Seismic methods use seismic waves created by impacts on the surface to map underground structures. The waves travel through underground layers and are reflected or refracted at boundaries between different materials. Analysis of the travel times and velocities of the waves allows determining the depth and type of geological layers. Seismic reflection techniques involve creating waves at shot points and recording them with receivers at different offsets to generate common midpoint gathers. Processing the gathers yields a seismic section that images layer boundaries like an echo sounder. Seismic refraction uses refracted head waves along interfaces to build a shallow velocity model for near-surface layers. Both methods together provide structural and physical characterization of underground features like buried valleys.

1. 4.2 Seismic methods
33
4.2 Seismic methods
Seismic measurements are well known from their
use in hydrocarbon exploration, but can also be
applied for mapping of shallower underground
structures such as buried valleys. The method is
comparable to a marine echo sounder: seismic
waves are created by a hit on the surface and
they travel underground. Like sound waves, they
are reflected and refracted when they reach a
boundary between different layers in the
underground. Using the time required for the
wave to come back to the surface and the
velocity of travel, we can determine the depth of
different geological boundaries. The velocity
value of the waves carries information on the
type of sediment or rock. This method is
important not only for structural information, e.g.
in delineating faults or valley structures, but also
for physical characterization of layers and thus is
very useful in hydrogeological investigations.
Since the 1920’s, seismic reflection techniques
have been used to search for petroleum and
refraction techniques have been used in
engineering applications. Additionally, since the
1980’s, significant strides have been made in
both near-surface seismic reflection surveying
and in the development of shallow-seismic
refraction methods.
Near-surface methods use an adaptation of
parameters to high resolution information – that
is the capacity to discriminate layers – and may
provide results also from layers that are 500 m in
depth, such as deep buried valleys.
The main references for this Section are Pelton
(2005), Steeples (2005), various chapters on
seismic methods in Knödel et al. (1997), Rabbel
(2006), Yilmaz (2001).
4.2.1 Physical base
Seismic waves include body waves that travel
three-dimensionally through solid earth volumes
and surface waves that travel near the surface of
the earth volume (Fig. 4.2.1). Surface waves are
categorized further as Love waves and Rayleigh
waves; the ground roll described later, e.g., is a
Rayleigh wave. For seismic investigation of the
ground, the use of body waves is standard. Here
Fig. 4.2.1: Types of seismic waves, particle motion
and – in red – sample of seismic pulse as function of
time: a) compressional (P-)wave travelling in a block
of material, b) vertical polarized and c) horizontal
polarized shear wave travelling in a block of
material, d) Rayleigh wave travelling in a section of
the earth‘s surface, e) Love wave travelling along a
section of the earth’s surface (after Steeples 2005).
we have to differ between compressional waves
(P-waves) and shear waves (S-waves); the
difference is in the particle motion of the wave
propagating through the underground material
(Fig. 4.2.1). The velocities of these waves depend
on the elasticity and density of the underground
material and can be expressed by:

2. HELGA WIEDERHOLD
34
ρ
μ3
4+k
=VP (4.2.1)
ρ
μ
=VS (4.2.2)
with the elastic constants k (= bulk modulus) and
μ (= shear modulus) and the mass density ρ of
the material through which the wave is
propagating.
For unconsolidated sediments like gravel, sand,
till, or clay, P-wave velocities range from 200 –
800 m/s for dry, and 1500 – 2500 m/s for water-
saturated material. S-wave velocities are much
slower, in the range of 100 – 500 m/s, and do
not differ between dry and water-saturated
material. Due to its slowness, the S-wave arrives
later than the P-wave and is named secondary (S)
wave in contrast to the primary (P) wave.
In sedimentary material, elasticity and density
strongly depend on porosity (Sect. 4.1). At a layer
boundary, e.g. between sand and clay or till, a
porosity change normally occurs, leading to
contrasting densities and seismic velocities. A
seismic wave impinging on this layer boundary
will be partly reflected and partly refracted (Fig.
4.2.2). The intensity of the reflected wave
depends on the magnitude of the contrast
between seismic velocities and densities at the
boundary, regardless of the sign of the contrast.
The product of velocity V and density ρ is the
acoustic impedance I = V ρ of a medium. The
strength of a reflection from an acoustic contrast
interface is defined by the reflection coefficient R
12
12
I+I
II
=R
-
(4.2.3)
with I1
= acoustic impedance of the first layer and
I2
= acoustic impedance of the second layer.
Equation 4.2.3 is valid for normal incident rays or
waves (ray path perpendicular to layer boundary).
The discussion of seismic waves can be in terms
of wavefronts or raypaths, the latter being a line
perpendicular to the wavefronts (for wave
definitions see Fig. 4.2.3.). The energy of a
seismic wave is proportional to the square of its
amplitude. An important relation of frequency to
Fig. 4.2.2: Sketch of seismic survey: layer model,
seismic rays (green: direct travelling wave, blue:
(critical) refracted or head wave, red: reflected
waves) and resulting seismogram with appropriate
seismic signals.
space and time is the wavelength (λ), which
describes the distance in space between
successive peaks (or troughs) of the seismic wave
and restricts seismic resolution, i.e. the capacity
to discriminate layers. Layers with thickness less
than λ/4 are not resolvable with the seismic
reflection method. The propagation velocity (V)
of a wave is the product of its frequency (f) and
wavelength: λf=V . As V is a physical property
intrinsic to the material, in seismic data, higher
frequencies result in shorter wavelength and
better resolution.
For geometrical ray propagation the
fundamentals of optics are valid, e.g. Fermat’s
principle of least-time path and Snell’s law,
describing how the wave changes direction when
crossing the boundary between media one and
two:

3. 4.2 Seismic methods
35
2
2
1
1
V
)i(sin
=
V
)i(sin
(4.2.4)
with i1
, i2
angles of incidence and V1
, V2
velocities
of the media. A special type of wave propagation
occurs at layer boundaries with increasing seismic
velocities (V2
> V1
). At an angle of incidence called
critical angle (ic
; 21c VV=isin ) the (critically)
refracted wavefront propagates along the
interface rather than into the medium itself. This
is the head wave used in the refraction seismic
method (Fig. 4.2.2). For the reflection seismic
method, rays with angles of incidence less than
the critical angle are usually used, allowing
transmission into the next medium; with angles
of incidence larger than the critical angle, total
reflection occurs with the effect of relatively
strong amplitudes. Both reflected and refracted
waves can be recorded at the surface and their
travel times can be measured and used for
detection of underground structures (Fig. 4.2.2).
Fig. 4.2.3: Wave definitions for sinusoids: a) how
displacement varies at a particular location with
time, b) how a wave looks at different places at a
given instant (after Sheriff 2002). Concerning the
nonperiodic seismic wavelet we speak of dominant
period or frequency and dominant wavelength.
Time and period are usually given in seconds (s) or
milliseconds (ms), frequency in hertz (Hz),
wavelength in meters (m) and velocity in meters per
second (m/s).
4.2.2 Seismic measurements
Depending on the travel path of the seismic
wave, we differentiate between the seismic
refraction method and the seismic reflection
method (see also Fig. 4.2.2).
A special feature of the refracted or head wave is
that it travels along the interface with the velocity
of the higher speed medium. Remember that this
wave is only created if the velocity on the
underside of an interface is greater than in the
overlying layer. Therefore, the wave can travel
faster than reflections in the overlying medium,
which results in it being the first arrival in the
seismogram. This is valid at least from a critical
offset that is dependent on the critical angle (see
also Fig. 4.2.9). Being restricted to geologic
conditions of increasing seismic velocity with
depth, this method alone is not recommended
for buried valleys that are incised in sedimentary
surroundings with similar physical parameters
relative to the valley fill itself. Here the reflection
seismic method is adequate and offers much
more details.
Reflections, which arrive later than the refractions
in the seismogram, successively give the images
of layer boundaries in depth or seismic traveltime.
The depth of penetration is limited by the energy
of the seismic source and loss of energy through
attenuation in the earth material. A reflection
seismic measurement includes the near-surface
refracted signals as first arrivals. These are
interpreted for the very near-surface velocity and
depth model and so may complement the seismic
reflection interpretation that usually lacks
information for the very near-surface area (e.g. 2
to 10 meters). This model is also used for static
corrections (see below). Refraction interpretation
methods are described in detail, e.g., by Rabbel
2006.
The aim of seismic reflection measurements is a
zero-offset seismic section where source and
receiver points coincide (Fig. 4.2.4 bottom); this
presents the image of a geologic cross section or
depth section of geologic boundaries and is what
an echo sounder usually yields. As a field
technique the common midpoint method is
established (CMP method; Fig. 4.2.4). The basic
idea is that a subsurface point is covered by
several rays or waves with different angles of

4. HELGA WIEDERHOLD
36
incident or different shot-receiver offsets.
Presupposing horizontally layering, this
subsurface point is graphically the midpoint
between shot and receiver location. The number
of rays or waves covering the subsurface point is
known as fold or coverage. By using different
offsets of this so-called CMP gather and the
different arrival times for a reflection, the velocity
of the subsurface medium can be derived. With
this velocity, the traces are corrected to zero-
offset and stacked to a single trace (Fig. 4.2.4).
The advantage of the CMP method in regard to a
single fold zero-offset measurement is the
derivation of seismic velocities and an improved
signal/noise ratio by the multifold coverage. In
practice, a shot is recorded by several receivers
with different offsets and this arrangement is
moved successively. In a later data processing
step, the traces belonging to one CMP are sorted
from the shot gathers. The (in-line) coordinates
xCMP
of CMP, xS
of source and xG
of receiver
location are related to each other by:
2/x+x=x GSCMP (4.2.5)
The CMP spacing is half of the receiver interval.
The fold of the CMP (NCMP
) is given by the receiver
spread length (= number of receivers NG
times
receiver interval ΔxG
) and the shot interval ΔxS
( )SGGCMP xΔ2/xΔ×N=N (4.2.6)
The interpretation of the seismic reflection
section can be much improved by borehole
information. The data are linked by a vertical
seismic profile (VSP) that allows the accurate
determination of the travel time from the surface
to various geologic units.
4.2.3 Field techniques
For the field layout of a seismic survey,
independent of reflection or refraction, we need
a seismic source, several seismic receivers
(geophones) connected by cable, and connected
to the seismograph (Fig. 4.2.2). Usually the survey
will be done along profiles determined by
logistics and costs but 3D information should be
the optimum. The equipment and configuration
Fig. 4.2.4: Sketch rays for common midpoint (CMP)
method: top: a reflecting point is covered by
different shot-receiver configurations (“shot
gather”); middle: the rays or seismic traces
belonging to a CMP are gathered (“CMP gather”);
bottom: normal moveout correction and stacking
results in a single (zero-offset) ray or trace (stacked
CMP trace); this trace resembles a zero-offset shot-
receiver configuration.
have to be adapted to what we are investigating
to make sure to get the best quality data possible
for the given objective. We next look at the
equipment in detail to facilitate its correct use.

5. 4.2 Seismic methods
37
Seismic source
There are different kinds of seismic sources in
practice; in general we have to decide between
impulsive sources and the vibroseis method. The
main factors to consider when choosing the
source - beside costs, efficiency, convenience and
safety - are spectral characteristics, amount of
energy, and repeatability. Taking local geologic
conditions into account, surface seismic source or
shot holes can be important. E.g., in the pilot
area Cuxhavener Rinne we see data collected
with a surface source and parts with poor data
due to near surface inhomogeneities (Gabriel et
al. 2003, Wiederhold et al. 2005; Fig. 5.5.8
Lüdingworth CMP 800–900). In these special
parts of the profile a source placed below the
inhomogeneous layers would give better results.
Acquiring high resolution seismic reflection data
requires the use of high frequencies accompanied
by broad bandwidth. The ideal seismic source
signal would produce a spike with a white
frequency spectrum and arbitrarily high
frequencies and thus would give highest
resolution (e.g. trace 1 in Fig. 4.2.6). However, in
practice an ideal spike is impossible to achieve.
The signals always have a limited length or
frequency band. A realistic estimate for the
maximum achievable frequencies in the near-
surface seismic application is 500 Hz, limiting the
wavelength of a several hundred meters per
second velocity P-wave to 2 m (this would be
extremely good!). With shear waves, shorter
wavelengths are achievable due to their low
velocity. But the problem always remains of
bringing these high frequency seismic waves into
the deep ground since high frequencies will be
stronger attenuated than lower frequencies.
Let us return to high resolution (after Knapp and
Steeples 1986b): Wavelet pulse width and
frequency bandwidth are reciprocal and linked by
an uncertainty relation. That means that for a
good resolution of the wave signal, we need a
broad bandwidth source. But it also means that
signals in the frequency band of 10 to 50 Hz
have the same resolving capabilities as the band
160 to 200 Hz. This is demonstrated in Figure
4.2.5. Although the frequencies of Figure 4.2.5b
are higher than those of Figure 4.2.5a, the pulse
width or wavelet length is the same (see red
bracket). The “ringiness” of the pulse in Figure
4.2.5b might make it less desirable as a wavelet
than the pulse in Figure 4.2.5a, even though it is
of higher frequency. If we approach the pulse-
width/frequency-bandwidth question in terms of
octaves (the interval between two frequencies
having a ratio of 2), it is clear that a bandwidth of
a couple of octaves has a greater resolving power
if the bandwidth is of high frequency (Fig.
4.2.5d). For the desirable source signal, this
means that primary emphasis must be on
improving the bandwidth but it is likewise
important to increase frequency values.
Fig. 4.2.5: a) and b) time-frequency pairs for two
wavelets of constant frequency bandwidth; c) and
d) time frequency pairs for two wavelets with
constant octave bandwidth. Red bracket marks the
wavelet length.
For the different appearance between an impulse
seismic source and the vibroseis method, see
Figure 4.2.6. Vibroseis means that a controlled
wave train with continuously varying frequencies
is generated over a period of time (e.g. 10
seconds). This wave train is called “sweep”,
where the frequency is usually changed linearly
with time starting at the lowest frequency
(upsweep). Advantages of Vibroseis, beside the
controlled sweep, are that there is less ground
damage (no shot holes), operation on roads is
possible (suited for urban areas; Fig. 4.2.7), the
seismic signal is less sensitive to noise from

6. HELGA WIEDERHOLD
38
impulsive source (footsteps, single cars, traffic
etc.). In rural areas with high water table an
impulsive source may be the better choice. E.g.,
in the pilot area Groningen very good results
were achieved with seismic blasting caps and
only little charges of explosives (Fig. 5.6.7).
With seismic sources operating from the surface,
signal enhancement in the field is simply possible
by repeatedly “shooting” at a single point and
summing the outputs (vertical stacking). The
desired signals, e.g. the reflections, will be
strengthened and the undesired signals, i.e.
random noise, will remain random. Thus the
signal-to-noise ratio (S/N ratio) is improved; it
Fig. 4.2.6: Simple three-layer model and reflection
response: trace 1 spike signal; trace 2 minimum
phase signal typical for impulsive seismic source;
trace 3 zero phase signal resulting from vibroseis
correlation of trace 7; traces 4, 5 and 6 vibroseis
response (uncorrelated) for the three reflectors;
trace 7 shows the superposition of traces 4, 5 and
6. The zoom in clarifies the different onset of the
signals: the spike and the minimum phase signal
start with the first break but the zero phase signal
with the maximum amplitude (the hatched green
line marks the beginning or reflection time break).
increases as the square root of the number of
pulses stacked. A good repeatability of the source
signal is necessary and independent which kind
of source is used, we traditionally speak of a
“shot”.
Receivers, geophones, seismometers
The geophone is the instrument used to
transform seismic energy into an electrical
voltage. It ordinarily responds to only one
component of the grounds displacement,
velocity, or acceleration associated with the
passage of a seismic wave. For a seismic
reflection survey with P-waves, this is the vertical
component. A motion-sensitive transducer
converts ground motion to an electrical signal.
The transducer in nearly all modern geophones is
a moving-coil electrodynamic type and consists of
a coil suspended by one or more springs in a
magnetic field that is fixed relative to the
geophone case (Fig. 4.2.8). A seismic wave
Fig. 4.2.7: Seismic sources: a) Vibroseis vehicle
GGA-Institut, b) seismic impulse source system Sissy
(Buness et al. 2000), c) seismic blasting cap.

7. 4.2 Seismic methods
39
moves the case and the magnet, but the coil
remains relatively stationary because of its inertia.
The relative movement of a magnetic field with
respect to the coil generates a voltage across the
coil that is transmitted by wire to the
seismograph. Depending on the frequency
characteristics of the geophone, the voltage is
proportional to the relative velocity of the coil
with respect to the magnet (when movement is
above the natural frequency of the geophone) or
proportional to frequency and hence to the
acceleration involved in the seismic passage
(when movement is below the natural
frequency). The first case, the so-called velocity
geophone, is commonly used. For shallow seismic
reflection surveys a natural resonant frequency in
the range of 30–50 Hz is recommended by
Steeples et al. (1997). Details on performance
characteristics of geophones are given e.g. by
Knapp & Steeples (1986a) or Pelton (2005). The
quality of the recorded seismic signals is last but
not least dependent on how the geophone is
coupled to the ground. In the field, one must
take care to use a good planting of the
geophone by a metal spike to the ground and to
make sure that it is oriented in the direction of
particle movement of the seismic wave (for a P-
wave this is the vertical direction). For signal
enhancement, geophones may be grouped, with
several geophones feeding a single channel of
the seismograph, and the signals are summed
(see below).
Seismograph
The seismograph is the instrument for controlling
and recording the data in a seismic survey. The
amount of data within seismic reflection work is
enormous. Imagine a recording time of 1 second
with 1 millisecond sampling interval that is 1000
data samples for the response of one geophone
(that is one data channel or trace). Multiply this
by the number of channels the seismograph can
process (at least 48 but may be more than 100)
and we have the data samples acquired for one
shot. Now imagine we want a seismic section of
one kilometre in length and we need a shot every
10 meters; thus we will have 100 shots ×
48 channels × 1000 samples = 4,800,000 data
values for 1 km of seismic line. With four bytes
needed for writing a data value and 240 bytes
per trace header, we have about 20 megabytes
Fig. 4.2.8: Top: geophone in use, connected by
black and red clips to the cable, the connectors are
raised from wet ground by white rod and
unplugged geophone; bottom: cut-away animation
of Sensor SM-24 geophone (Image provided by
Sensor Nederland: www.geophone.com).
of information. With today’s technology, the
display and recording of these data amounts is
not a problem. Even for the near-surface
applications, where usually less money is available
than for hydrocarbon exploration, high quality
multichannel seismographs are at hand.
Principally there are two possibilities: transmitting
the voltage response from the geophone
analogue via cable to the seismograph where it is
amplified, possibly filtered and converted to
digital samples (traditional seismograph) or
digitising the analogue signals already near the
geophone and transmitting the digital value
(distributed seismograph). The advantage of the
latter is less electrical noise, e.g., interference
from power lines, crosstalk etc.

8. HELGA WIEDERHOLD
40
The seismograph is also the controlling unit of
the survey. Via noise monitor, the response of
each geophone is monitored and the operator
can check whether the geophone is in working
order, whether it is planted well, and how
extensive is the microseism or “noise”. When the
noise level is low, the operator gives the start
signal for the shot. And with the shot, the
seismograph is triggered and starts recording.
The recorded seismogram can then be evaluated
and saved to disk or other media.
An important criterion of the seismograph is the
dynamic range that is defined as the ratio of the
largest to the smallest recoverable signal. Signal
intensity is usually expressed in decibel (dB) units,
which is the logarithm of amplitude or power
ratio, defined as 20log10
of the amplitude ratio or
10log10
of the power ratio. Seismologists usually
use amplitude rather than power. An increase of
6 dB in signal approximately doubles the
amplitude, 60 dB in signal is a factor of 1000 in
amplitude, and 120 dB is a factor of a million.
For example, the dynamic range for a meter stick
marked in increments of 1 mm and used to
measure length, is usually given as 0.2 – 1000
mm, where 0.2 mm is considered the smallest
length that can be judged to be different from
zero with the naked eye. Expressed in dB, the
meter bar has a dynamic range of 74 dB. The
dynamic range of a seismograph is related to the
number of bits in a binary number in the output
of the analogue-to-digital converter. For a fixed-
gain seismograph, it can be estimated from the
number of bits produced by the analog/digital
converter as follows: estimated-dynamic-range =
6 (Nb
– 1) dB, where Nb
is the number of bits in
the binary code. One bit is reserved for the
algebraic sign and each signal bit represents very
nearly 6 dB.
Today seismographs with dynamic ranges of 100
dB or more are available and very small signals
may be enhanced by digital signal processing.
With seismographs of dynamic range less than
100 dB, Knapp & Steeples (1986b) recommend a
balancing of the spectrum of the data during
recording to detect weak but high frequency
signals.
Field acquisition parameter design
Proper configuration of the field parameters is
essential for the success of the seismic survey.
Among the important field parameters are
geophone spacing, shot spacing, and shot point
offset to the geophone. It is important to
consider carefully what it is that we want to see.
A simple model including travel time curves for
the key reflectors and the expected arrival times
of coherent noise, like ground roll or surface
waves and air-coupled waves, may be very
helpful and may be calculated by simple
formulas. This is done for the case of a buried
valley in sedimentary environment. The result is
shown in Figure 4.2.9.
Direct waves, surface waves (ground roll), or air-
coupled waves start travelling from time zero,
that is with triggering the shot, and proceed
directly to the receivers at distance x with
generally relatively low velocity V (and low
frequency and high amplitude). The traveltime is
V
x
=tdirect (4.2.7)
These waves are “noise” – that is unwanted
signals – in a seismic reflection survey and form a
so-called “noise cone” (Fig. 4.2.9).
After a certain time delay, the refracted wave (or
head wave) overtakes the direct travelling waves.
The traveltime for the simple two-layer case can
be calculated by
1)
V
V
(
V
z2
+
V
x
=t 2
1
2
22
refracted - (4.2.8)
with thickness z of the first layer.
Reflected waves are not restricted to velocity
increase but are generated at any interface in the
subsoil where the density or velocity changes
discontinuously. The arrival time of the reflection
at the surface will always be later than the
refracted wave from the same interface or at
most tangent to the refracted travel time. The
travel time can be evaluated by

9. 4.2 Seismic methods
41
Fig. 4.2.9: Velocity-depth model and appropriate traveltime-distance model of expected seismic response and
coherent noise. Reflections are marked in the colour of the layer boundary in the velocity-depth model on the left
side. The refraction breaks of the layer boundaries at 10 m and 50 m, with 1600 m/s or 2000 m/s velocities, are
marked by dashed lines (circles in zoom in mark critical offset for refractions). The “noise cone” is defined by the
wide angle reflection from the 10 m layer boundary (orange colour; 600 m/s) and the air-coupled wave (330 m/s)
and the surface wave or ground roll (220 m/s).
22
reflected z4+xV
1=t (4.2.9)
This gives the shape of a symmetrical hyperbola
in the traveltime-distance plot or, considering a
layer dip of angle δ from the horizontal a
hyperbola where the apex is displaced from the
center:
)sin(+xz4+z4+xV
1=t 22
reflected δ (4.2.10)
For the multilayer case, for this simple calculation
the average velocity Vaverage
, calculated from
interval velocities Vi
and thickness zi
of the i layers
(traveltime across each layer is ti
= zi
/ Vi
) should
be used:
∑
∑
i i
i
i
i
average
v
z
z
=V (4.2.11).
or the root mean square velocity Vrms
which is
more equivalent to the normal moveout velocity
VNMO
that we need later for dynamic corrections:
∑
∑
i
i
i
i
2
i
rms
t
tV
=V (4.2.12)

10. HELGA WIEDERHOLD
42
RMS velocities are typically a few percent larger
than corresponding average velocities due to the
specific travelpaths.
For the design of field parameters and to best
record the reflected wavefield the maximum and
the minimum offset must be defined. The
maximum offset should be as large as possible to
aid velocity analysis. At the same time, it must be
small enough to avoid wide angle reflection
distortion (reflections with angle of incidence
near or greater the critical angle). It must also be
small enough so that the most important
reflection arrives just below the mute zone
applied during processing (see below). A rule of
thumb is to set maximum offset equal to the
depth to the deepest target reflector. Another
point to keep in mind is that many seismic
sources generate noise (like ground roll etc.) with
large amplitudes that superpose the reflection
energy in the noise cone (see also Fig. 4.2.9 and
Fig. 4.2.12). Often, filtering of the noise is a
problem and one has to mute, or zero, this part
of the data during processing.
The minimum offset should be close to zero. On
one side we then have control for velocity and
timing. On the other side it is useful to have first
arrival (refraction) information near the source for
static and datum correction. When minimum
offset becomes too large these events are not
recorded. Near-surface reflections are often
difficult to record because of the noise cone.
The geophone interval is a function of maximum
offset, minimum offset, number of traces
available in the seismograph, the required spatial
sampling, and the spatial resolution. The latter
are the most important to consider. A strict
criterion for the reconstruction of a wavefield is
that there must be two or more samples per cycle
for the highest frequency present (Nyquist
theorem). This determines the sampling interval
of the time series (see below) recorded at a fixed
position, i.e. the geophone, as well as the wave
at different places at a given instant, i.e. the
spatial sampling interval or the spacing of the
geophones. To make this more clear, look at the
wavelength definitions in Figure 4.2.10.
The apparent surface wavelength is a function of
emergent angle of the seismic ray. Surface waves
propagating horizontally along the ground have
an apparent surface wavelength equal to their
true wavelength. The shallowly emergent
reflected signal has an apparent surface
wavelength greater than its true wavelength, but
less than the apparent surface wavelength of
more steeply emergent reflected energy. In
general, apparent surface wavelength λa
is true
wavelength λ divided by the sine of the angle of
emergence Θ: Θsin/λ=λa . For vertically
incident rays (sinΘ=0), the apparent surface
wavelength is infinite; this concerns most
reflected signals so the above considerations are
not as critical for reflections from horizontal
layers, but for dipping layer reflections. Thus for
the proper spatial sampling of a reflection from a
dipping reflector the geophone spacing Δx must
be less than half the projection of the shortest
wavelength onto the surface. That is
δsin
fV
5.0=
δsin
5.0≤x
maxavemin
max
λ
Δ (4.2.13)
with δ maximum dip of reflector.
Fig. 4.2.10: Apparent surface wavelength versus
angle of emergence. If a wavefront approaches at
an angle θ, the apparent surface wavelength λa will
differ from true wavelength λ.

11. 4.2 Seismic methods
43
From the reflection signal point of view, another
consideration in determining receiver interval
involves the concept of the first Fresnel zone.
Reflected energy represents a sampling from a
relatively large area of the reflecting surface and
this is related to the first Fresnel zone. The size
and shape of the first Fresnel zone depend upon
reflector depth z and wavelength λ of the
reflected energy:
f
T
V5.0=
2
z
=R 0λ
(4.2.14)
with R the radius of the first Fresnel zone, V
velocity and T0
two-way traveltime. If T0
= 0.1 s,
V = 1600 m/s and f = 150 Hz, the size of the first
Fresnel zone is 40 m. This is roughly the size of
the reflecting “point”. With a receiver interval
including at least 2 traces (that are 4 CMPs) per
Fresnel zone, the reflector is well sampled.
Spatial considerations can also be used to
attenuate or to improve waves by grouping
geophones or shots in special arrays. In
exploration seismology, linear arrays are used to
attenuate the ground roll that usually is
characterized by relatively low velocity, low
frequency, and high amplitude. Arrays start to
attenuate signals when their length is a quarter
of the apparent surface wavelength and larger
(Fig. 4.2.11). Thus to attenuate the unwanted
ground roll that has a relatively large wavelength,
the array also must be relatively large. On the
other hand, to enhance reflection signals of
possibly high frequency, the array length may not
be larger than a quarter of their apparent surface
wavelength. Therefore the array length should in
no case be larger then
2
max
2
max
max
x
z
4+1
f
V
25.0≤L (4.2.15)
with z the depth to the shallowest reflector, xmax
the maximum source-receiver offset, fmax the
highest frequency contained in the reflection
signal, V the average velocity to the reflector and
Lmax the maximuim array length. If we accept as a
rule of thumb that the maximum source-receiver
offset is roughly equal to the target depth for
reflected energy that is not a wide-angle reflec
Fig. 4.2.11: Geophone array response versus
apparent surface length λa. If the group length is
small in relation to λa the response will be large
(blue geophone group); if the group length is large
in relation to λa the response is diminished (red
geophone group).
tion, then the following equation can be used:
max
max
f
V56.0
≤L (4.2.16)
In shallow, high-resolution reflection seismology,
arrays cannot be effectively employed to
attenuate ground roll (Knapp & Steeples 1986b).
Now to answer the question where to place the
shot in the active geophone line: it is always
preferable to use a symmetrical split-spread with
the geophones evenly split on either side of the
source. When the number of data channels
available is not sufficient, end-on geometry with
the source on one side of the geophone line is
used to get the offset required for the target
reflection (the sketch in Fig. 4.2.1 shows end-on
geometry). When reflections from dipping
horizons are expected, preferred end-on
geometry is that where the geophones are placed
updip from the source.
Additionally, one must consider the record time
length, that is the least time needed to record the
reflection from the deepest target horizon; e.g., if
the depth z of the buried valley is 400 m and an
average velocity V of 2000 m/s for the sedi-
mentary fill can be assumed, then the reflection
time t of the valley base would be v/z2=t and
thus be 400 ms or 0.4 s. This is the two-way
reflection time. To image also the surrounding or
geological setting, the recording time in this case
should be 1 s. If we want to look deeper, we
would have to raise this time value. For a proper
sampling of a cycle, at least two samples are

12. HELGA WIEDERHOLD
44
necessary. Expressed in relation to frequency, this
means that the highest frequency that can be
resolved, the Nyquist frequency fNy, needs the
time between two sample points or sampling
interval to be Nyf2/1=tΔ with Δt in milliseconds
(ms) and f in hertz (Hz). In practice, four samples
are recommended, or Nyf4/1=tΔ . Example: with
a sampling interval of 1 ms, frequencies up to
250 Hz are well sampled; the Nyquist frequency
is 500 Hz. To avoid aliasing, frequencies above
the Nyquist frequency must be removed before
sampling. The inverse of the sample interval is
called sample rate ( tΔ1= ).
4.2.4 Data processing
Figure 4.2.12 shows an example of a data set
obtained by one shot – a so-called shot gather.
The different kinds of waves that clearly can be
seen are the direct and/or refracted wave (1), the
airwave (2), the ground roll (3), and several
reflections (R). For the reflection seismic method,
the reflections are the only data we want, the
others (1–3) are “noise”. This noise generated by
the seismic source itself is coherent noise, in
contrast to random noise.
To convert the data recorded in the field to the
final seismic section, preferably a depth section,
sophisticated processing is necessary. The general
steps are described in the following:
Geometry and editing
■ transferring the data from the seismograph
to the seismic processing system (there are
standard data formats used in exploration
seismology; SEG standards)
■ vibroseis correlation (if relevant)
■ installation of geometry including
coordinates, elevation, and shot-receiver
configuration
■ elimination of bad or noisy traces
■ attenuation of coherent linear noise.
Fig. 4.2.12: Typical field record (shot gather); raw data (scaled) on the left side, the data on the right side are
scaled and filtered. (1) Refraction signals, (2) air-coupled wave, (R) reflection signals. The ground roll (3) is, in this
example, spatially aliased, i.e. sampled not properly, as shown by the apparent phase velocity of the ground roll in
a direction opposite to that of first arrivals. With a dominant frequency of 62,5 Hz and an apparent velocity of
220 m/s the resulting wavelength is 3,5 m and thus smaller than the receiver spacing of 5 m. This wave should be
muted in further processing steps.

13. 4.2 Seismic methods
45
Signal enhancement (scaling, filtering,
muting)
If we would look at the raw shot gather without
any scaling, we would clearly see the decrease of
amplitudes with distance and time. The earth has
two effects on a propagating wavefield: (1)
energy density decays proportionately to 1/r
2
where r is the radius of the wavefront. Wave
amplitude then, being proportional to the square
root of energy density, decays with 1/r. As
velocity usually increases with depth, this causes
further divergence of the wavefront and a more
rapid decay in amplitudes with distance. (2) The
frequency content of the initial source signal
changes in a time-variant manner as it
propagates. In particular, high frequencies are
absorbed more rapidly than low frequencies (due
to intrinsic attenuation). These effects must be
compensated by a time-variant scaling.
By a time-invariant scaling, the amplitudes for
each trace may be scaled or balanced with regard
to the gather or individually. Also, automatic gain
functions like AGC can be applied, but be aware
that the true amplitude information is lost.
Typically, prestack deconvolution (inverse
filtering, spectral whitening, shaping the
amplitude-frequency response) is aimed at
improving temporal resolution by compressing
the effective source wavelet contained in the
seismic trace to a spike. After deconvolution, a
wide band-pass filter is often needed.
In the extreme case that ground roll is not
attenuated or eliminated after the above
processes, this area of the shot gather should be
muted (zeroing the amplitudes) (Fig. 4.2.12).
Travel time corrections (static corrections,
dynamic corrections)
Concerning corrections of the traveltime, we
differentiate between static and dynamic
corrections.
Static corrections (in short statics) are independ-
ent of the travel time of a reflection and the
source-receiver offset. They are applied to seismic
data to compensate for the effects of variations
in elevation, weathering thickness, weathering
velocity, or reference to a datum (Fig. 4.2.13).
Fig. 4.2.13: Principle of static corrections: Shot
and receivers are moved to a flat plane, the datum
or reference surface. Near surface velocity changes
are replaced by a correction velocity Vc.
The objective is to determine the reflection arrival
times which would have been observed if all
measurements had been made on a (usually) flat
plane with no weathering or low velocity material
present. This, of course, only makes sense if this
material is not the target of the survey. These
corrections are based on (1) uphole data (direct
measurement of traveltime from a buried seismic
source), (2) refraction first breaks and/or (3) event
smoothing. (2) is the most common method (also
called refraction statics), especially when using
surface seismic sources. Seismic refraction
interpreting methods like intercept-time method,
generalized reciprocal method, delay time
method or refraction tomography, are used to
determine the near-surface model and the travel
time correction values. Travel times of reflection
signals in a shot or CMP gather should be more
regular in the hyperbolic moveout after this time
correction. Further irregularities in the reflection
arrival times due to near surface variations may
be smoothed by statistical methods (3), also
called residual statics.
Dynamic corrections or normal-moveout
corrections (NMO corrections), concern the
longer ray path or travel time of the reflection
due to the shot-receiver offset and correct the
travel time to zero-offset or vertical ray path. To
do this, the velocity of the medium above the
reflecting interface must be known. This can be

14. HELGA WIEDERHOLD
46
evaluated from the CMP gather by several
methods (Fig. 4.2.14): (1) simply find the velocity
that best fits the hyperbola to the common-
midpoint data; (2) semblance analysis: assume a
normal moveout, measure the coherency at that
normal moveout, and then vary the normal
moveout in order to maximize the coherency; (3)
make trial stacks assuming several trial velocities
that are constant in time and space and
determine the stacking velocities that produce
the best result. The result is the so-called stacking
or normal moveout velocity VNMO
because the
normal-moveout corrected traces of one CMP
will afterwards be stacked to one trace. When
working with real data, it becomes clear that the
quality of the velocity analysis depends on the
fold. By averaging CMP’s (e.g. three), a so-called
supergather is composed that may help when
fold is small.
Where all reflectors are horizontal and where
velocity varies only with depth, the stacking
velocity is approximately the root-mean-square
velocity (Eq. 4.2.12) and is a little higher than the
average velocity of the medium (Eq. 4.2.11).
Otherwise, stacking velocities are parameters
used to get the optimum seismic section and are
sensitive to the dip of the reflecting interface.
As a result of the normal-moveout corrections,
traces are stretched causing their frequency
content to shift toward the low end of the
spectrum. This distortion increases at shallow
times and large offsets. To prevent the
degradation of especially shallow events, the
amplitudes in the distorted zones are zeroed out
(muted) before stacking (Fig. 4.2.14c).
CMP stacking
After applying the prestack processing described
above, all traces belonging to a CMP are summed
resulting in the stacked seismic section. The
vertical scale of this section is usually arrival time
(two-way time TWT).
Fig. 4.2.14: Velocity analysis to determine dynamic corrections: a) CMP gather, b) semblance analysis, c) CMP
after normal moveout correction, d) stack with 20 neighbouring CMP’s.

15. 4.2 Seismic methods
47
If all reflectors are horizontal, this is our final
result that we can convert with the help of the
stacking velocity into a depth section or, as
already above mentioned (Eq. 4.2.11 and 4.2.12),
the true medium velocity will be about some
percent less than the stacking velocity. So we will
get an optimum result when using for depth
conversion stacking velocity reduced by, e.g.,
10%. A problem arises with nonhorizontal
layering and this is the usual case. The reflection
points (or amplitudes) of tilted layer boundaries
are plotted in the stacked section normal to the
surface but their true location is normal to the
layer (Fig. 4.2.15). This is corrected for by a
process called migration.
Fig. 4.2.15: Migration principle: the reflection
segment AB moves to segment A’B’ when migrated.
Migration
Migration is an inversion operation involving
rearrangement of seismic information elements
so that reflections are plotted at their true
subsurface positions and diffractions collapse
thus increasing spatial resolution and yielding a
seismic image of the subsurface. As we are
dealing with buried valleys and their steeply
dipping rims, migration is an indispensable
process. There will be three effects: (1) the dip
angle of the reflector in the final section is
greater than in the time section; thus migration
steepens reflectors. In Figure 4.2.15 we see that
the dip angle of the reflection segment is
tan(δ) = Δt/Δx and after migration the dip angle
is sin(δ’) = Δt/Δx. And as arc sine of an angle is
greater or equal arc tangent of an angle the
migrated segment is steeper. (2) The length of
the reflector is shorter; thus migration shortens
reflectors. (3) Migration moves reflectors in the
updip direction (Figs. 4.2.15 and 4.2.16).
Migration requires the true medium velocity, i.e.
we must use a velocity field that is independent
of dip and that means that stacking velocities
may be problematic (see above). After migration,
the section will be converted to a depth section
with adequate velocity information (true medium
velocity).
4.2.5 What can we expect? Results
The results of a (conventional) seismic survey as
described above include:
■ the stacked time section
■ the migrated time section
■ the depth section
■ near-surface velocity and depth model (from
first break analysis)
■ stacking velocity information.
The (migrated) depth section that is most similar
to the geologic cross section along the seismic
line is what we want. However, the migrated
section is commonly displayed in time. One
reason for this is that velocity estimation based
on seismic data is limited in accuracy. Therefore,
depth conversion is not completely accurate.
Another reason is that interpreters prefer to
evaluate the validity of migrated sections by
comparing them to the unmigrated data.
The seismic section will be displayed in “wiggle
trace/variable area mode” (e.g. Fig. 5.5.8) or a
colour scale will be applied to the amplitudes
(e.g. Fig. 4.2.16).

16. HELGA WIEDERHOLD
48
Fig. 4.2.16: Effect of migration (example from Ellerbeker Rinne): Left: stacked section, right: migrated section.
4.2.6 Restrictions, uncertainties, error
sources and pitfalls
Like all geophysical methods, the seismic
reflection method has limitations. Some of the
restrictions to be considered when selecting
acquisition parameters are (Steeples 2005):
■ the vertical and horizontal limits of resolution
■ the wavelength and frequency of the
recorded data and the bandpass of the
recording components
■ the presence of noise from electronic and
other cultural sources
■ out of plane reflections caused by off-line
geological structures or three dimensional
features
■ velocity variations with vertical and horizontal
location in the near surface.
Vertical resolution decreases with depth as the
dominant wavelength for seismic reflections
normally increases with depth (due to increasing
velocity but decreasing frequency). The expected
frequency often is difficult to estimate during the
planning stage of a seismic survey. Near-surface
geology and depth of water table may have
strong influences. In areas where thick, dry sand
is present at the surface, dominant frequencies
above a few tens of hertz usually cannot be
obtained; conversely in areas where the water
table is near the surface, data with dominant
frequencies of several hundred hertz sometimes
can be acquired (Steeples 2005). Another
important prerequisite for good results is that a
sufficient impedance contrast is present.
The seismic section may contain some pitfalls:
■ In the case of very shallow reflections,
interference of refractions with reflections is
a major problem. When refractions stack on
seismic sections, they usually appear as
wavelets whose frequencies are lower than
those of reflections. Refractions must be
removed (muted) during processing.
■ Remnants of air-wave signals may be
present. These show up as very steep dipping
signals with relatively short wavelength and,
in the time section, a characteristic velocity of
335 m/s. Dependent on the spread
arrangement of the survey they run forward
or backward.
■ Surface waves, if not removed carefully
during processing, may stack to reflection
like signals especially in the near surface
range.

17. 4.2 Seismic methods
49
■ Migration effects, i.e., if velocities higher
than the actual medium velocity are used for
migration typical “smiles” may occur. If we
use too low velocities there may be remnants
of diffractions.
■ Multiples, that is seismic energy which has
been reflected more than once, are identified
by their travel times, and/or may be identified
during velocity analysis by their velocity.
Multiples are not a severe problem of
onshore near surface seismic data.
Principally, to validate a seismic section and their
conclusions, interpreters must have access to at
least one field file, along with display copies of
one or more of the intermediate processing steps
whenever possible (Steeples & Miller 1998).
Vertical seismic profiles allow the accurate
determination of the travel time of seismic waves
to various geologic units and thus allow the
accurate determination of seismic velocities. They
are recommended to secure depth sections and
interpretations.
4.2.7 References
Buness AH, Druivenga G, Wiederhold H (2000):
SISSY – eine tragbare und leistungsstarke
seismische Energiequelle. – Geol. JB. E52: 63–
88.
Gabriel G, Kirsch R, Siemon B, Wiederhold H
(2003): Geophysical investigation of buried
Pleistocene subglacial valleys in Northern
Germany. – Journal of Applied Geophysics 53:
159–180.
Knapp RW, Steeples DW (1986a): High-resolution
common-depth-point seismic reflection
profiling – Instrumentation. – Geophysics 51:
276–282.
Knapp RW, Steeples DW (1986b): High-resolution
common-depth-point reflection profiling –
Field acquisition parameter design. –
Geophysics 51: 283–294.
Knödel K, Krummel H, Lange G (1997):
Geophysik. – Handbuch zur Erkundung des
Untergrundes von Deponien und Altlasten
Band 3, Springer; Berlin Heidelberg.
Pelton JR (2005): Near-Surface Seismology:
Surface-Based Methods. – In: Butler DK (Ed.),
Near-Surface Geophysics: 219–264, Soc. of
Expl. Geophys.; Tulsa, USA.
Rabbel W (2006): Seismic methods. – In: Kirsch R
(Ed.), Groundwater geophysics – A tool for
hydrogeology: 23–84; Springer; Berlin
Heidelberg.
Sheriff RE (2002): Encyclopedic Dictionary of
Exploration Geophysics (4
th
ed.). – Soc. of
Expl. Geophys.; Tulsa, USA.
Steeples DW (2005): Shallow seismic methods. –
In: Rubin Y, Hubbard SS (Eds.),
Hydrogeophysics: 215–251, Springer;
Dordrecht, the Netherlands.
Steeples DW, Miller RD (1998): Avoiding pitfalls
in shallow seismic reflection surveys.
Geophysics 63: 1213–1224.
Steeples DW, Green AG, McEvilly TV, Miller RD,
Doll WE, Rector JW (1997): A workshop
examination of shallow seismic reflection
surveying. – The Leading Edge 16: 1641–
1647.
Wiederhold H, Gabriel G, Grinat M (2005):
Geophysikalische Erkundung der Bremer-
haven-Cuxhavener Rinne im Umfeld der
Forschungsbohrung Cuxhaven. – Z. Angew.
Geol. 51(1): 28–38.
Yilmaz O (2001): Seismic Data Analysis (vol 1 and
2, 2nd ed.). – Soc. of Expl. Geophys.; Tulsa,
USA.

18. HELGA WIEDERHOLD
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Summary: Schedule of seismic survey