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.

Time domain waveform inversion—A frequency domain view: How well we need to match waveforms?

1991 ◽  
Vol 81 (6) ◽  
pp. 2351-2370
Author(s):  
Zoltan A. Der ◽  
Robert H. Shumway ◽  
Michael R. Hirano
Keyword(s):  
Time Domain ◽  
High Frequency ◽  
Waveform Inversion ◽  
Quantitative Measure ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Waveform Modeling ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

Abstract Waveform modeling in the time domain matches the various frequency components of seismic signals unevenly; the agreement is better at low frequencies and becomes progressively worse towards higher frequencies. The net effect of this kind of time-domain modeling is that the resolution in the spatial details of the source is less than optimal since the high-frequency components of the signal with their short wavelengths to resolve finer details do not fit the data. These problems are demonstrated by numerical simulations and by the reanalysis of some aspects of the El Golfo earthquake in using a new seismic imaging technique based on a generalization of an f-k algorithm. This procedure computes a statistic that can be used to derive confidence limits of the parameters sought in the inversion, thus providing a quantitative measure of the uncertainties in the results.

Laplace-domain full-waveform inversion of seismic data lacking low-frequency information

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. R199-R206 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Single Frequency ◽  
Frequency Content ◽  
Laplace Domain ◽  
Frequency Information ◽  
Velocity Models ◽  
Gaussian Source

The lack of the low-frequency information in field data prohibits the time- or frequency-domain waveform inversions from recovering large-scale background velocity models. On the other hand, Laplace-domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions. In theory, frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the Laplace domain. Because the constant can be retrieved using the source estimation process, the frequency content of the seismic data does not affect the gradient direction of the Laplace-domain waveform inversion. We obtained inversion results of the frequency-filtered field data acquired in the Gulf of Mexico and two synthetic data sets obtained using a first-derivative Gaussian source wavelet and a single-frequency causal sine function. They demonstrated that Laplace-domain inversion yielded consistent results regardless of the frequency content within the seismic data.

scholarly journals Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data

2019 ◽  
Vol 11 (16) ◽  
pp. 1839
Author(s):  
Xu Meng ◽  
Sixin Liu ◽  
Yi Xu ◽  
Lei Fu
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Radar Data ◽  
Dominant Frequency ◽  
Data Set ◽  
Laplace Domain ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
The Time Domain ◽  
Ground Penetrating

Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly nonlinear. The conventional way to obtain the initial models for GPR FWI is ray-based tomogram inversion which suffers from several inherent shortcomings. In this paper, we develop a Laplace domain waveform inversion to obtain initial models for the time domain FWI. The gradient expression of the Laplace domain waveform inversion is deduced via the derivation of a logarithmic object function. Permittivity and conductivity are updated by using the conjugate gradient method. Using synthetic examples, we found that the value of the damping constant in the inversion cannot be too large or too small compared to the dominant frequency of the radar data. The synthetic examples demonstrate that the Laplace domain waveform inversion provide slightly better initial models for the time domain FWI than the ray-based inversion. Finally, we successfully applied the algorithm to one field data set, and the inverted results of the Laplace-based FWI show more details than that of the ray-based FWI.

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.

A Proposal for the Time Domain Modeling of Split Air Conditioners for Consumer Reimbursement Studies

ENERGYO ◽  
2018 ◽  
Author(s):  
Paulo Henrique Oliveira Rezende ◽  
Afonso Bernardino Almeida Junior ◽  
Isaque Nogueira Gondim ◽  
José Carlos Oliveira
Keyword(s):  
Time Domain ◽  
Domain Modeling ◽  
Air Conditioners ◽  
Time Domain Modeling ◽  
The Time Domain

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
Author(s):  
Jianyong Bai ◽  
David Yingst ◽  
Robert Bloor ◽  
Jacques Leveille
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Field Data ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Difference Methods ◽  
The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

Frequency‐domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 626-632 ◽  
Author(s):  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Equations Of Motion ◽  
Domain Modeling ◽  
Multiple Sources ◽  
State Equations ◽  
Migration Imaging ◽  
Time Domain Modeling ◽  
Frequency Components ◽  
The Time Domain

The migration, imaging, or inversion of wide‐aperture cross‐hole data depends on the ability to model wave propagation in complex media for multiple source positions. Computational costs can be considerably reduced in frequency‐domain imaging by modeling the frequency‐domain steady‐state equations, rather than the time‐domain equations of motion. I develop a frequency‐domain approach in this note that is competitive with time‐domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required.

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