Higher-Order Squeezing of a Generic Quadratically-Coupled Optomechanical SystemIOSRJAP
Using short-time dynamics and analytical solution of Heisenberg equation of motion for the Hamiltonian of quadratically-coupled optomechanical system for different field modes, we have investigated the existence of higher-order single mode squeezing, sum squeezing and difference squeezing in absence of driving and dissipation. Depth of squeezing increases with order number for higher-order single mode squeezing. Squeezing factor exhibits a series of revival-collapse phenomena for single mode, which becomes more pronounced as order number increases. In case of sum squeezing amounts of squeezing is greater than single mode higher-order squeezing (n = 2). It is also greater than from difference squeezing for same set of interaction parameters. Sum squeezing is prominently better for extracting information regarding squeezing.
Simulation Analysis of Single Column Plate Phononic Crystals At Low Frequency...IJRESJOURNAL
ABSTRACT: In this paper, locally resonant single side column plate phononic crystals are studied. Based on the finite element method, the material properties of the scatterer and the effect of the plate shape on the band gap characteristics of the locally resonant single side column plate phononic crystals are calculated and analyzed by use of the multi-physics software COMSOL. Based on the analysis on the effects of the density, the elastic modulus, the poisson ratio and the shape of the scatterer, it is shown that the density, the elastic modulus and the shape of the scatterer can obviously affect the band gaps of phononiccrystals .
Discovery of rotational modulations in the planetary mass companion 2m1207b i...Sérgio Sacani
Rotational modulations of brown dwarfs have recently provided powerful constraints on the properties
of ultra-cool atmospheres, including longitudinal and vertical cloud structures and cloud evolution.
Furthermore, periodic light curves directly probe the rotational periods of ultra-cool objects. We
present here, for the first time, time-resolved high-precision photometric measurements of a planetarymass
companion, 2M1207b. We observed the binary system with HST/WFC3 in two bands and with
two spacecraft roll angles. Using point spread function-based photometry, we reach a nearly photonnoise
limited accuracy for both the primary and the secondary. While the primary is consistent with
a flat light curve, the secondary shows modulations that are clearly detected in the combined light
curve as well as in di↵erent subsets of the data. The amplitudes are 1.36% in the F125W and 0.78%
in the F160W filters, respectively. By fitting sine waves to the light curves, we find a consistent period
of 10.7+1.2
−0.6 hours and similar phases in both bands. The J- and H-band amplitude ratio of 2M1207b
is very similar to a field brown dwarf that has identical spectral type but di↵erent J-H color. Importantly,
our study also measures, for the first time, the rotation period for a directly imaged extra-solar
planetary-mass companion.
Higher-Order Squeezing of a Generic Quadratically-Coupled Optomechanical SystemIOSRJAP
Using short-time dynamics and analytical solution of Heisenberg equation of motion for the Hamiltonian of quadratically-coupled optomechanical system for different field modes, we have investigated the existence of higher-order single mode squeezing, sum squeezing and difference squeezing in absence of driving and dissipation. Depth of squeezing increases with order number for higher-order single mode squeezing. Squeezing factor exhibits a series of revival-collapse phenomena for single mode, which becomes more pronounced as order number increases. In case of sum squeezing amounts of squeezing is greater than single mode higher-order squeezing (n = 2). It is also greater than from difference squeezing for same set of interaction parameters. Sum squeezing is prominently better for extracting information regarding squeezing.
Simulation Analysis of Single Column Plate Phononic Crystals At Low Frequency...IJRESJOURNAL
ABSTRACT: In this paper, locally resonant single side column plate phononic crystals are studied. Based on the finite element method, the material properties of the scatterer and the effect of the plate shape on the band gap characteristics of the locally resonant single side column plate phononic crystals are calculated and analyzed by use of the multi-physics software COMSOL. Based on the analysis on the effects of the density, the elastic modulus, the poisson ratio and the shape of the scatterer, it is shown that the density, the elastic modulus and the shape of the scatterer can obviously affect the band gaps of phononiccrystals .
Discovery of rotational modulations in the planetary mass companion 2m1207b i...Sérgio Sacani
Rotational modulations of brown dwarfs have recently provided powerful constraints on the properties
of ultra-cool atmospheres, including longitudinal and vertical cloud structures and cloud evolution.
Furthermore, periodic light curves directly probe the rotational periods of ultra-cool objects. We
present here, for the first time, time-resolved high-precision photometric measurements of a planetarymass
companion, 2M1207b. We observed the binary system with HST/WFC3 in two bands and with
two spacecraft roll angles. Using point spread function-based photometry, we reach a nearly photonnoise
limited accuracy for both the primary and the secondary. While the primary is consistent with
a flat light curve, the secondary shows modulations that are clearly detected in the combined light
curve as well as in di↵erent subsets of the data. The amplitudes are 1.36% in the F125W and 0.78%
in the F160W filters, respectively. By fitting sine waves to the light curves, we find a consistent period
of 10.7+1.2
−0.6 hours and similar phases in both bands. The J- and H-band amplitude ratio of 2M1207b
is very similar to a field brown dwarf that has identical spectral type but di↵erent J-H color. Importantly,
our study also measures, for the first time, the rotation period for a directly imaged extra-solar
planetary-mass companion.
A measurement of_the_black_hole_mass_in_ngc_1097_using_almaSérgio Sacani
Artigo descreve a maneira como os astrônomos usaram pela primeira vez o ALMA para medir a massa de um buraco negro supermassivo no interior de uma galáxias espiral barrada.
MAGNETOSTATIC SURFACE WAVES IN A LEFT HANDED / FERRITE/ METAL-STRIP-GRATING S...ijrap
The dispersion characteristics for magnetostatic surface waves in a left handed ( LHM)/ferrite/ metal-stripgrating
structure have been investigated. We found that, the waveguide supports backward TE waves
since both permittivity and magnetic permeability of LHM are negative. We also illustrated the
dependence of wave frequency on the reduced wave number for a grating shielding parameter, g values
restricted by the range 0 ≤ g ≥ 1. It is shown that the grating shielding parameter, g induces
magnetostatic backward shorter waves . The leakage through the grating increases with the wave number. The shorter backward magnetostatic waves are guided by the thicker waveguide where the best confinement is achieved
Optical coupling and transport phenomena in chains of spherical dielectric mi...Shashaanka Ashili
The optical transmission properties of chains or circuits of touching polystyrene microspheres with sizes in the 3–20 mm range and a size dispersion of ,1% are studied. The dye-doped spheres with fluorescent peaks due to whispering gallery modes were attached to one end of the chains. The effects of optical transport were detected using spatially resolved scattering spectroscopy. The
attenuation was shown to be ,3 to 4 dB per sphere for the modes with the best transport properties. A mechanism for the observed transport is suggested based on the formation of strongly coupled photonic modes in the systems of randomly detuned resonators with size disorder. It is shown that such circuits possess broad bandpass waveguiding characteristics essential for applications in integrated all-optical network devices.
FREQUENCY RESPONSE ANALYSIS OF 3-DOF HUMAN LOWER LIMBSIJCI JOURNAL
Frequent and prolonged expose of human body to vibrations can induce back pain and physical disorder
and degeneration of tissue. The biomechanical model of human lower limbs are modeled as a three degree
of freedom linear spring-mass-damper system to estimate forces and frequencies. Then three degree of
freedom system was analysed using state space method to find natural frequency and mode shape. A
program was develop to solve simplified equations and results were plotted and discussed in detail. The
mass, stiffness and damping coefficient of various segments are taken from references. The optimal values
of the damping ratios of the body segments are estimated, for the three degrees of freedom model. At last
resonance frequencies are found to avoid expose of lower limbs to such environment for optimum comfort.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Design of MEMS capacitive accelerometer with different perforated proof- mass...IOSR Journals
This work represents a study of perforated proof mass of a micro fabricated accelerometer with
different perforation shapes, by application of load stress and displacement is measuredto know the deflection and
flexibility of the proof mass. Perforation shapes of proof mass of capacitive accelerometer affects the sensitivity and
other performance parameters of accelerometer.Eigen frequency analysis is done to know the stress and
displacement distribution on vibrating proof mass which are used to measure and compare the sensitivity and
mechanical strength of proof mass. As a result of this study it has been found that the proof mass with perforation
shape of nozzle/diffuser is the most efficient perforation shape to get better performance from an capacitive micro
fabricated accelerometers.
The build up_of_the_c_d_halo_of_m87_evidence_for_accretion_in_the_last_gyrSérgio Sacani
Observações recentes obtidas com o Very Large Telescope do ESO mostraram que Messier 87, a galáxia elíptica gigante mais próximo de nós, engoliu uma galáxia inteira de tamanho médio no último bilhão de anos. Uma equipe de astrônomos conseguiu pela primeira vez seguir o movimento de 300 nebulosas planetárias brilhantes, encontrando evidências claras deste evento e encontrando também excesso de radiação emitida pelos restos da vítima completamente desfeita.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
The propagation of electromagnetic waves in a cold magnetized plasma with ferromagnetic grains (MPFG)
in the high frequency domain is studied theoretically. The dispersion of MPFG which is controlled by the
simultaneous characterization of the permittivity and permeability tensors. is investigated theoretically and
numerically near the resonance frequency. It is found that MPFG becomes transparent for the waves that
cannot propagate in conventional magnetized electron-ion plasma. The refractive index of the waves
propagating parallel to the applied magnetic field is found to be negative for the extraordinary wave in
certain frequency domain. The results obtained show that in a narrow band of the super-high-frequency
range near the electron cyclotron frequency, MPFG possess all the known characteristics of negative
refractive index media, which would make it as a viable alternative medium to demonstrate the known and
predicted peculiar properties of media having negative index of refraction.
The hazardous km-sized NEOs of the next thousands of yearsSérgio Sacani
The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring
analyses search for possible impacts over the next 100 years and none of the km-sized objects represent
an impact threat over that time interval. Assessing the impact risk over longer time scales is a challenge
since orbital uncertainties grow. To overcome this limitation we analyze the evolution of the Minimum
Orbit Intersection Distance (MOID), which bounds the closest possible encounters between the asteroid
and the Earth. The evolution of the MOID highlights NEOs that are in the vicinity of the Earth for
longer periods of time, and we propose a method to estimate the probability of a deep Earth encounter
during these periods. This metric is used to rank the km-sized catalog in terms of their long-term
impact hazard to identify targets of potential interest for additional observation and exploration.
Magnetized Plasma with Ferromagnetic Grains as a Viable Negative Refractive I...ijrap
The propagation of electromagnetic waves in a cold magnetized plasma with ferromagnetic grains (MPFG)
in the high frequency domain is studied theoretically. The dispersion of MPFG which is controlled by the
simultaneous characterization of the permittivity and permeability tensors. is investigated theoretically and
numerically near the resonance frequency. It is found that MPFG becomes transparent for the waves that
cannot propagate in conventional magnetized electron-ion plasma. The refractive index of the waves
propagating parallel to the applied magnetic field is found to be negative for the extraordinary wave in
certain frequency domain. The results obtained show that in a narrow band of the super-high-frequency
range near the electron cyclotron frequency, MPFG possess all the known characteristics of negative
refractive index media, which would make it as a viable alternative medium to demonstrate the known and
predicted peculiar properties of media having negative index of refraction.
A measurement of_the_black_hole_mass_in_ngc_1097_using_almaSérgio Sacani
Artigo descreve a maneira como os astrônomos usaram pela primeira vez o ALMA para medir a massa de um buraco negro supermassivo no interior de uma galáxias espiral barrada.
MAGNETOSTATIC SURFACE WAVES IN A LEFT HANDED / FERRITE/ METAL-STRIP-GRATING S...ijrap
The dispersion characteristics for magnetostatic surface waves in a left handed ( LHM)/ferrite/ metal-stripgrating
structure have been investigated. We found that, the waveguide supports backward TE waves
since both permittivity and magnetic permeability of LHM are negative. We also illustrated the
dependence of wave frequency on the reduced wave number for a grating shielding parameter, g values
restricted by the range 0 ≤ g ≥ 1. It is shown that the grating shielding parameter, g induces
magnetostatic backward shorter waves . The leakage through the grating increases with the wave number. The shorter backward magnetostatic waves are guided by the thicker waveguide where the best confinement is achieved
Optical coupling and transport phenomena in chains of spherical dielectric mi...Shashaanka Ashili
The optical transmission properties of chains or circuits of touching polystyrene microspheres with sizes in the 3–20 mm range and a size dispersion of ,1% are studied. The dye-doped spheres with fluorescent peaks due to whispering gallery modes were attached to one end of the chains. The effects of optical transport were detected using spatially resolved scattering spectroscopy. The
attenuation was shown to be ,3 to 4 dB per sphere for the modes with the best transport properties. A mechanism for the observed transport is suggested based on the formation of strongly coupled photonic modes in the systems of randomly detuned resonators with size disorder. It is shown that such circuits possess broad bandpass waveguiding characteristics essential for applications in integrated all-optical network devices.
FREQUENCY RESPONSE ANALYSIS OF 3-DOF HUMAN LOWER LIMBSIJCI JOURNAL
Frequent and prolonged expose of human body to vibrations can induce back pain and physical disorder
and degeneration of tissue. The biomechanical model of human lower limbs are modeled as a three degree
of freedom linear spring-mass-damper system to estimate forces and frequencies. Then three degree of
freedom system was analysed using state space method to find natural frequency and mode shape. A
program was develop to solve simplified equations and results were plotted and discussed in detail. The
mass, stiffness and damping coefficient of various segments are taken from references. The optimal values
of the damping ratios of the body segments are estimated, for the three degrees of freedom model. At last
resonance frequencies are found to avoid expose of lower limbs to such environment for optimum comfort.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Design of MEMS capacitive accelerometer with different perforated proof- mass...IOSR Journals
This work represents a study of perforated proof mass of a micro fabricated accelerometer with
different perforation shapes, by application of load stress and displacement is measuredto know the deflection and
flexibility of the proof mass. Perforation shapes of proof mass of capacitive accelerometer affects the sensitivity and
other performance parameters of accelerometer.Eigen frequency analysis is done to know the stress and
displacement distribution on vibrating proof mass which are used to measure and compare the sensitivity and
mechanical strength of proof mass. As a result of this study it has been found that the proof mass with perforation
shape of nozzle/diffuser is the most efficient perforation shape to get better performance from an capacitive micro
fabricated accelerometers.
The build up_of_the_c_d_halo_of_m87_evidence_for_accretion_in_the_last_gyrSérgio Sacani
Observações recentes obtidas com o Very Large Telescope do ESO mostraram que Messier 87, a galáxia elíptica gigante mais próximo de nós, engoliu uma galáxia inteira de tamanho médio no último bilhão de anos. Uma equipe de astrônomos conseguiu pela primeira vez seguir o movimento de 300 nebulosas planetárias brilhantes, encontrando evidências claras deste evento e encontrando também excesso de radiação emitida pelos restos da vítima completamente desfeita.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
The propagation of electromagnetic waves in a cold magnetized plasma with ferromagnetic grains (MPFG)
in the high frequency domain is studied theoretically. The dispersion of MPFG which is controlled by the
simultaneous characterization of the permittivity and permeability tensors. is investigated theoretically and
numerically near the resonance frequency. It is found that MPFG becomes transparent for the waves that
cannot propagate in conventional magnetized electron-ion plasma. The refractive index of the waves
propagating parallel to the applied magnetic field is found to be negative for the extraordinary wave in
certain frequency domain. The results obtained show that in a narrow band of the super-high-frequency
range near the electron cyclotron frequency, MPFG possess all the known characteristics of negative
refractive index media, which would make it as a viable alternative medium to demonstrate the known and
predicted peculiar properties of media having negative index of refraction.
The hazardous km-sized NEOs of the next thousands of yearsSérgio Sacani
The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring
analyses search for possible impacts over the next 100 years and none of the km-sized objects represent
an impact threat over that time interval. Assessing the impact risk over longer time scales is a challenge
since orbital uncertainties grow. To overcome this limitation we analyze the evolution of the Minimum
Orbit Intersection Distance (MOID), which bounds the closest possible encounters between the asteroid
and the Earth. The evolution of the MOID highlights NEOs that are in the vicinity of the Earth for
longer periods of time, and we propose a method to estimate the probability of a deep Earth encounter
during these periods. This metric is used to rank the km-sized catalog in terms of their long-term
impact hazard to identify targets of potential interest for additional observation and exploration.
Magnetized Plasma with Ferromagnetic Grains as a Viable Negative Refractive I...ijrap
The propagation of electromagnetic waves in a cold magnetized plasma with ferromagnetic grains (MPFG)
in the high frequency domain is studied theoretically. The dispersion of MPFG which is controlled by the
simultaneous characterization of the permittivity and permeability tensors. is investigated theoretically and
numerically near the resonance frequency. It is found that MPFG becomes transparent for the waves that
cannot propagate in conventional magnetized electron-ion plasma. The refractive index of the waves
propagating parallel to the applied magnetic field is found to be negative for the extraordinary wave in
certain frequency domain. The results obtained show that in a narrow band of the super-high-frequency
range near the electron cyclotron frequency, MPFG possess all the known characteristics of negative
refractive index media, which would make it as a viable alternative medium to demonstrate the known and
predicted peculiar properties of media having negative index of refraction.
Comparison of Different Absorbing Boundary Conditions for GPR Simulation by t...IJMER
This paper compares three boundary conditions, i.e. transmitting boundary condition, Sarma
absorbing boundary condition and the uniaxial complete matched layerabsorbing boundary condition for
simulation of ground penetrating radar (GPR) by the time domain finite element (FEM) method. The
formulations of the three boundary conditions for the FEM method are described. Their effectiveness in
absorbing the incident electromagnetic waves are evaluated by the reflection coefficient on the boundary
of a simple GPR model.The results demonstrate that UPML boundary condition can yield a reflection
coefficient smaller than -50 dB, which is -20 dB smaller than other two boundary conditions.
Exact Analytical Expression for Outgoing Intensity from the Top of the Atmosp...IOSR Journals
This research is a part of the work devoted on the application of analytical Discrete Ordinate (ADO) method to the polarized monochromatic radiative transfer equation undergoing anisotropic scattering with source function matrix in a finite coupled Atmosphere –Ocean media having flat interface boundary conditions involving specular reflection and transmission matrix. Discontinuities in the derivatives of the Stokes vector with respect to the cosine of the polar angle at smooth interface between the two media with different refractive indices (air and water) is tackled by using a suitable quadrature scheme devised earlier. Atmosphere and ocean are assumed to be homogeneous. No stratification is adopted in the two media. Exact expression for the
emergent radiation intensity vector from the top of the atmosphere is derived. Exact expressions for the emergent polarized radiation intensity vector from the air-water interface as well as from any point of the two medium in any direction can also be derived in terms of eigenvectors and eigenvalues.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Effect of Rotation on a Layer of Micro-Polar Ferromagnetic Dusty Fluid Heated...IJERA Editor
This paper deals with the theoretical investigation of effect of rotation on micro-polar ferromagnetic dusty fluid
layer heated from below in a porous medium. Linear stability analysis and normal mode analysis methods are
used to find an exact solution for a flat micro-polar ferromagnetic fluid layer contained between two free
boundaries . In case of stationary convection, the effect of various parameters like medium permeability
parameter, non-buoyancy magnetization parameter, micro-polar coupling parameter, spin-diffusion parameter,
micro-polar heat conduction parameter, dust particles parameter and rotation parameter has been analyzed and
results are depicted graphically. In the absence of dust particles, rotation, micro-viscous effect and micro-inertia,
the sufficient condition is obtained for non-oscillatory modes
The distribution and_annihilation_of_dark_matter_around_black_holesSérgio Sacani
Uma nova simulação computacional feita pela NASA mostra que as partículas da matéria escura colidindo na extrema gravidade de um buraco negro pode produzir uma luz de raios-gamma forte e potencialmente observável. Detectando essa emissão forneceria aos astrônomos com uma nova ferramenta para entender tanto os buracos negros como a natureza da matéria escura, uma elusiva substância responsável pela maior parte da massa do universo que nem reflete, absorve ou emite luz.
Nano mechanics, geo-materials, Nano scale friction, governing equations, macro-Nano behavior of geomaterials, factors affecting Nano scale friction, behavior of soil at Nano scale, scale effect, Micro-Nano transition for frictional forces, review paper, best paper award, best paper presenter award, at PP Savani University, Kosamba, Surat.
1. This article appeared in a journal published by Elsevier. The attached
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2. Author's personal copy
Computers & Geosciences 34 (2008) 603–610
Programs to compute magnetization to density ratio
and the magnetization inclination from 3-D gravity
and magnetic anomalies$
Carlos A. Mendonc-aÃ,1
, Ahmed M.A. Meguid2
Instituto de Astronomia, Geofı´sica e Cieˆncias Atmosfe´ricas, Universidade de Sa˜o Paulo, Rua do Mata˜o, no. 1226,
Cidade Universita´ria, CEP: 05508-090 Sa˜o Paulo, Brazil
Received 13 June 2006; received in revised form 24 September 2007; accepted 26 September 2007
Abstract
Vector field formulation based on the Poisson theorem allows an automatic determination of rock physical properties
(magnetization to density ratio—MDR—and the magnetization inclination—MI) from combined processing of gravity
and magnetic geophysical data. The basic assumptions (i.e., Poisson conditions) are: that gravity and magnetic fields share
common sources, and that these sources have a uniform magnetization direction and MDR. In addition, the previously
existing formulation was restricted to profile data, and assumed sufficiently elongated (2-D) sources. For sources that
violate Poisson conditions or have a 3-D geometry, the apparent values of MDR and MI that are generated in this way
have an unclear relationship to the actual properties in the subsurface. We present Fortran programs that estimate MDR
and MI values for 3-D sources through processing of gridded gravity and magnetic data. Tests with simple geophysical
models indicate that magnetization polarity can be successfully recovered by MDR–MI processing, even in cases where
juxtaposed bodies cannot be clearly distinguished on the basis of anomaly data. These results may be useful in crustal
studies, especially in mapping magnetization polarity from marine-based gravity and magnetic data.
r 2007 Elsevier Ltd. All rights reserved.
PACS: PRISM3D; MDRMI
Keywords: Potential fields; Poisson theorem; MDR; MI
1. Introduction
The Poisson theorem can be used to extract
information about rock properties directly from
processing of gravity and magnetic anomaly data.
This theorem provides a simple linear relationship
connecting gravity and magnetic potentials and, by
extension, field components that are commonly
derived from geophysical surveys (Blakely, 1995).
The assumptions underlying the Poisson theorem
ARTICLE IN PRESS
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0098-3004/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cageo.2007.09.013
$
Code available from server at http://www.iamg.org/
CGEditor/index.htm
ÃCorresponding author.
E-mail address: mendonca@iag.usp.br (C.A. Mendonc-a).
1
Supported by CNPq (3051005/2002-07) and (140603/2003-4).
2
Assistant researcher at the Egyptian Petroleum Researches
Institute (EPRI), Ph.D. candidate at IAG-USP.
3. Author's personal copy
(or Poisson conditions) are that: (i) causative dense
and magnetic sources are common; (ii) magnetiza-
tion direction is constant; and (iii) magnetization to
density ratio (MDR) is constant. For geological
structures satisfying such constraints, it is possible
to use gravity and magnetic anomalies to estimate
the source MDR, which is related to the slope of the
linear Poisson relationship, and its magnetization
inclination (MI). Poisson-based methods have been
applied to interpret many geological problems in
marine geophysics (Bott and Ingles, 1972; Cordell
and Taylor, 1971) and regional studies of continen-
tal crust (Chandler et al., 1981; Hildebrand, 1985;
Chandler and Malek, 1991).
Two main approaches have been used to apply
Poisson theorem. In the first approach, filtering is
applied to produce the vertical derivative of gravity
anomaly and the magnetic anomaly reduced to pole
(vertically polarized) (Bott and Ingles, 1972; Chand-
ler et al., 1981; Chandler and Malek, 1991). The
second approach (Baranov, 1957; Cordell and
Taylor, 1971) filters the magnetic anomaly solely,
to produce a pseudo-gravity anomaly, which
involves magnetic reduction to the pole and its
integration along the magnetization direction. In
either case, transformed anomalies should be coin-
cident if Poisson conditions are upheld. If the
direction of magnetization is known, MDR values
can be readily calculated by either approach
through a linear regression of the transformed
gravity and magnetic data. Both approaches can
also be used to estimate an unknown magnetization
direction by a trying range of trial and error
directions until a maximum correlation is attained.
However, such trial and error methods lack the
efficiency of a one-step approach and are prone to
error when Poisson conditions are not upheld.
A one-step method that estimates both MDR and
MI values from profile data has been developed by
using a vector field formulation for the Poisson
theorem (Mendonc-a, 2004). In this approach, the
gravity anomaly is processed to furnish its gradient,
and the magnetic anomaly processed to give its
parent anomalous vector field. MDR is then
obtained by rationing the amplitude of these fields,
and MI by taking their inner product. For 2-D
sources, this approach provides accurate MDR and
MI estimations with no prior knowledge of magne-
tization direction and no need of iterative proce-
dures. Sources violating Poisson conditions lead to
apparent MDR and MI values that do not truly
reflect subsurface sources, but they nonetheless can
be used to discern geological contacts and infer
spatial variations in rock physical properties (Men-
donc-a, 2004). Unfortunately, little is known about
the significance of apparent MDR and MI values
that are derived in this way from sources that are
actually 3-D.
This paper presents two Fortran programs that
use gridded gravity and magnetic data to estimate
MDR and MI values for 3-D sources. Program
PRISM3D computes responses over simple 3-D
models and gives some guidance for interpreting
field-acquired data sets. Program MDRMI can be
used to process field-acquired gravity and magnetic
data sets to estimate MDR and MI values for the
causative sources. MATLAB scripts to visualize
program outputs are also included.
2. Poisson relationship in vectorial form
Poisson theorem (Blakely, 1995) relates the
magnetic potential, Vm, to gravity potential, U, as
Vm ¼ Àp
qU
qm
, (1)
under the assumption that Poisson conditions are
held. By Eq. (1), magnetization direction is given by
unit vector m,
p ¼ c
DM
Dr
, (2)
where DM is the intensity of the magnetization
contrast DM ¼ DMm (bold types denoting vectors),
Dr is the source density contrast, c ¼ m0=4pG,
where m0 ¼ 4p10À7
H=m is vacuum magnetic per-
meability and G ¼ 6:67 Â 10À11
m3
kgÀ1
sÀ2
is the
gravitational constant.
Gravity anomaly, gz
, is obtained from gravity
potential U as gz
¼ z Á rU, with r denoting the
gradient operator, and z a unit vector aligned to the
vertical (positive downward). Total field magnetic
anomaly, Tt
m, is obtained from magnetic potential
Vm as Tt
m ¼ Àt Á rVm, where t is the unit vector
along the local magnetic field.
For 2-D sources (Mendonc-a, 2004), the MDR,
r DM=Dr, is obtained by
r ¼
1
c
jTmj
jrgzj
(3)
and MI, a, such that
sinðaÞ ¼
Tm Á rgz
jTmjjrgzj
. (4)
ARTICLE IN PRESS
C.A. Mendonc-a, A.M.A. Meguid / Computers Geosciences 34 (2008) 603–610604
4. Author's personal copy
For 3-D sources, the vector quantities related in
Eqs. (3) and (4) are such that
Tm ¼ Tx
mex þ Ty
mey þ Tz
mez (5)
and
rgz
¼
qgz
qx
ex þ
qgz
qy
ey þ
qgz
qz
ez. (6)
For real 3-D sources, substitution of fields (5) and
(6) in Eqs. (3) and (4) yields apparent values for
quantities r and a (MDR and IM, respectively),
which eventually may reflect the true values for the
underlying sources.
3. MDR–MI from 3-D models
The basic building block of our formulation is a
vertical prism with a horizontal top and bottom. By
compounding blocks we can readily compute the
field components and derivatives that reflect a
complex, multi-source data set. Vector fields Tm
and rgz
can be evaluated simply by adding
magnetic field components and gravity derivatives
from adjacent prisms. Once obtained, these fields
enter Eqs. (3) and (4) to give MDR and MI.
To evaluate magnetic fields from an isolated
prism, we use formula adapted from Plouff (1976),
Tt
m ¼
m0
4p
DM ðmN þ nMÞ
1
2
log
R À x
R þ x
þ ðlN þ nLÞ
1
2
log
R À y
R þ y
þ ðlM þ mLÞ
1
2
log
R À z
R þ z
þ lL tan
yz
xR
þ mM tan
xz
yR
þ nN tan
xy
zR
, ð7Þ
in which ðL; M; NÞ and ðl; m; nÞ are cosine directors,
respectively, for unit vectors t (geomagnetic field
direction) and m (magnetization direction) and
R ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðx2 þ y2 þ z2Þ
p
. For a local field with inclina-
tion I and declination D, L ¼ cosðIÞ cosðDÞ,
M ¼ cosðIÞ sinðDÞ, and N ¼ sinðIÞ. For a magneti-
zation direction with inclination i and declination d,
l ¼ cosðiÞ cosðdÞ, m ¼ cosðiÞ sinðdÞ, and n ¼ sinðiÞ.
Using Eq. (7), the field components Tx
m, Ty
m and Tz
m
can be evaluated by assigning cosine directions
ðL; M; NÞ, respectively, equal to ð1; 0; 0Þ, ð0; 1; 0Þ
and ð0; 0; 1Þ.
For gravity field evaluation, we start from Banerjee
and Das Gupta (1977) formula,
gz
¼
1
2
GDr x log
R À y
R þ y
þ y log
R À x
R þ x
þ 2z tan
xy
zR
ð8Þ
obtaining gravity derivatives as
qgz
qx
¼
1
2
GDr log
R À y
R þ y
,
qgz
qy
¼
1
2
GDr log
R À x
R þ x
,
qgz
qz
¼ GDr tan
xy
zR
. (9)
To our knowledge, the expressions in (9) were not
published previously and they were consequently
tested by comparing their results with numerically
evaluated derivatives that were derived through a
finite difference scheme with Eq. (8).
As shown in Eqs. (7)–(9), field components and
derivatives are evaluated at the origin of the
coordinate system. To be evaluated at a generic
position ðx0; y0; z0Þ, terms ðx; y; zÞ are substituted
by ðx0 À xi; y0 À zi; z0 À ziÞ, i ¼ 1; 2, in which
terms ðxi; yi; ziÞ denote the coordinates for a prism
vertices.
4. MDR–MI from data processing
Current potential field data provide only a single
component for underlying vector anomalous
fields. In magnetic surveys, the measured quantity
commonly is regarded as being the total field
anomaly, Tt
m, which means the field component
along the direction t, of the local geomagnetic
field (Blakely, 1995). Gravity surveys carried out
with common gravimeters provide the vertical
component, gz
, of the anomalous gravity field.
Therefore, a processing scheme is required to
evaluate magnetic field components and gravity
derivatives in Eqs. (5) and (6), and by extension in
Eqs. (3) and (4). It can be done by exploiting well-
known properties of potential fields, which allow to
compute field components and derivatives by
applying a suitable set of linear transforms (Gunn,
1975; Blakely, 1995).
In the wavenumber domain, a potential field
Cðx; yÞ measured at a constant height can be
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C.A. Mendonc-a, A.M.A. Meguid / Computers Geosciences 34 (2008) 603–610 605
5. Author's personal copy
transformed into a field Dðx; yÞ by making
FfDðx; yÞg ¼ Fðkx; kyÞFfCðx; yÞg, (10)
in which F denotes the Fourier transform, Fðkx; kyÞ
is a mathematical (or filter) expression for the
desired transformation, written in terms of wave-
numbers kx and ky corresponding to directions x
and y of a Cartesian system. For operations
involving a component change from a measured
total field anomaly, filter Fðkx; kyÞ assumes a
general form of
Fðkx; kyÞ ¼
Aðkx; kyÞ
iLkx þ iMky þ Njkj
, (11)
with Aðkx; kyÞ being equal to ikx, iky, and jkj
ðk2
x þ k2
yÞ1=2
to, respectively, compute x, y, and z
components of Tm. To compute derivatives of
gravity anomaly, term Fðkx; kyÞ is made equal to
ikx, iky, and jkj, respectively, to provide derivatives
along x, y, and z directions. A flow chart to
compute MDR and MI is presented in Fig. 1.
5. Program description
We describe here two main programs developed
under Fortran 90 environment. The first one,
PRISM3D, implements Eqs. (7)–(9) to calculate
magnetic field components, gravity derivatives,
and MDR–MI parameters from a set of juxtaposed
prisms. It works as a forward model for MDR
and MI quantities in the sense that from a known
prism model, one can evaluate MDR–MI values
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Fig. 1. Flow diagram for MDR–MI processing of gravity anomaly gz
and total field magnetic anomaly Tt
m. Tt
m, for t ¼ x; y; z; t, is t
component of the anomalous vector field Tm; FfCg denotes the Fourier transform of C, h is the continuation height (positive downward)
for gravity and magnetic fields, kx and ky are wavenumber for the x and y directions, i ¼
ffiffiffiffiffiffiffi
À1
p
, and jkj ¼ ðk2
x þ k2
yÞ1=2
. Geomagnetic field
direction, t, is defined by director cosines ðL; M; NÞ, and magnetization direction, m, by director cosines ðl; m; nÞ. Unit vectors et, for
t ¼ x; y; z, define the axis of the coordinate system.
C.A. Mendonc-a, A.M.A. Meguid / Computers Geosciences 34 (2008) 603–610606
6. Author's personal copy
expected from fields observable at the ground
surface. The input of a particular geophysical model
is done by file modpar.txt, by entering basic
information on grid size, number of reading points,
observation height, local geomagnetic field, and
number and size of prisms. For each prism, 11
parameters are required; two to define prism
position, six to define size and depth, four to
assign physical properties and one to establish the
rotation angle with respect to northward pointing
x-axis. PRISM3D was validated in comparison
with the gravity and magnetic anomalies evaluated
with programs gbox and mbox developed by
Blakely (1995, p. 377 and 379). Besides a joint
evaluation of gravity and magnetic fields,
PRISM3D evaluates fields from rotated prisms,
which is not implemented in published versions of
gbox and mbox.
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Fig. 2. Magnetic anomaly, MDR and MI evaluated from PRISM3D program for models with two adjacent prisms, 2.5 km tick and depth
to the top at 1 km. In all cases, the magnetization of the southern prism is 0:25 A=m, with inclination of 40
and declination of 10
,
coincident with the local geomagnetic field. The northern prism, otherwise, assumes variable magnetization intensity of 0.25, 0.50, and
0:50 A=m, respectively, in Cases (a), (b), and (c), as well as variable direction (reversed, normal, reversed) in Cases (a), (b), and (c). Both
prisms have a density contrast of 0:1 g=cm3
. MDR values for Cases (a), (b), and (c) are then 2.5, 5.0, and 5:0 mA:m2
=kg3
.
C.A. Mendonc-a, A.M.A. Meguid / Computers Geosciences 34 (2008) 603–610 607
7. Author's personal copy
Our second program, MDRMI, implements the
algorithm presented in Fig. 1, by calling a set of
subroutines. Subroutine tmag evaluates the mag-
netic fields components Tx
m, Ty
m and Tz
m from
processing the total field anomaly Tt
m. It has a
same structure of program signal, which evaluates
x, y, and z derivatives for gravity anomaly gz
.
Auxiliary programs fmdr and finc compute Eqs. (3)
and (4) to estimate MDR and MI values. Sub-
routine fourn from Press et al. (1990) was used to
compute the discrete Fourier transform for a grid
data set in both tmag and signal routines. Sub-
routine signal to compute jrgz
j was kindly provided
by Richard Blakely (personal communication).
Functions dircos (to compute direction cosines from
inclination and declination of an unitary vector) and
kvalue (to evaluate wavenumber coordinates for
subroutine fourn) are found in Blakely (1995).
Grid gravity and magnetic data entering in
MDRMI is read by program read_matlab, in a
format able to be plotted by using load and pcolor
functions from MATLAB. Output from programs
PRISM3D and MDRMI can be displayed by
MATLAB script files prism3d.m and mdrmi.m.
6. Numerical experiments
We apply program PRISM3D to obtain MDR
and MI estimates over a model composed by two
juxtaposed prismatic bodies. The southern body of
the model has induced magnetization only whereas
the northern one has a variable magnetization as
illustrated by Cases (a), (b), and (c) in Fig. 2. In
Case (a), magnetization intensity is constant in all
bodies but the northern one is reversely magnetized.
In Case (b), magnetization direction is the same for
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Fig. 3. MDR and MI evaluated from the model in Case (c) of Fig. 2 (left column) and obtained by applying program MDRMI on
corrupted noise data for both gravity and magnetic anomalies. Additive uniformly distributed noise with amplitude equal to 1% of the
peak-to-peak anomalies was applied.
C.A. Mendonc-a, A.M.A. Meguid / Computers Geosciences 34 (2008) 603–610608
8. Author's personal copy
the two bodies but magnetization intensity is twice
as much in the northern body. Finally, in Case (c),
the northern body has a doubled magnetization
intensity and a reversed magnetization direction
relative to the southern body. MDR for the south-
ern body is 2:5 mA m2
=kg3
, whereas for the north-
ern body it is equal to 2.5, 5.0, and 2:5 mA m2
=kg3
,
respectively. Magnetization polarity for northern
body is reversed, normal, and reversed, respectively.
An induced magnetization with inclination of 40
was assumed, normal (positive) polarity and re-
versed (negative) polarity are relative to this
direction.
Fig. 2 demonstrates that even when the two
sources cannot be clearly discriminated from the
magnetic anomaly data, they are readily discernable
in the MDR and MI data. In all cases magnetization
polarity is well recovered from MI mapping and
good MDR estimates are obtained over the central
portions of the prisms. These results suggests a
potential application of MDR–MI mapping in
crustal studies, especially with regard to mapping
the magnetization polarity of the ocean floor in
marine geophysics.
Fig. 3 illustrates the capacity of the method in
recovering suitable MDR and MI values from
gravity and magnetic anomalies in the presence of
noise. The left column of the figure shows MDR
and MI values evaluated from the model by using
forward program PRISM3D program; its right
column shows corresponding values obtained with
processing program MDRMI applied to noise-
corrupted data. To simulate noise in data, gravity
and magnetic anomalies were disturbed with ad-
ditive, uniformly distributed noise, with amplitude
equal to 1% of the peak-to-peak anomalies.
7. Concluding remarks
Results from MDR–MI analysis can be degraded
in two major ways: (1) the computation of gravity
anomaly gradient involves the application of a noise
enhancing derivative filter, and (2) the evaluation of
magnetic z component for fields measured at low
magnetic latitudes. The latter operation exhibits the
same sort of instability previously recognized in
reducing to the pole, a total field magnetic anomaly
measured close to the magnetic equator. In this
transformation, the denominator of filter expression
in Eq. (11) tends to zero at a particular direction in
the kx–ky plane, thus unboundedly enhancing data
spectral content along this direction. For field in low
magnetic latitudes, specialized procedures (Silva,
1986; Mendonc-a and Silva, 1993) to stabilize the
operation of component change must be applied.
Noisy data should be low-pass filtered prior to the
application of MDRMI or upward continued to a
suitable height. Upward continuation attenuates the
data’s short wavelength content, thus indirectly
diminishing noise effects. Having managed noise
amplification in gravity and magnetic data proces-
sing, we believe programs presented here can be
used to process real data sets in continental and
marine studies.
Acknowledgements
Thanks are given to Val Chandler for significant
improvement in text clarity and Richard Blakely for
providing subroutine signal.for.
Appendix A. Supplementary data
Supplementary data associated with this article
can be found in the online version, at doi:10.1016/
j.cageo.2007.09.013
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