scholarly journals Spatial Mesh Refinement using Cubic Smoothing Spline Interpolation in Simulation of 2-D Elastic Wave Equation: Forward Modeling of Full-waveform Inversion

2021 ◽  
pp. 66-83
Author(s):  
Amila Sudu Ambegedara ◽  
U. G. I. G. K. Udagedara ◽  
Erik M. Bollt
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Spline Interpolation ◽  
Waveform Inversion ◽  
Mesh Refinement ◽  
Forward Modeling ◽  
Smoothing Spline ◽  
Small Scale ◽  
Elastic Wave Equation ◽  
Full Waveform

Full-waveform inversion (FWI) is a non-destructive health monitoring technique that can be used to identify and quantify the embedded anomalies. The forward modeling of the FWI consists of a simulation of elastic wave equation to generate synthetic data. Thus the accuracy of the FWI method highly depends on the simulation method used in the forward modeling. Simulation of a 3-D seismic survey with small-scale heterogeneities is impossible with the classic finite difference approach even on modern super computers. In this work, we adopted a mesh refinement approach for simulation of the wave equation in the presence of small-scale heterogeneities. This approach uses cubic smoothing spline interpolation for spatial mesh refinement step in solving the wave equation. The simulation results for the 2-D elastic wave equation are presented and compared with the classic finite difference approach.

True-amplitude linearized waveform inversion with the quasi-elastic wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R827-R844 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Elastic Wave Equation ◽  
P Waves ◽  
Time Migration

We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the same as that for the elastic wave equation, and only requires the solution of two acoustic wave equations for each shot gather. This means that the quasi-elastic wave equation can be used for true-amplitude linearized waveform inversion (also known as least-squares reverse time migration) of elastic PP reflections, in which the corresponding misfit gradients are with respect to the perturbations of density and the P- and S-wave impedances. The perturbations of elastic parameters are iteratively updated by minimizing the [Formula: see text]-norm of the difference between the recorded PP reflections and the predicted pressure data modeled from the quasi-elastic wave equation. Numerical tests on synthetic and field data indicate that true-amplitude linearized waveform inversion using the quasi-elastic wave equation can account for the elastic PP amplitudes and provide a robust estimate of the perturbations of P- and S-wave impedances and, in some cases, the density. In addition, true-amplitude linearized waveform inversion provides images with a wider bandwidth and fewer artifacts because the PP amplitudes are accurately explained. We also determine the 2D scalar quasi-elastic wave equation for P-SV reflections and the 3D vector equation for PS reflections.

scholarly journals Pseudoelastic pure P-mode wave equation

Geophysics ◽  
2021 ◽  
Vol 86 (6) ◽  
pp. T469-T485
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Waveform Inversion ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Mode Wave ◽  
Wave Velocities ◽  
Simulation Engine

We have developed a pseudoelastic wave equation describing pure pressure waves propagating in elastic media. The pure pressure-mode (P-mode) wave equation uses all of the elastic parameters (such as density and the P- and S-wave velocities). It produces the same amplitude variation with offset (AVO) effects as PP-reflections computed by the conventional elastic wave equation. Because the new wave equation is free of S-waves, it does not require finer grids for simulation. This leads to a significant computational speedup when the ratio of pressure to S-wave velocities is large. We test the performance of our method on a simple synthetic model with high-velocity contrasts. The amplitude admitted by the pseudoelastic pure P-mode wave equation is highly consistent with that associated with the conventional elastic wave equation over a large range of incidence angles. We further verify our method’s robustness and accuracy using a more complex and realistic 2D salt model from the SEG Advanced Modeling Program. The ideal AVO behavior and computational advantage make our wave equation a good candidate as a forward simulation engine for performing elastic full-waveform inversion, especially for marine streamer data sets.

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