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.

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.

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.

Inversion of seismic refraction and reflection data for building long-wavelength velocity models

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. R81-R93 ◽  
Author(s):  
Haiyang Wang ◽  
Satish C. Singh ◽  
Francois Audebert ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Short Wavelength ◽  
Velocity Model ◽  
Density Model ◽  
Data Set ◽  
Reflected Waves ◽  
Long Wavelength ◽  
Velocity Models ◽  
Computation Efficiency ◽  
Refracted Waves

Long-wavelength velocity model building is a nonlinear process. It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves. We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves. The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data. To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints. The use of reflected waves required scale separation. We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively. The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb all the short-wavelength impedance contrasts. To improve the computation efficiency, the density model was converted into the zero-offset traveltime domain, where it was invariant to changes of the long-wavelength velocity model. After the wave-equation tomography has derived an optimized long-wavelength velocity model, full-waveform inversion was used to invert all the data to retrieve the short-wavelength velocity structures. We developed our method in two synthetic tests and then applied it to a marine field data set. We evaluated the results of the use of refracted and reflected waves, which was critical for accurately building the long-wavelength velocity model. We showed that our wave-equation tomography strategy was robust for the real data application.

Recovering long wavelength of the velocity model using waveform inversion in the Laplace domain: Application to field data

2011 ◽  
Author(s):  
Henri Calandra ◽  
Christian Rivera ◽  
Changsoo Shin ◽  
Sukjoon Pyun ◽  
Youngseo Kim ◽  
...  
Keyword(s):  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Laplace Domain ◽  
Long Wavelength

Analysis of the wavelength content of the longitudinal profiles for C-LTPP test sections

2002 ◽  
Vol 29 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Guy Doré ◽  
Martin Flamand ◽  
Pierre Pascale
Keyword(s):  
Short Wavelength ◽  
Profile Analysis ◽  
Moving Average ◽  
Longitudinal Profile ◽  
Pavement Performance ◽  
Analysis Approach ◽  
New Approach ◽  
Long Wavelength ◽  
Pavement Structures ◽  
Longitudinal Profiles

A new approach for pavement longitudinal profile analysis is described in this paper. In this approach, based on a simple moving average filtering technique, the results are expressed in terms of the proportion of the calculated international roughness index associated with different wavelengths of pavement surface deformations. The new approach has been successfully used in the assessment of the performance of Canadian Long-Term Pavement Performance (C-LTPP) test sites. The proposed analysis approach can help in identifying the source of problems causing pavement roughness. It can thus help in identifying the proper pavement rehabilitation technique. The new analysis approach has also helped in assessing the performance of the different rehabilitation techniques used in C-LTPP. It was found that 80–130 mm thick overlays give the best results in reducing roughness associated with short wavelength deformations. The benefit of these overlays is, however, limited to several years. Moreover, overlays do not have any significant impact on long wavelength deformations. It has also been found that long wavelength distortions tend to dominate the longitudinal profiles of thin pavement structures or pavements built on soft fine grained soils. Short wavelength distortions are dominant in longitudinal profiles of cracked thick pavement structures or that are built on strong soils.Key words: pavement, performance, longitudinal profile, wavelength, IRI, roughness, deformations.

scholarly journals Mitigating elastic effects in marine 3-D full-waveform inversion

2019 ◽  
Vol 220 (3) ◽  
pp. 2089-2104
Author(s):  
Òscar Calderón Agudo ◽  
Nuno Vieira da Silva ◽  
George Stronge ◽  
Michael Warner
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Data Sets ◽  
Acoustic Wave Equation ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform

SUMMARY The potential of full-waveform inversion (FWI) to recover high-resolution velocity models of the subsurface has been demonstrated in the last decades with its application to field data. But in certain geological scenarios, conventional FWI using the acoustic wave equation fails in recovering accurate models due to the presence of strong elastic effects, as the acoustic wave equation only accounts for compressional waves. This becomes more critical when dealing with land data sets, in which elastic effects are generated at the source and recorded directly by the receivers. In marine settings, in which sources and receivers are typically within the water layer, elastic effects are weaker but can be observed most easily as double mode conversions and through their effect on P-wave amplitudes. Ignoring these elastic effects can have a detrimental impact on the accuracy of the recovered velocity models, even in marine data sets. Ideally, the elastic wave equation should be used to model wave propagation, and FWI should aim to recover anisotropic models of velocity for P waves (vp) and S waves (vs). However, routine three-dimensional elastic FWI is still commercially impractical due to the elevated computational cost of modelling elastic wave propagation in regions with low S-wave velocity near the seabed. Moreover, elastic FWI using local optimization methods suffers from cross-talk between different inverted parameters. This generally leads to incorrect estimation of subsurface models, requiring an estimate of vp/vs that is rarely known beforehand. Here we illustrate how neglecting elasticity during FWI for a marine field data set that contains especially strong elastic heterogeneities can lead to an incorrect estimation of the P-wave velocity model. We then demonstrate a practical approach to mitigate elastic effects in 3-D yielding improved estimates, consisting of using a global inversion algorithm to estimate a model of vp/vs, employing matching filters to remove elastic effects from the field data, and performing acoustic FWI of the resulting data set. The quality of the recovered models is assessed by exploring the continuity of the events in the migrated sections and the fit of the latter with the recovered velocity model.

A decade of tomography

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE5-VE11 ◽  
Author(s):  
Marta Jo Woodward ◽  
Dave Nichols ◽  
Olga Zdraveva ◽  
Phil Whitfield ◽  
Tony Johns
Keyword(s):  
Standard Model ◽  
Short Wavelength ◽  
Model Building ◽  
Azimuthal Anisotropy ◽  
Data Sets ◽  
Depth Imaging ◽  
Anisotropic Models ◽  
Long Wavelength ◽  
Order Of Magnitude ◽  
Velocity Tomography

Over the past 10 years, ray-based postmigration grid tomography has become the standard model-building tool for seismic depth imaging. While the basics of the method have remained unchanged since the late 1990s, the problems it solves have changed dramatically. This evolution has been driven by exploration demands and enabled by computer power. There are three main areas of change. First, standard model resolution has increased from a few thousand meters to a few hundred meters. This order of magnitude improvement may be attributed to both high-quality, complex residual-moveout data picked as densely as [Formula: see text] to [Formula: see text] vertically and horizontally, and to a strategy of working down from long-wavelength to short-wavelength solutions. Second, more and more seismic data sets are being acquired along multiple azimuths, for improved illumination and multiple suppression. High-resolution velocity tomography must solve for all azimuths simultaneously, to prevent short-wavelength velocity heterogeneity from being mistaken for azimuthal anisotropy. Third, there has been a shift from predominantly isotropic to predominantly anisotropic models, both VTI and TTI. With four-component data, anisotropic grid tomography can be used to build models that tie PZ and PS images in depth.

scholarly journals A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE119-VE133 ◽  
Author(s):  
Changsoo Shin ◽  
Wansoo Ha
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Frequency Component ◽  
Inversion Method ◽  
Local Minima ◽  
Objective Functions ◽  
Laplace Domain ◽  
Velocity Models ◽  
Domain Inversion

In the frequency domain, gradient-based local-optimization methods of waveform inversions have been unsuccessful at inverting subsurface parameters without an accurate starting model. Such methods could not correct automatically for poor starting models because multiple local minima made it difficult to approach the true global minimum. In this study, we compared the behavior of objective functions in the frequency and Laplace domains. Wavefields in the Laplace domain correspond to the zero-frequency component of a damped wavefield; thus, the Laplace-domain waveform inversion can image smooth velocity models. Objective functions in the Laplace-domain inversion have a smoother surface and fewer local minima than in the frequency-domain inversion. We applied the waveform inversion to a 2D slice of the acoustic SEG/EAGE salt model in the Laplace domain and recovered smooth velocity models from inaccurate initial velocity conditions. We also successfully imaged velocities of the salt, SEG overthrust, and Institut Francais du Petrole Marmousi models with the frequency-domain inversion method by using the inverted velocity model of the Laplace-domain inversion as the initial model.

Surface wave attenuation of seismic records with the co-core trace transform filter

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. V115-V128 ◽  
Author(s):  
Ning Wu ◽  
Yue Li ◽  
Baojun Yang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Field Data ◽  
Wave Attenuation ◽  
Seismic Events ◽  
Data Sets ◽  
Transform Domain ◽  
Recent Developments ◽  
Seismic Records ◽  
Trace Transform

To remove surface waves from seismic records while preserving other seismic events of interest, we introduced a transform and a filter based on recent developments in image processing. The transform can be seen as a weighted Radon transform, in particular along linear trajectories. The weights in the transform are data dependent and designed to introduce large amplitude differences between surface waves and other events such that surface waves could be separated by a simple amplitude threshold. This is a key property of the filter and distinguishes this approach from others, such as conventional ones that use information on moveout ranges to apply a mask in the transform domain. Initial experiments with synthetic records and field data have demonstrated that, with the appropriate parameters, the proposed trace transform filter performs better both in terms of surface wave attenuation and reflected signal preservation than the conventional methods. Further experiments on larger data sets are needed to fully assess the method.

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