scholarly journals Seismic shot-encoding schemes for waveform inversion

2020 ◽  
Vol 17 (5) ◽  
pp. 906-913 ◽  
Author(s):  
Edwin Fagua Duarte ◽  
Carlos A N da Costa ◽  
João M de Araújo ◽  
Yanghua Wang ◽  
Ying Rao
Keyword(s):  
Waveform Inversion ◽  
Random Phase ◽  
Computational Cost ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Seismic Waveform ◽  
Rotation Scheme ◽  
Iterative Inversion ◽  
Inversion Procedure ◽  
The Time Domain

Abstract A shot-encoding technique can be used in seismic waveform inversion to significantly reduce the computational cost by reducing the number of seismic simulations in the inversion procedure. Here we developed two alternative shot-encoding schemes to perform simultaneous-sources waveform inversion. The first scheme (I) encodes shot gathers with random-phase rotations applied to seismic traces. The second scheme (II) encodes shot gathers with random static time shifts. The well-known polarity encoding scheme (III) is just a special case of the random-phase rotation scheme. The second scheme is a variation of the conventional static shift encoding (IV), but the static time shifts in the second scheme are limited to one period of the dominant frequency. All encoded shot gathers are added up into a single super-shot gather for seismic waveform inversion. We perform the time-domain waveform inversion, using these shot-encoding schemes in conjunction with a restarted L-BFGS algorithm in the iterative inversion. The effectiveness and efficiency analyses demonstrate that the two shot-encoding schemes (I and II) proposed in this paper may improve the convergence of the iterative inversion, reduce the crosstalk effect among shots and consequently produce a subsurface velocity model with a high resolution.

An application of full-waveform inversion to land data using the pseudo-Hessian matrix

2016 ◽  
Vol 4 (4) ◽  
pp. T627-T635
Author(s):  
Yikang Zheng ◽  
Wei Zhang ◽  
Yibo Wang ◽  
Qingfeng Xue ◽  
Xu Chang
Keyword(s):  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Surface Velocity ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Near Surface ◽  
Full Waveform ◽  
The Time Domain

Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

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.

Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 902-914 ◽  
Author(s):  
R. Gerhard Pratt ◽  
Richard M. Shipp
Keyword(s):  
Frequency Domain ◽  
Field Data ◽  
Sedimentary Environment ◽  
Waveform Inversion ◽  
Normal Fault ◽  
Velocity Model ◽  
Viscous Effects ◽  
Seismic Waveform ◽  
Wavefield Inversion ◽  
High Degree

A crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section. Initial traveltime inversions produced stable but low‐resolution images from which the fault could be only vaguely inferred. To image the fault, wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies. Our wavefield inversion scheme uses a classical, descent‐type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations. Our propagator is a full‐wave equation, frequency‐domain, acoustic, finite‐difference method. The use of the frequency‐space domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects. By running wavefield inversion on the field data, a quantitative velocity image was produced that yielded a significantly improved image of the fault (when compared with the original traveltime inversions). Because the original field data were noisy and contained a high degree of multiple scattering (from the layering of the sediments), the transmitted arrivals were selectively windowed to enhance the image. The sediments at the site were strongly attenuating; we therefore used a viscoacoustic model during the modeling and the inversion that correctly simulated the observed decrease in amplitude with increasing frequency and source‐receiver offset. Furthermore, since the traveltime inversion indicated a high degree of anisotropy at the site, a fixed, homogeneous level of anisotropy was used during the inversion. Tests at varying levels of anisotropy confirmed the improvement in image quality and in data fit when anisotropy was incorporated. The final image was verified by examining the distribution of the residuals in the frequency domain, by comparing time‐domain modeled wavefields with the observed data, and by direct comparison with borehole logs.

Multiscale seismic waveform inversion

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1457-1473 ◽  
Author(s):  
Carey Bunks ◽  
Fatimetou M. Saleck ◽  
S. Zaleski ◽  
G. Chavent
Keyword(s):  
Iterative Methods ◽  
Global Minimum ◽  
Multigrid Method ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Local Minima ◽  
Data Set ◽  
Seismic Waveform ◽  
Inversion Methods ◽  
Iterative Inversion

Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low‐frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.

scholarly journals Seismic observations with broadband instruments at Santorini volcano

2018 ◽  
Vol 40 (3) ◽  
pp. 1150 ◽  
Author(s):  
A. Kolaitis ◽  
P. Papadimiriou ◽  
I. Kassaras ◽  
K. Makropoulos
Keyword(s):  
Low Frequency ◽  
Volcanic Tremor ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Depth Range ◽  
Traveltime Inversion ◽  
Time Frequency ◽  
Inversion Procedure ◽  
Santorini Volcano ◽  
Better Than

Two arrays equipped with broadband sensors were installed for a period of 10 months, in order to study the seismic activity in the area of Santorini (Thira) volcano. During these periods, about 330 earthquakes were recorded and located within a radius of 50 km from the center of the caldera. An iterative damped traveltime inversion procedure yielded a local 1-D Ρ-wave velocity model and improved locations with an accuracy better than 5 Km in both horizontal and vertical components for 135 earthquakes. Those are mainly distributed within a depth range 5-18 Km, in the vicinity of the submarine Kolumbo Reef (NE of Santorini Island). Signal analysis of the recorded volcanic earthquakes including typical Fourier transformations and several operations in the time-frequency domain, allowed their dominant frequency determination and their classification into three groups based on waveform appearance and frequency content: (1) highfrequency events; (2) low-frequency events; and (3) volcanic tremor. Frequencytime analysis of tremor, detected at three stations, revealed two kinds of harmonic tremor with one sharp peak, at 3-5 Hz and 8.5-10 Hz.

Least-squares reverse time migration in the presence of velocity errors

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S567-S580 ◽  
Author(s):  
Jizhong Yang ◽  
Yunyue Elita Li ◽  
Arthur Cheng ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Resolution Limit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Large Velocity ◽  
Iterative Inversion ◽  
Inversion Procedure

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

Iterative multiparameter waveform inversion of precritical reflection data using prestack time Kirchhoff approximation

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. R15-R27 ◽  
Author(s):  
Hassan Khaniani ◽  
John C. Bancroft ◽  
Eric von Lunen
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Real Data ◽  
Forward Modeling ◽  
Kirchhoff Approximation ◽  
Amplitude Variation With Offset ◽  
Reflection Data ◽  
Elastic Wave Scattering ◽  
Iterative Inversion ◽  
And Migration

We have studied elastic wave scattering and iterative inversion in the context of the Kirchhoff approximation. The approach is more consistent with the weak-contrast reflectivity functions of Zoeppritz equations as compared to the Born approximation. To reduce the computational cost associated with inversion, we demonstrated the use of amplitude-variation-with-offset (AVO) analysis, prestack time migrations (PSTMs), and the corresponding forward modeling in an iterative scheme. Forward modeling and migration/inversion operators are based on the double-square-root (DSR) equations of PSTM and linearized reflectivity functions. All operators involved in the inversion, including the background model for DSR and AVO, are defined in P-to-P traveltime and are updated at each iteration. Our method is practical for real data applications because all operators of the inversion are known to be applicable for standard methods. We have evaluated the inversion on synthetic and real data using the waveform characteristics of P-to-P and P-to-S data.

Frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC79-WCC89 ◽  
Author(s):  
Hansruedi Maurer ◽  
Stewart Greenhalgh ◽  
Sabine Latzel
Keyword(s):  
Information Content ◽  
Seismic Data ◽  
Velocity Model ◽  
Similar Amount ◽  
Data Sets ◽  
Data Set ◽  
Waveform Data ◽  
Velocity Models ◽  
Seismic Waveform ◽  
Iterative Inversion

Analyses of synthetic frequency-domain acoustic waveform data provide new insights into the design and imaging capability of crosshole surveys. The full complex Fourier spectral data offer significantly more information than other data representations such as the amplitude, phase, or Hartley spectrum. Extensive eigenvalue analyses are used for further inspection of the information content offered by the seismic data. The goodness of different experimental configurations is investigated by varying the choice of (1) the frequencies, (2) the source and receiver spacings along the boreholes, and (3) the borehole separation. With only a few carefully chosen frequencies, a similar amount of information can be extracted from the seismic data as can be extracted with a much larger suite of equally spaced frequencies. Optimized data sets should include at least one very low frequencycomponent. The remaining frequencies should be chosen fromthe upper end of the spectrum available. This strategy proved to be applicable to a simple homogeneous and a very complex velocity model. Further tests are required, but it appears on the available evidence to be model independent. Source and receiver spacings also have an effect on the goodness of an experimental setup, but there are only minor benefits to denser sampling when the increment is much smaller than the shortest wavelength included in a data set. If the borehole separation becomes unfavorably large, the information content of the data is degraded, even when many frequencies and small source and receiver spacings are considered. The findings are based on eigenvalue analyses using the true velocity models. Because under realistic conditions the true model is not known, it is shown that the optimized data sets are sufficiently robust to allow the iterative inversion schemes to converge to the global minimum. This is demonstrated by means of tomographic inversions of several optimized data sets.

Temporal windowing and inverse transform of the wavefield in the Laplace-Fourier domain

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. R207-R222 ◽  
Author(s):  
Sangmin Kwak ◽  
Hyunggu Jun ◽  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Fourier Transform ◽  
Time Window ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Fourier Domain ◽  
Gain Function ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Derivatives Of ◽  
Complex Damping

Temporal windowing is a valuable process, which can help us to focus on a specific event in a seismogram. However, applying the time window is difficult outside the time domain. We suggest a windowing method which is applicable in the Laplace-Fourier domain. The window function we adopt is defined as a product of a gain function and an exponential damping function. The Fourier transform of a seismogram windowed by this function is equivalent to the partial derivative of the Laplace-Fourier domain wavefield with respect to the complex damping constant. Therefore, we can obtain a windowed seismogram using the partial derivatives of the Laplace-Fourier domain wavefield. We exploit the time-windowed wavefield, which is modeled directly in the Laplace-Fourier domain, to reconstruct subsurface velocity model by waveform inversion in the Laplace-Fourier domain. We present the windowed seismograms by introducing an inverse Laplace-Fourier transform technique and demonstrate the effect of temporal windowing in a synthetic Laplace-Fourier domain waveform inversion example.

scholarly journals Seismic Waveform Inversion by Stochastic Optimization

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Tristan van Leeuwen ◽  
Aleksandr Y. Aravkin ◽  
Felix J. Herrmann
Keyword(s):  
Stochastic Optimization ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Optimization Methods ◽  
Batch Size ◽  
Stochastic Methods ◽  
Seismic Waveform ◽  
Recent Developments ◽  
Order Of Magnitude ◽  
Batch Sizes

We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique calledrandomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.

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