2. A rarefaction ͑q.v.͒.
dilatational wave: P-wave ͑q.v.͒.
dilation: A transformation that changes only the size of a
geometric figure.
dilution of precision: The geometrical contribution to the
uncertainty in a kinematic position fix.
dimensional analysis: Equating units in a physical rela-
tionship so that the dimensions as well as the number
values balance.
dimensionless induction number: See induction number.
dimensionless units: Ratios that do not depend on the
units in which quantities are measured. For example,
distance is often measured in terms of wavelengths,
frequency is often expressed as a ratio to natural fre-
quency, etc. Often the same as normalized units; see
normalize.
dimple: A shallow velocity anomaly ͑such as might result
from local permafrost variation͒ that depresses or raises
all seismic data seen through it and distorts the normal
moveout of deeper events by velocity focusing.
dim spot: A local decrease of the amplitude of a seismic
event. Where a significant acoustic impedance contrast
occurs in the absence of hydrocarbons ͑as in a reservoir
with higher acoustic impedance than the surrounding
rock͒, the presence of hydrocarbons may lessen the
acoustic impedance contrast and hence the amplitude of
a reflection. See Figure H-10. Antonym: bright spot.
Dinoseis: A seismic energy source in which a plate is
driven against the ground by a confined explosion of
gas. An ARCO Oil and Gas tradename.
diode transistor logic „DTL…: A family of semiconductor
logic formed by diode gates that are diode-coupled to
the base of the output transistor. DTL logic is charac-
terized by medium speed, low power dissipation, high
drive capability, and low cost.
diodic: ͑dı¯’ ‫ץ‬d ik͒ 1. Behaving differently in different
directions, i.e., like a diode. 2. The traveltimes of
common-conversion point PS-waves change if shot in
opposite directions unless also changing P-source to
S- and S-receiver to P.
diodic moveout: With C-wave gathers the moveout will
not be symmetric and the arrival time expression is
tc
2
͑x͒ϭtC0
2
[1ϩC1ͩ x
tC0VCNMO
ͪϩ
x2
tC0
2
VCNMO
2
ϩC1ͩ x
tC0VCNMO
ͪ2
Ϫ
C4͓x/͑tC0VCNMO͔͒4
1ϩC5͓x/͑tC0VCNMO͔͒2,
FIG. D-13. Diffraction curves or curves of maximum convexity. (From Hagedoorn, 1954, 116.)
DIL 92 diodic moveout

16. that is, it involves odd as well as even powers of x ͑see
Thomsen, 2002: 5–1͒.
dip: The angle that a plane surface makes with the hori-
zontal. 1. The angle that bedding makes with the hori-
zontal. 2. The angle that a reflector or refractor makes
with the horizontal. 3. Apparent dip is the angle
between horizontal and the component of dip in the
plane of a section. 4. Electromagnetic pitch ͑q.v.͒.
dip-angle method: An electromagnetic surveying method
in which the dip angle of the total magnetic field is
measured. The secondary field resulting from eddy
currents in a conducting body changes the direction of
the total field ͑horizontal in the case of a vertical
transmitter loop͒ which would be measured in the
absence of the conductor. See Keller and Frischknecht
͑1966͒.
dip-azimuth map: Displays of the azimuth of the dip
along horizon slices following correlated reflection
events through a 3-D volume of seismic data, usually
displayed by color encoding. Also called azimuth map.
Sometimes a display incorporating both dip magnitude
„dip map… and dip azimuth.
dip calculation: Calculation of the dip or dip component
of a reflecting or refracting interface from observations
of the variation of arrival time of seismic events as the
observing point is moved. May involve resolving cross-
spread ͑q.v.͒ data. The dip angle for a reflection mea-
sured at the surface is usually less than the angle at the
reflector because of raypath curvature.
dip decomposition method: A Fourier-domain method of
DMO processing ͑q.v.͒, superceded by the log-stretch
trick ͑q.v.͒. See Jakubowicz ͑1984͒.
dip filter: See velocity filter.
dip line: A seismic line that is perpendicular to the strike
of reflecting interfaces of interest.
dip log: A dipmeter ͑q.v.͒ log. Diplog is a Dresser Atlas
tradename.
dip map: A horizon slice color coded to indicate the dip
magnitude.
dipmeter: The tool for measuring the dip of formations,
i.e., for making a dipmeter log ͑q.v.͒. The resistivity
dipmeter includes ͑a͒ three or more microresistivity
readings made using sensors distributed in azimuth
about the logging sonde, ͑b͒ a reading of the azimuth of
one of these, ͑c͒ a reading of the hole deviation or drift
angle, ͑d͒ its bearing, and ͑e͒ one or two caliper mea-
surements. Earlier dipmeters used three SP curves,
three wall scratchers, etc.
dipmeter log: 1. A well log from which the magnitude and
azimuth of formation dip can be determined; see Figure
D-14a. The microresistivity curves are correlated to
determine the differences in depth of bedding markers
on different sides of the hole and dip calculations are
based on such correlations. 2. A log showing the for-
mation dips calculated from the above, such as a tad-
pole plot or stick plot; see Figure D-14b.
dip migration: See migration.
dip moveout: 1. A change in the arrival time of a reflec-
tion because of the dip of the reflector. The quantity
⌬td/⌬x in Figure R-9. 2. See also DMO processing.
dip needle: A magnetic needle free to rotate about a
horizontal axis.
dipole: ͑dı¯’ po¯l͒ 1. A pair of equal charges or poles of
opposite signs that ideally are infinitesimally close
together. 2. In resistivity and IP surveying, a pair of
nearby current electrodes that approximates a dipole
field from a distance, or a voltage-detecting electrode
pair. Where the electrode separation is large, it is some-
times called a bipole. 3. In electromagnetic surveying,
FIG. D-14. Dipmeter log. „a… Log of field data. „b… Calculated dipmeter log or tadpole plot. (Courtesy Schlumberger.)
dip 93 dipole

17. an electric- or magnetic-field transmitting or receiving
antenna which is small enough to be represented math-
ematically as a dipole. The near fields ͑electric and
magnetic͒ from a magnetic and electric dipole ͑respec-
tively͒ vary as the inverse cube of the distance.
dipole array: Dipole-dipole array ͑q.v.͒.
dipole-dipole array: Inline electrode array used in
induced polarization, electrical, and electromagnetic
surveying, where both current and potential-measuring
electrodes are closely spaced. See Figure A-19.
dipole field: The major part of the magnetic field of the
Earth ͑q.v.͒.
dipole moment: Two equal charges q ͑or poles p͒ of
opposite sign separated by the distance ␦x giving a
dipole strength of q␦x ͑or p␦x͒.
dipole moment per unit volume: A measure of the inten-
sity of polarization of a material. Units are ampere-
meters per cubic meter.
dipole sonic log: A sonic array tool in which sources are
dipoles as opposed to radially symmetric monopoles, so
that it generates both P- and S-waves in formations.
Analysis involves mode identification and analysis of
dispersion curves and yields both P- and S-wave veloci-
ties. A variant ͑crossed dipole mode͒ is an orthogonal
set of horizontal dipole transmitters and an array of
orthogonal dipole receivers to measure azimuthal
anisotropy. This arrangement is suitable for detecting
azimuthal velocity variations in a borehole. The dipole
sonic imager „DSI… is a multiconfigurable tool that can
emulate a BHC sonic, a standard monopole array tool,
or an array dipole tool. Modes are configured to meet
the logging conditions presented by different borehole
environments. While monopoles work well in hard
formations where mode conversion is required for
S-wave recording, dipoles excite flexural modes
directly and are efficient for generating Stoneley waves
in slow formations. The analysis of the proper disper-
sion curves ͑modes͒ leads to the estimation of S-wave
velocities in slow formations. Dipoles are directional
and are sensitive to azimuthal velocity variations.
dipole strength: See dipole moment.
dip resolution: 1. Calculation of true dip from cross-
spread data. 2. Recognition and separation of events
having nearly the same dip.
dip shooting: 1. A seismic field method wherein the pri-
mary concern is determining the dip of reflectors. May
involve either isolated or continuous profiles or cross-
spreads. 2. An attempt to acquire data so that the
source-receiver directions parallel geologic dip.
dip spectrum: 1. A graph showing the frequency with
which different dips occur. 2. Sometimes used for a
sonograph that displays coherent energy as a function
of apparent velocity ͑or dip͒ and arrival time.
dip sweeping: See Rieber mixing.
dip time slice: See dip map and double time slice.
dip vector: An arrow on a map pointing in the direction of
dip. The arrow length sometimes indicates ͑a͒ the dip
magnitude, sometimes ͑b͒ the contour spacing, and
sometimes ͑c͒ the portion of the line over which such a
dip direction is evident.
Dirac comb: A comb ͑q.v.͒; a series of equally spaced
delta functions.
Dirac function: ͑di rak’͒ A delta function or impulse
͑q.v.͒. Named for Paul Adrien Maurice Dirac ͑1902–
1984͒, British physicist.
direct arrival: Energy that travels by straight or shallow
diving raypaths from source to detector.
direct coupling: See coupling.
direct current apparent resistivity: See apparent resis-
tivity.
direct detection: A measurement ͑never ‘‘direct’’͒ that
may indicate the presence or absence of hydrocarbons.
Sometimes considered synonomous with bright spot
͑q.v.͒. Effective under some circumstances, but no uni-
versal method has been found. Also called direct
hydrocarbon detection or indication ͑DHD or DHI͒.
See hydrocarbon indicator and Figure H-10.
direct interpretation: 1. Solution of the direct problem
͑q.v.͒ or forward solution. 2. Direct mathematical
solution of a potential-field problem without use of
precomputed curves or models.
directional charge: 1. An explosive charge or charge
array in which the explosion front travels at approxi-
mately the velocity of seismic waves in the surrounding
rock, so that energy traveling in a desired direction
͑usually vertically͒ adds constructively as opposed to
that traveling in other directions. The charge must
either be shaped to focus the energy in the desired
direction or have a length that is a significant fraction of
a wavelength to achieve appreciable directivity. Some-
times involves the use of broomstick charges, delay
caps, impulse blasters, or sausage powder. In refraction
shooting, a horizontal directional charge detonating at
the refractor velocity is sometimes used to concentrate
the energy traveling as a head wave. 2. Shaped charges
as used for armor piercing or perforating casing.
directional derivatives: The derivative of ␾ in the direc-
tion r1 is ٌ␾•r1.
directional drilling: Intentionally drilling a well in a
direction other than vertical.
directional survey: 1. Measurement of drift, which is the
azimuth and inclination of a borehole from the vertical.
Often made from dipmeter survey data. Sometimes
involves a continuous log and sometimes measure-
ments made only at discrete levels. 2. An IP or
resistivity-survey method starting from a position such
as a drill hole to find the trend direction of an anoma-
lous subsurface body.
directivity graph: 1. A plot ͑often in polar coordinates͒ of
the relative intensity versus direction of an outgoing
seismic wave such as that resulting from a directional
charge or from a source pattern; see Figure D-15a. The
directivity results from the interference of the waves
from the various components of the pattern. 2. A plot of
the relative response of a geophone pattern or of direc-
tivity resulting from mixing; see Figure D-15b. Direc-
tivity graphs may be specified in various units ͑apparent
velocity for a certain frequency, apparent wavelength,
frequency arriving from a certain direction, apparent
velocity, etc.͒, as indicated in Figure D-15b. The verti-
cal scale is often logarithmic ͑i.e., given in dB͒ rather
than linear. The effect on wavelets can be very different
from the effect on a sinusoidal wavetrain so that use of
steady-state patterns can be misleading. A plot in f-k
space is a form of directivity graph showing also the
frequency-dependency. See also Figure C-3.
direct modeling: Calculating the effects of a model ͑q.v.͒.
dipole array 94 direct modeling

18. direct problem: Computation of the effects of a certain
model; as opposed to the inverse problem of determin-
ing a possible model from observation of effects. See
Figure M-14. Also called forward problem.
direct-push: The use of the weight of a truck or other
heavy vehicle to push a metal probing device into the
ground. The force required to move the probe down-
ward is sometimes monitored to produce a vertical log
of penetration resistance. The probe is often instru-
mented with geophysical logging tools to obtain physi-
cal parameters of engineering or environmental interest.
No soil or rock samples are brought to the surface with
this technique. The hole may be backfilled with grout as
the probe is removed from the ground. Sometimes
referred to as a Geoprobe technique, which is a trade-
name.
direct recording: Magnetic tape recording in which the
magnetization intensity is proportional to the signal
strength ͑or signal strength plus a bias͒.
direct wave: A wave that travels directly by the shortest
path. Other waves traveling by longer routes may arrive
earlier because they travel at higher velocity.
Dirichlet conditions: ͑dir’ ‫ץ‬ kla¯͒ The necessary and suf-
ficient conditions for a Fourier series: In any region: ͑a͒
f(x) is continuous except for a finite number of finite
discontinuities and ͑b͒ it has only a finite number of
maxima and minima. Named for Peter Guster Dirichlet
͑1805–1859͒, German mathematician.
Dirichlet problem: An initial-value problem where the
behavior of the points bounding a spatial region of
interest are specified as a function of time.
dirty: Shaly; containing appreciable amounts of shale dis-
persed in the interstices. Such shale lowers the perme-
ability and effective porosity and affects the readings of
many types of logs. A composite electrolyte system of
clay and sand can be responsible for membrane polar-
ization effects. Clay particles in the sand act as selective
ion sieves and surface conduction along the clay min-
erals causes low resistivity.
DISC: Distinguished Instructor Short Course, one of the
SEG’s annual lecturer series and corresponding books.
disc hydrophone: A piezoelectric hydrophone similar to a
bender. Two piezoelectric discs are supported around
their circumference so that pressure tends to bend them,
causing stresses that generate a voltage across the disc
thickness.
disconformity: An unconformity in which formations on
opposite sides of it are parallel to the unconformity.
discovered: See resource.
discrete Fourier transform: A Fourier transform ͑q.v.͒
FIG. D-15. Directivity graphs. „a… Polar plot showing the relative amplitude of a radiated wave (or the relative sensitivity
to waves approaching a geophone array from different directions). The horizontal axis can be expressed in various
ways. „b… Directivity of five inline geophones spaced 10 m apart. „c… Response of a tapered array of five geophones
spaced 20 m apart and weighted 1:2:3:2:1; such weighting could be achieved with nine geophones distributed as the
weighting. (d) Response of nine geophones equally spaced 5.5 m apart. The solid curves are for harmonic (steady-
state) waves, the dashed curves for a transient with a bell-shaped spectrum peaked at 30 Hz and a width of 30 Hz.
(From Sheriff and Geldart, 1995, 249.)
direct problem 95 discrete Fourier transform

19. calculated for a wavelet over a finite interval so that
values are given only for the fundamental frequency
͑the reciprocal of the interval͒ and its harmonics.
discriminant function: One of a set of mathematical rela-
tions used to divide measurement space into decision
regions in classification. Such functions usually result
from the study of a learning ͑training͒ set.
discriminator: An electronic circuit that responds only to
␥-ray energies greater than some threshold value.
disharmonic folding: ͑dis’ har mon, ik͒ Folding in which
there is an abrupt change in fold profile across a dec-
ollement surface.
disjunction: ͑dis jungh’ sh‫ץ‬n͒ The logical operation,
‘‘either A or B’’ ͑written A ഫ B͒, performed by an OR
gate. Also called union. See Figure B-5.
diskette: A floppy disk ͑q.v.͒.
dispersion: 1. Variation of velocity with frequency. Dis-
persion distorts the shape of a wavetrain; peaks and
troughs advance toward ͑or recede from͒ the beginning
of the wave as it travels. Leads to the concept of group
velocity U distinct from phase velocity V. Where ␭
ϭwavelength, fϭfrequency, and Vϭphase velocity,
Vϭf␭ϭf/͑1/␭͒.
Uϭdf/d͑1/␭͒.
The dispersion of seismic body waves is very small
under most circumstances, but surface waves may show
appreciable dispersion in the presence of near-surface
velocity layering. See Figure D-16. The dispersion of
electromagnetic body waves is large in most earth
materials. For ground roll and channel waves ͑see Fig-
ure C-2c, d͒, phase velocity decreases with frequency,
sometimes called normal dispersion, and where veloc-
ity increases with frequency, inverse dispersion. 2. A
statistical term for the amount of deviation of a value
from the norm. See statistical measures. 3. Angular
dispersion is variation of velocity with direction, as in
an anisotropic medium. Leads to the concept of ray
velocity distinct from phase velocity; see Figure A-14a.
dispersion curve: A plot of wave velocity as a function of
frequency. See normal modes.
dispersion equation: A relation between angular wave-
number ␬, angular frequency ␻, and velocity V:
␬2
ϭ␬x
2
ϩ␬y
2
ϩ␬z
2
ϭ␻2
/V2
.
See Hilbert transform and Yilmaz ͑2001, 489͒.
dispersive filter: A phase-shifting filter that does not
affect the amplitude spectrum.
displacement: 1. The distance a particle is removed from
its equilibrium position, as in the ground motion asso-
ciated with a seismic wave. 2. Relative movement of
the two sides of a fault. 3. The amount by which
refraction data are displaced horizontally from the geo-
phone positions to indicate where the head-wave energy
presumably left the refractor. Sometimes called offset
or transplacement. See Figure O-1. 4. See displacement
current.
displacement current: A current that is proportional to
the time rate of change of electric flux density. In most
earth materials, displacement currents are negligible
compared with conduction currents for the range of
frequencies used in electromagnetic methods, but dis-
placement currents dominate in radar methods.
display: 1. A graphic hard-copy representation of data,
especially of seismic data. See Figure D-17. A graph of
amplitude as a function of time gives a wiggle trace,
squiggle, or conventional display. Variable area dis-
play has the area under the wiggle trace shaded to make
coherent events more evident; it often involves a bias
and trace clipping. A variable density display repre-
sents amplitude values by the intensity of shades of
FIG. D-16. Dispersion. „a… Change in wavelet shape because of dispersion in a Voigt solid. Amplitudes have been
normalized. „b… Change of waveshape because of energy shifting to later cycles. The axes of time and offset could be
interchanged on either graph. (From Balch and Smolka, 1970.)
discriminant function 96 display

20. gray. Superimposed modes or combined modes
involve the use of both wiggle trace and variable area or
variable density simultaneously; they retain many of
the good features of each type display. Data are also
represented by color encoding ͑see Fig. C-7͒, and in
other ways. Color displays of different types are shown
in Figures D-18 and H-8. 2. A soft-copy representation
of data on a cathode-ray tube or similar nonpermanent
device.
disseminated sulfide mineralization: Sulfide minerals
scattered as specks and veinlets through rock and con-
stituting not over 20% of the total volume.
distal: ͑dis’ t‫ץ‬l͒ Referring to the portion of a sedimentary
unit remote from the sediment source.
distance meter: A device for measuring line-of-sight dis-
tances, generally by transmitting a light pulse to a prism
reflector at a station and timing the arrival of the
reflected light.
distortion: An undesired change in waveform, as opposed
to desired changes in waveshape like those from modu-
lation. „a… Amplitude distortion is caused by undesired
amplitude-versus-frequency characteristics. „b… Har-
monic distortion is a nonlinear distortion characterized
by the generation of harmonics of an input frequency.
The percent harmonic distortion is a measure of fidel-
ity; if Ef is the rms voltage of the fundamental and En
is the rms voltage of the nth harmonic, the percent
harmonic distortion is
100͚ͩ En
2
ͪ1/2
ͲEf.
„c… Intermodular distortion is a nonlinear distortion
characterized by the appearance in the output of fre-
quencies equal to the sum and difference of integral
multiples of the component frequencies present in the
input. „d… Nonlinear distortion is caused by a devia-
tion from a linear relationship between input and out-
put. „e… Phase distortion results when phase shift is not
linear with frequency over the bandpass or where it is
linear but where the zero frequency intercept is not a
multiple of ␲. Where the intercept is a multiple of n␲,
the waveshape is not changed in n is even and is
inverted if n is odd, although the entire waveform may
be delayed. See linear-phase filter.
distortional wave: S-wave ͑q.v.͒.
distortion point: The input amplitude for which the
distortion-generated third harmonic becomes a certain
percentage, generally 3% but sometimes 1%. For
smaller inputs the system is nearly linear.
FIG. D-17. Display modes. „a… Wiggle (or squiggle)
trace. „b… Variable area. „c… Variable density. „d… Wiggle
trace superimposed on variable area. „e… Wiggle trace
superimposed on variable density.
FIG. D-18. Displaying data at a work station. „a…
Synthetic seismogram or other data may be inserted into a
seismic section to aid in correlating. „b… A two-level
display showing data from two nearby time slices super-
imposed to illustrate dip magnitude and direction; the
black is 8 ms shallower than the green. See also Figure
T-6. (From Brown, 1999, 57.)
disseminated sulfide mineralization 97 distortion point

21. distortion tail: A correlation ghost. Harmonic distortion
with vibroseis surface sources produces spurious corre-
lations, especially for the second harmonic ͑which may
be very large͒. This produces a distortion tail that
follows the correlation for a down-sweep and appears
as a forerunner for an upsweep.
distributed: Referring to electric circuits, the smearing
out of resistive, capacitative, or inductive circuit ele-
ments such as with a transmission line. Opposite of
lumped.
distributed computing: Use of multiple, loosely coupled
processing systems to accomplish a task; distributed
processing.
distributed systems: 1. A seismic recording system where
signals from one or more geophone groups are col-
lected at remote units before transmitting them to the
recording truck. 2. At-the-geophone digitization rather
than each geophone group having its own dedicated
channel to the recording system.
distribution function: A relationship that describes the
probability that a quantity will have a value less than a
particular value. It is thus the cumulative integral of the
probability density P[x] of the random variable x
͑which is not necessarily a proper function͒:
F͑x͒ϭ͵P͓x͔dx.
diurnals: ͑dı¯ ur’ n‫ץ‬ls͒ Phenomena with a periodicity of
about one day. Changes in the geomagnetic field related
principally to the rotation of the Earth in the magneto-
sphere ͑q.v.͒ and also involving amplitude and phase
variations with season and latitude ͑by as much as 100
nT͒; records from a stationary magnetometer are used
for their removal. Average daily changes in radio-wave
propagation because of diurnal changes in the iono-
sphere affect radio-positioning systems. Published
tables allow one to correct for major skywave varia-
tions with systems like Omega, but unpredictable local
skywave variations and sun-spot effects remain.
diurnal variation: Daily fluctuations, also called diurnals
͑q.v.͒.
divergence: 1. The decrease in amplitude of a wavefront
because of geometrical spreading. The energy in body
waves spreads out as the spherical wavefront expands,
causing the energy density to vary inversely as the
square of the distance ͑spherical divergence͒. With
surface waves the energy density varies inversely as the
distance ͑cylindrical divergence͒. Tube waves do not
suffer energy loss because of divergence. Energy den-
sity also decreases because of raypath curvature,
absorption, and other reasons. 2. The divergence of a
vector field is expressed in Figure C-14 for rectangular,
cylindrical, and spherical coordinates.
divergence theorem: The flux ␾ through a surface ͑or the
integral of the vector flux density g over a closed
surface͒ equals the divergence of the flux density inte-
grated over the volume contained by the surface:
␾ϭ ͵ ͵g•dsϭ ͵ ͵ ͵“•g dx dy dz.
Commonly called Gauss’s theorem.
divergent reflections: A reflection configuration ͑see Fig-
ure R-8͒ indicating differential subsidence.
diversity stack: A stack in which amplitudes that exceed
some threshold are excluded; amplitudes less than this
threshold may not be affected. Used with vertical stack-
ing to prevent occasional large bursts of noise ͑such as
traffic noise͒ from dominating the stacked record, and
also used with common-midpoint stacking to discrimi-
nate against ground roll and similar high-amplitude
wavetrains.
diving waves: Refraction in a strong velocity-gradient
zone may reverse the downward component of seismic
ray travel and bend the rays back to the surface. Such
refraction arrivals have apparent velocity appropriate to
that at their greatest depth of penetration even when
they have no appreciable path through a distinctive
refractor. See Figure D-19. If there are no velocity
reversals, diving waves may be used to derive the
velocity distribution by means of the Wiechert-Herglotz
integral. See Meissner ͑1966͒, Sheriff ͑1989, 217 and
262͒, and Blondeau method.
divining: ͑di vı¯n’ ‫ץ‬ng͒ Use of a forked stick ͑or other
device͒ that allegedly bends toward water, petroleum or
other sought-for accumulations; used meaning ‘‘unsci-
entific.’’
Dix formula: ͑dicks͒ For reflections from a sequence of
flat, parallel layers and small offsets, the interval veloc-
ity in the nth layer Vn is given by
VnϭͫVn
2
tnϪVnϪ1
2
tnϪ1
tnϪtnϪ1
ͬ1/2
,
where VnϪ1 and Vn are the stacking velocities from the
datum to reflectors above and below the layer and tnϪ1
and tn are reflection arrival times. This formula is often
misused to calculate interval velocities in situations that
do not satisfy Dix’s assumptions. Named for C. Hewitt
Dix ͑1905–1984͒, American geophysicist. See Dix
͑1955͒. Some call this the Postma equation.
D-layer: 1. The innermost layer of the ionosphere. It
occurs at heights of 50 to 90 km during daylight hours,
reflects ELF, VLF, and LF waves, absorbs MF waves,
and partially absorbs HF waves. Some consider the
D-layer as starting at 70-80 km and merging with the
E-layer. See Figure A-22. 2. A layer within the Earth;
see Figure E-1.
DMO „dip moveout… processing: A seismic processing
operation to correct for the fact that, for dipping reflec-
tions, the component traces of a CMP gather do not
involve a common reflecting point. Dip-moveout pro-
cessing creates apparent common-reflection-point gath-
ers by a convolution applied to adjacent common-
midpoint gathers, with the feature that the moveout
with offset for reflections from a dipping bed no longer
depend on the dip angle ͑see Figure C-9b͒. DMO
effectively corrects for the reflection-point smear that
results when dipping reflectors are stacked by the CMP
method. After DMO is applied, events with various dips
stack with the same velocity. DMO stands for dip
moveout, but it is different from the classical dip
moveout that is simply the effect of dip on arrival
times. DMO can be performed in a number of ways,
including prestack partial migration ͑Yilmaz and Claer-
bout, 1980͒, time-domain, finite-difference methods
͑offset continuation͒ ͑Bolondi et al., 1982͒, Fourier-
domain implementation ͑Hale, 1984͒, integral ͑Kirch-
distortion tail 98 DMO „dip moveout… processing

22. FIG. D-19. Diving waves. „a… Raypaths are curved because of vertical velocity gradient. The inverse of the slope of the
time-distance curve indicates the velocity at the bottom of the travel path. „b… A large velocity gradient can produce a
reverse branch on traveltime-versus-distance curves. „c… An inversion of velocity may produce a gap in the time-
distance curve, but the gap (if small) may not be evident because diffracted energy may fill the gap. The lower velocity
layer constitutes a hidden layer (q.v.). „d… Diving waves reflected on their upward travel are called turning waves (q.v.);
they often show negative moveout with offset. Turning waves are sometimes used to map the overhanging flank of a salt
dome or the footwalll of a fault.
DMO „dip moveout… processing 99 DMO „dip moveout… processing

23. FIG. D-20. DMO. „a… Depth section showing the updip movement of the reflecting point for an offset geophone for
constant velocity; ⌬ϭ(h2
/D)cos ␰ sin ␰, where ␰ is the dip (Levin, 1971). To avoid reflection point smearing, an offset
trace should be gathered with the updip zero-offset trace at a distance Gϭ(Ϫh2
/D)sin ␰, but such a gather is not
hyperbolic; the DMO correction makes this gather hyperbolic. „b… A diffraction in location-offset space, a Cheops
pyramid, is not a hyperboloid. „c… Applying NMO changes the Cheops pyramid into a saddle-shaped surface. „d…
Applying DMO along with NMO yields data that can be stacked without reflection-point smear. „e… NMO corrects for the
time delay on an offset trace assuming horizontality, DMO moves the data to the correct zero-offset trace for a dipping
reflection, and migration further moves it to its subsurface location. (After Deregowski, 1986, 13.)
DMO „dip moveout… processing 100 DMO „dip moveout… processing

24. hoff͒ methods ͑Deregowski, 1985͒. Velocity-dependent
DMO is usually applied after velocity-dependent NMO.
Gardner’s DMO ͑Forel and Gardner, 1988͒ applies
velocity-independent DMO prior to velocity-dependent
NMO. See Figure D-20 and double square-root equa-
tion.
DNAPL: Dense NonAqueous Phase Liquids, the most
commonly found environmental pollutants, typically
chlorinated solvents that are denser than water. Their
flow may be controlled by geology and gravity inde-
pendently of groundwater flow. Compare LNAPL.
DNMO: Differential Normal MoveOut ͑q.v.͒.
document: A unit of information sent from servers to
clients; a file.
DOD: U.S. Department Of Defense.
DOE: U.S. Department Of Energy.
doghouse: The hut ͑or cab͒ that contains seismic or well-
logging recording instruments in the field.
dog-leg: An abrupt angular change in direction, as in a
survey traverse or in a borehole.
dolomitization: ͑do¯, l‫ץ‬ m‫ץ‬d ‫ץ‬ za¯’ sh‫ץ‬n͒ The process by
which limestone is converted to dolomite or dolo-
mitized limestone by magnesium carbonate replacing
calcium carbonate. Usually produced by flushing with
magnesium-bearing meteoric water or seawater.
domain: 1. The set of elements to which a mathematical
or logical variable is limited; the set on which a func-
tion is defined; the set of values that an independent
variable may take. 2. The class of terms that have a
given relation to something is called the ‘‘domain of
that relation.’’ Thus, when we speak of a seismic trace
in the time domain, we mean that time is the indepen-
dent variable; in the frequency domain, frequency is
the independent variable; in the f,k domain or f,k
space, frequency and wavenumber are the independent
variables; etc. 3. A region of magnetic polarization in a
single direction ͑magnetic moments parallel͒ that
behaves as a unit during change in magnetization. The
dimensions of magnetic domains are about 1␮m. 4. The
areal extent of a given lithology or environment. 5. The
region occupied by a cluster set in cluster analysis.
dome: A structure where all of the beds dip away from a
central area; e.g., a salt dome.
Domenico effect: ͑do¯ men’ i co¯͒ A few percent of gas in a
rock’s pore space may have more effect on seismic
velocity than complete saturation; see Domenico
͑1974͒.
dominant frequency: The dominant frequency is usually
determined by measuring the time between successive
peaks or troughs and taking the reciprocal. See Figure
W-2.
dominant wavelength: The wavelength associated with
the dominant frequency ͑q.v.͒.
donor: See n-type semiconductor.
doodlebugger: A geophysicist engaged in field work.
Originally used derisively to mean unscientific.
doors: Paravanes, devices that hold streamers apart.
doping mud: Adding paramagnetic material to drilling
mud to kill the mud influence on NMR measurements.
Generally not required with modern instrumentation.
Doppler count: ͑dop’ l‫ץ‬r͒ 1. The apparent frequency of a
constant frequency signal broadcast by a satellite varies
because of the velocity of the satellite with respect to
the observing station ͑Doppler effect, q.v.͒ ͑see Figure
D-21͒. A count of the number of cycles in a given time
interval ͑Doppler count͒ along with knowledge of the
satellite’s position in its orbit ͑which the satellite broad-
casts͒ can be used to determine an observer’s location
and velocity. This forms the basis of the Global Posi-
tioning System ͑q.v.͒, as it did with the Transit system
͑q.v.͒. 2. Doppler counting is also used in connection
with Doppler radar and Doppler sonar.
Doppler effect: Apparent change in frequency of a wave
caused by motion of a source with respect to a receiver
and/or vice-versa. Frequencies are increased if the
source and receiver are approaching, decreased if they
are moving apart; see Figure D-21. For sound and water
waves, the observed frequency fo is given in terms of
the source frequency fs the velocity of propagation V,
the velocity of the source Vs, and the velocity of the
observer Vo ͑components of velocity toward each
other͒:
foϭfs
VϩVo
VϪVs
.
The relationship for light and radio waves is slightly
different because of relativistic effects and the con-
stancy of the velocity of electromagnetic waves irre-
spective of any motion of source and observer:
foϭfsͫVϩVoϪVs
VϪVoϩVs
ͬ1/2
.
See Doppler navigation. Named for Christian Johann
Doppler ͑1803–1853͒, Austrian physicist.
Doppler navigation: Positioning in which frequency shift
because of the Doppler effect is involved. Usually
refers to Doppler radar ͑for aircraft͒ or Doppler sonar
͑for ships͒, occasionally to satellite navigation ͑see
Doppler count͒.
Doppler radar: A radio-navigation system used by air-
craft. A radio beam transmitted from the aircraft and
reflected back by various landscape features is received
at the aircraft. Because the aircraft transmitter and
receiver are in motion, the signal undergoes a frequency
shift ͑the Doppler effect͒ which is measured and con-
verted to aircraft velocity. A computer on the aircraft
determines the plane’s position by integrating the
velocity over time. Actually, two transmitter-receivers
beam to the ground ahead of and behind the aircraft to
determine the forward speed and two transmitters beam
to the right and left of the aircraft to determine the
crosstrack speed. The arrangement is similar to that
used with Doppler sonar ͑Figure D-21b͒. The Doppler
data combined with a compass heading give the direc-
tion of the aircraft. Velocity can be measured to about
0.5%, somewhat less over water because the surface of
the water may itself be in motion.
Doppler shift: 1. Change in observed frequency because
of the Doppler effect ͑q.v.͒. 2. The shift toward lower
frequencies that results from stretching long-offset seis-
mic traces in the removal of normal moveout.
Doppler sonar: A sonic location system used by ships,
based on the Doppler effect. See Figure D-21b. Velocity
measurements together with gyro-compass direction
may be integrated to give position. Signals are reflected
from the sea floor or from the water mass ͑volume
reverberation or water-track mode, often when the
DNAPL 101 Doppler sonar

25. FIG. D-21. „a… Doppler effect in observing a satellite. Along with knowledge of the satellite’s orbit, s, the time of closest
approach of a satellite in near-polar orbit gives the latitude and the rate of change of frequency gives the longitude. The
quantity measured is often the beat frequency (offset frequency) between the signal from the satellite and a reference
frequency. „b… Doppler sonar uses four transducers to send sonar beams fore and aft and to each side, and to receive
the reflections of these beams from the sea floor. The use of four beams allows the effects of the ship’s roll, pitch, and
yaw to be reduced. The ship’s velocity is computed from the Doppler-effect frequency shift of the reflected beams.
(Courtesy Marquardt.)
Doppler sonar 102 Doppler sonar

26. water is deeper than 600–1000 ft, but resulting in
poorer accuracy͒.
DOS: Disc Operating System ͑q.v.͒. Often refers to an
IBM-compatible operating system used with personal
computers. IBM tradename.
DOSECC: Deep Observation and Sampling of the Earth’s
Continental Crust, a National Science Foundation pro-
gram to increase knowledge of the continental lithos-
phere, particularly by deep drilling for scientific pur-
poses.
dot chart: A chart used to hand-compute the theoretical
gravity ͑or other potential͒ effect of a 2-D mass distri-
bution; see Figure D-22. The number of dots within the
mass outline when a chart is superimposed on a scaled
cross-section of the mass multiplied by the anomalous
density is proportional to the gravity effect at the chart
origin. Also called graticule.
double: Two joints of drill pipe or casing screwed
together.
dot product: The dot product ͑also called inner product͒
of the vectors Xϭ[x1,x2,x3,...,xn] and Y
ϭ[y1,y2,y3,...,yn] is
X•Yϭ͓x1y1ϩx2y2ϩx3y3ϩ...ϩxnyn͔.
The dot-product reverse is
͓x1ynϩx2ynϪ1ϩx3ynϪ2ϩ...ϩxny1͔.
Compare cross product.
double Bouguer correction: 1. The Bouguer correction
͑q.v.͒ to sea level for measurements made on the ocean
floor involves a correction to replace the upward attrac-
tion of the sea water above the meter with the replace-
ment density of rock. 2. Corrections for measurements
made in mines or in boreholes, usually involving mea-
surements made both above and below a layer.
double coverage: Reverse control ͑q.v.͒.
double dipole array: Dipole-dipole array ͑q.v.͒.
double layer: The layers of molecular ions and charged
dipoles at a solid/solution interface. It is electrically
analogous to a capacitor in that there is charge separa-
tion between the solid ͑electrode͒ and the charge center
of the oriented ions or dipoles. Next to an electrode
there may be an adsorbed fixed layer of ions called the
inner Helmholtz double layer. A diffuse layer ͑outer
Helmholtz double layer͒ in the electrolyte contains an
excess of ions that is usually of the same charge as the
electrode but opposite to that of the fixed layer. The
thickness of the double layer is less than 100 A˚ ng-
stroms (10Ϫ8
m). The double-layer capacitance is
effectively in parallel with the Warburg impedance.
double-layer weathering: Situation where corrections
must be made for two distinctive near-surface low-
velocity layers.
double precision: The retention of twice as many digits
͑bits͒ to specify a quantity as the computer normally
uses.
double refraction: See birefringence.
double-run: A resurvey of a traverse to tie back to the
same reference point, to reinforce the certainty that
errors have not been made. Used where tie to an inde-
pendent reference point is not feasible.
double-square-root equation: The traveltime surface of a
point diffractor in offset space where raypaths are
straight and the source and receiver are not coincident;
see Figure D-20b. If xϭmidpoint location and y
ϭoffset ͑source-geophone distance͒, it is the surface
t(x,y)
tϭ͓͑h/2V͒2
ϩ͑mϩy/2͒2
/V2
͔1/2
ϩ͓͑h/2V͒2
ϩ͑mϪy/2͒2
/V2
͔1/2
,
where mϭinline distance from diffracting point to the
midpoint and h its depth. The surface is called a Cheops
pyramid ͑ke’ ops͒. This equation contrasts with the
FIG. D-22. Dot chart (2D). The gravity effect at the origin of a mass anomaly of a given cross-section is k ⌬␳n, where
k is a scale constant, ⌬␳ is the density contrast, n is the number of dots lying in the anomalous mass when superim-
posed on the dot chart.
DOS 103 double-square-root equation