A solution of an inverse problem in the 1 D wave equation application to the inversion of vertical seismic profiles

2005 ◽  
pp. 309-323
Author(s):  
D. Macé ◽  
P. Lailly
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
D Wave

Efficient FDTD algorithm for plane-wave simulation for vertically heterogeneous attenuative media

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. H43-H53 ◽  
Author(s):  
Arash JafarGandomi ◽  
Hiroshi Takenaka
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Plane Wave ◽  
Wave Equations ◽  
Plane Waves ◽  
Computation Time ◽  
Staggered Grid ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Incident Waves

We propose an efficient algorithm for modeling seismic plane-wave propagation in vertically heterogeneous viscoelastic media using a finite-difference time-domain (FDTD) technique. In the algorithm, the wave equation is rewritten for plane waves by applying a Radon transform to the 2D general wave equation. Arbitrary values of the quality factor for [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) are incorporated into the wave equation via a generalized Zener body rheological model. An FDTD staggered-grid technique is used to numerically solve the derived plane-wave equations. The scheme uses a 1D grid that reduces computation time and memory requirements significantly more than corresponding 2D or 3D computations. Comparing the finite-difference solutions to their corresponding analytical results, we find that the methods are sufficiently accurate. The proposed algorithm is able to calculate synthetic waveforms efficiently and represent viscoelastic attenuation even in very attenuative media. The technique is then used to estimate the plane-wave responses of a sedimentary system to normal and inclined incident waves in the Kanto area of Japan via synthetic vertical seismic profiles.

A Widely Convergent Generalized Pulse- Spectrum Methods for 2-D Wave Equation Inversion

2003 ◽  
Vol 46 (2) ◽  
pp. 373-380 ◽  
Author(s):  
Guofeng FENG ◽  
Bo HAN ◽  
Jiaqi LIU
Keyword(s):  
Wave Equation ◽  
Pulse Spectrum ◽  
D Wave
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