Improved finite-difference formulation in frequency domain for three-dimensional scattering problems

1992 ◽  
Vol 40 (3) ◽  
pp. 540-546 ◽  
Author(s):  
K. Beilenhoff ◽  
W. Heinrich ◽  
H.L. Hartnagel
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Finite Difference Formulation

3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. F95-F105 ◽  
Author(s):  
Rita Streich
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Electric Fields ◽  
Three Dimensional ◽  
Simulated Data ◽  
3D Models ◽  
Small Computer ◽  
Domain Modeling ◽  
Controlled Source ◽  
Em Field

Three-dimensional modeling of marine controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic (EM) responses collected in increasingly complex geologic settings. A modeling tool for simulating 3D marine CSEM surveys, based on a finite-difference discretization of the Helmholtz equation for the electric fields, has been developed. Optimizations for CSEM simulations include the use of a frequency-domain technique, a staggering scheme that reduces inaccuracies especially for horizontal electric-dipole sources located near the seafloor, and a new interpolation technique that provides highly accurate EM field values for receivers located in the immediate vicinity of the seafloor. Source singularities are eliminated through a secondary-field approach, in which the primary fields are computed analytically for a homogeneous or a 1D layered background; the secondary fields are computed using the finite-difference technique. Exploiting recent advances in computer technology and algorithmic developments, the system of finite-difference equations is solved using the MUMPS direct-matrix solver. In combination with the other optimizations, this allows accurate EM field computations for moderately sized models on small computer clusters. The explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme. Comparisons of simulated data for (1) 1D models to data generated using a 1D reflectivity technique and (2) 3D models to published 3D data demonstrate the accuracy and benefits of the approach.

3-D finite‐difference modeling of elastic waves in borehole environments

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 793-804 ◽  
Author(s):  
Kwi‐Hyon Yoon ◽  
George A. McMechan
Keyword(s):  
Finite Difference ◽  
Finite Differences ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Fixed Time ◽  
Cylindrical Symmetry ◽  
Staggered Grid ◽  
Finite Difference Formulation ◽  
Borehole Waves ◽  
Sonic Logs

Full‐wavefield sonic logs may be simulated for arbitrarily complicated three‐dimensional (3-D) borehole environments using 3-D elastic finite differences. To ensure reliability through large contrasts in Poisson’s ratio (across mud‐casing‐lithology contacts), a staggered grid finite‐difference formulation is used. Cylindrical symmetry is not assumed so the responses of features such as asymmetrical washouts and dipping structure are easily obtained. When features are asymmetrical, seismic responses vary significantly at various points around the hole circumference at any depth. Even for simple hole geometries, observed responses are complicated because of coupling between waves inside and outside the hole. Observations are also sensitive to the source‐receiver separation. Output formats include fixed‐time snapshots of displacement, divergence, and curl, and seismograms for the center and edge of a borehole; this allows detailed arrival identification and interpretation. To our knowledge, this is the most comprehensive and flexible scheme for modeling borehole waves that has been implemented to date.

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