Efficient Laplace-domain modeling and inversion using an axis transformation technique

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R141-R148 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Wave Propagation ◽  
Computation Time ◽  
Dispersion Analysis ◽  
Domain Modeling ◽  
Memory Usage ◽  
Regular Grid ◽  
Transformation Technique ◽  
Laplace Domain ◽  
Domain Inversion ◽  
And Inversion

We tested an axis-transformation technique for modeling wave propagation in the Laplace domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling and inversion in the Laplace domain. We used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes. We demonstrated in a synthetic Laplace-domain inversion technique shows that this method is efficient and yields a result comparable to that of a Laplace-domain inversion using a regular grid. In a synthetic inversion example, the memory usage reduced to less than 33%, and the computation time reduced to 39% of those required for the regular grid case using a logarithmic transformation function.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

Dispersion analysis of an average-derivative optimal scheme for Laplace-domain scalar wave equation

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. T37-T42 ◽  
Author(s):  
Jing-Bo Chen
Keyword(s):  
Wave Equation ◽  
Dispersion Analysis ◽  
Domain Modeling ◽  
Scalar Wave ◽  
Laplace Domain ◽  
Optimal Scheme ◽  
Point Scheme ◽  
Sampling Intervals ◽  
Grid Points ◽  
Average Derivative

Laplace-domain modeling is an important foundation of Laplace-domain full-waveform inversion. However, dispersion analysis for Laplace-domain numerical schemes has not been completely established. This hampers the construction and optimization of Laplace-domain modeling schemes. By defining a pseudowavelength as a scaled skin depth, I establish a method for Laplace-domain numerical dispersion analysis that is parallel to its frequency-domain counterpart. This method is then applied to an average-derivative nine-point scheme for Laplace-domain scalar wave equation. Within the relative error of 1%, the Laplace-domain average-derivative optimal scheme requires four grid points per smallest pseudowavelength, whereas the classic five-point scheme requires 13 grid points per smallest pseudowavelength for general directional sampling intervals. The average-derivative optimal scheme is more accurate than the classic five-point scheme for the same sampling intervals. By using much smaller sampling intervals, the classic five-point scheme can approach the accuracy of the average-derivative optimal scheme, but the corresponding cost is much higher in terms of storage requirement and computational time.

scholarly journals VERIFICATION OF NUMERICAL WAVE PROPAGATION MODELS IN TIDAL INLETS

1988 ◽  
Vol 1 (21) ◽  
pp. 30 ◽  
Author(s):  
J.A. Vogel ◽  
A.C. Radder ◽  
J.H. De Reus
Keyword(s):  
Wave Propagation ◽  
Numerical Models ◽  
River Estuary ◽  
Regular Grid ◽  
Local Wind ◽  
Tidal Inlets ◽  
Propagation Models ◽  
Dutch Coast ◽  
Model Based ◽  
Numerical Wave

The performance of two numerical wave propagation models has been investigated by comparison with field data. The first model is a refractiondiffraction model based on the parabolic equation method. The second is a refraction model based on the wave action equation, using a regular grid. Two field situations, viz. a tidal inlet and a river estuary along the Dutch coast, were used to determine the influence of the local wind on waves behind an island and a breaker zone. It may be concluded from the results of the computations and measurements that a much better agreement is obtained when wave growth due to wind is properly accounted for in the numerical models. In complicated coastal areas the models perform well for both engineering and research purposes.

Why do Laplace-domain waveform inversions yield long-wavelength results?

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. R167-R173 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Short Wavelength ◽  
Field Data ◽  
Moving Average ◽  
Data Sets ◽  
Virtual Source ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Gradient Direction ◽  
Domain Inversion

Laplace-domain inversions generate long-wavelength velocity models from synthetic and field data sets, unlike full-waveform inversions in the time or frequency domain. By examining the gradient directions of Laplace-domain inversions, we explain why they result in long-wavelength velocity models. The gradient direction of the inversion is calculated by multiplying the virtual source and the back-propagated wavefield. The virtual source has long-wavelength features because it is the product of the smooth forward-modeled wavefield and the partial derivative of the impedance matrix, which depends on the long-wavelength initial velocity used in the inversion. The back-propagated wavefield exhibits mild variations, except for near the receiver, in spite of the short-wavelength components in the residual. The smooth back-propagated wavefield results from the low-wavenumber pass-filtering effects of Laplace-domain Green’s function, which attenuates the high-wavenumber components of the residuals more rapidly than the low-wavenumber components. Accordingly, the gradient direction and the inversion results are smooth. Examples of inverting field data acquired in the Gulf of Mexico exhibit long-wavelength gradients and confirm the generation of long-wavelength velocity models by Laplace-domain inversion. The inversion of moving-average filtered data without short-wavelength features shows that the Laplace-domain inversion is not greatly affected by the high-wavenumber components in the field data.

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

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