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.

scholarly journals Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

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.

3D prestack plane-wave, full-waveform inversion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE135-VE144 ◽  
Author(s):  
Denes Vigh ◽  
E. William Starr
Keyword(s):  
Plane Wave ◽  
Data Acquisition ◽  
Time Domain ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
The Time Domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.

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