Interpretation theory in applied geophysics: Grant, F S ... Interpretation theory in applied geophysics Unknown Binding – January 1, 1965 5.0 out of 5 stars 1 rating. See all formats and editions Hide other formats and editions. The Amazon Book Review Book recommendations, author interviews, editors' picks, and more. Read it now. Enter your mobile number or email address below and we'll send you a ...

Interpretation Theory in Applied Geophysics Grant (McGraw-Hill, 140s.)

We propose an accurate description for the dispersion of gold in the range of 1.24--2.48 eV. We implement this improved model in an FDTD algorithm and evaluate its efficiency by comparison with an analytical method. Extinction spectra of gold nanoparticle arrays are then calculated.

Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.

An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation

https://northumbria-test.eprints-hosting.org/id/document/266251

gprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar

The possibility to estimate accurately the subsurface electric properties from ground-penetrating radar (GPR) signals using inverse modeling is obstructed by the appropriateness of the forward model describing the GPR subsurface system. In this paper, we improved the recently developed approach of Lambot et al. whose success relies on a stepped-frequency continuous-wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic horn antenna. This radar configuration enables realistic and efficient forward modeling. We included in the initial model: 1) the multiple reflections occurring between the antenna and the soil surface using a positive feedback loop in the antenna block diagram and 2) the frequency dependence of the electric properties using a local linear approximation of the Debye model. The model was validated in laboratory conditions on a tank filled with a two-layered sand subject to different water contents. Results showed remarkable agreement between the measured and modeled Green's functions. Model inversion for the dielectric permittivity further demonstrated the accuracy of the method. Inversion for the electric conductivity led to less satisfactory results. However, a sensitivity analysis demonstrated the good stability properties of the inverse solution and put forward the necessity to reduce the remaining clutter by a factor 10. This may partly be achieved through a better characterization of the antenna transfer functions and by performing measurements in an environment without close extraneous scatterers.

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Modeling of ground-penetrating Radar for accurate characterization of subsurface electric properties

We have developed a finite-difference solution for three-dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell's equations in time using a staggered-grid technique. The time-stepping uses a modified version of the Du Fort-Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic field responses throughout the earth. Because it solves the coupled, first-order Maxwell's equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence-free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times.An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth-order difference method at early times and a second-order method at other times. Numerical checks against analytical, integral-equation, and spectral differential-difference solutions show that the solution provides accurate results.Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10 ms. That model contains 100 X 100 X 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 Omega . m. The execution time indicates that the solution is computer intensive, but it is valuable in providing much-needed insight about TEM responses in complicated 3-D situations.

/pdf/a-finite-difference-time-domain-solution-for-three-1mq2b4ctan.pdf

A finite-difference, time-domain solution for three-dimensional electromagnetic modeling

A three-dimensional (3D) time-domain numerical scheme for simulation of ground penetrating radar (GPR) on dispersive and inhomogeneous soils with conductive loss is described. The finite-difference time-domain (FDTD) method is used to discretize the partial differential equations for time stepping of the electromagnetic fields. The soil dispersion is modeled by multiterm Lorentz and/or Debye models and incorporated into the FDTD scheme by using the piecewise-linear recursive convolution (PLRC) technique. The dispersive soil parameters are obtained by fitting the model to reported experimental data. The perfectly matched layer (PML) is extended to match dispersive media and used as an absorbing boundary condition to simulate an open space. Examples are given to verify the numerical solution and demonstrate its applications. The 3D PML-PLRC-FDTD formulation facilitates the parallelization of the code. A version of the code is written for a 32-processor system, and an almost linear speedup is observed.

/pdf/finite-difference-time-domain-simulation-of-ground-3mktyd7a25.pdf

Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils

In this paper, we present a nonsplitting perfectly matched layer (NPML) method for the finite-difference simulation of elastic wave propagation. Compared to the conventional split-field approach, the new formulation solves the same set of equations for the boundary and interior regions. The nonsplitting formulation simplifies the perfectly matched layer (PML) algorithm without sacrificing the accuracy of the PML. In addition, the NPML requires nearly the same amount of computer storage as does the split-field approach. Using the NPML, we calculate dipole and quadrupole waveforms in a logging-while-drilling environment. We show that a dipole source produces a strong pipe flexural wave that distorts the formation arrivals of interest. A quadrupole source, however, produces clean formation arrivals. This result indicates that a quadrupole source is more advantageous over a dipole source for shear velocity measurement while drilling.

Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach

Electric anisotropy is considered an important property of hydrocarbon reservoirs. Its occurrence has great influence on estimation of formation water saturation and other properties derived from electromagnetic (EM) measurements. Conventional tools using coaxial coils often underestimate formation resistivity and thus overestimate water saturation. Multicomponent EM sensors provide the additional information needed for better resistivity‐based formation evaluation. We have developed a finite‐difference method to simulate multicomponent EM tools in a 3‐D anisotropic formation. The new method can model inhomogeneous media with arbitrary anisotropy. By using the coupled Maxwell’s equations, our method consumes about the same computational time to model an anisotropic formation as it would take to model an otherwise isotropic formation. We have verified the finite‐difference method using layered‐earth models that are typically encountered in hydrocarbon exploration and development. Our results show that the ...

3‐D electromagnetic anisotropy modeling using finite differences

The logging tool of this invention includes a transmitter conveyed on a drilling collar for exciting a quadrupole signal in a borehole being drilled by a drill bit and a receiver for receiving the signal The transmitter is operated at a frequency below the cut-off frequency of the quadrupole collar mode The received signal consists primarily of the formation quadrupole mode which, at low frequencies, has a velocity that approaches the formation shear velocity The transmitter, in one embodiment, consists of eight equal sectors of a piezoelectric cylinder mounted on the rim of the drilling collar The value of the cut-off frequency is primarily dependent on the thickness of the drilling collar Alternatively, the transmitter may be operated to produce both the collar mode and the formation mode and a processor may be used to filter out the collar mode

Tsili Wang

Papers

A finite-difference, time-domain solution for three-dimensional electromagnetic modeling

Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils

Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach

3‐D electromagnetic anisotropy modeling using finite differences

Method and apparatus for lwd shear velocity measurement