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

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.

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Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model

Geophysics ◽

10.1190/1.1444597 ◽

1999 ◽

Vol 64 (3) ◽

pp. 888-901 ◽

Cited By ~ 926

Author(s):

R. Gerhard Pratt

Keyword(s):

Finite Difference ◽

Frequency Domain ◽

Waveform Inversion ◽

Forward Modeling ◽

Scale Model ◽

Model Data ◽

Seismic Waveform ◽

Physical Scale ◽

Wavefield Inversion ◽

Selection Of

Seismic waveforms contain much information that is ignored under standard processing schemes; seismic waveform inversion seeks to use the full information content of the recorded wavefield. In this paper I present, apply, and evaluate a frequency‐space domain approach to waveform inversion. The method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data. The model data are computed using a full‐wave equation, viscoacoustic, frequency‐domain, finite‐difference method. Ray asymptotics are avoided, and higher‐order effects such as diffractions and multiple scattering are accounted for automatically. The theory of frequency‐domain waveform/wavefield inversion can be expressed compactly using a matrix formalism that uses finite‐difference/finite‐element frequency‐domain modeling equations. Expressions for fast, local descent inversion using back‐propagation techniques then follow naturally. Implementation of these methods depends on efficient frequency‐domain forward‐modeling solutions; these are provided by recent developments in numerical forward modeling. The inversion approach resembles prestack, reverse‐time migration but differs in that the problem is formulated in terms of velocity (not reflectivity), and the method is fully iterative. I illustrate the practical application of the frequency‐domain waveform inversion approach using tomographic seismic data from a physical scale model. This allows a full evaluation and verification of the method; results with field data are presented in an accompanying paper. Several critical processes contribute to the success of the method: the estimation of a source signature, the matching of amplitudes between real and synthetic data, the selection of a time window, and the selection of suitable sequence of frequencies in the inversion. An initial model for the inversion of the scale model data is provided using standard traveltime tomographic methods, which provide a robust but low‐resolution image. Twenty‐five iterations of wavefield inversion are applied, using five discrete frequencies at each iteration, moving from low to high frequencies. The final results exhibit the features of the true model at subwavelength scale and account for many of the details of the observed arrivals in the data.

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Joint inversion of seismic traveltime and frequency-domain airborne electromagnetic data for hydrocarbon exploration

Geophysics ◽

10.1190/geo2017-0112.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. U9-U22 ◽

Cited By ~ 8

Author(s):

Jide Nosakare Ogunbo ◽

Guy Marquis ◽

Jie Zhang ◽

Weizhong Wang

Keyword(s):

Frequency Domain ◽

Joint Inversion ◽

Sedimentary Environment ◽

Computational Cost ◽

Velocity Model ◽

Two Dimensions ◽

Hydrocarbon Exploration ◽

Three Dimensions ◽

Data Sets ◽

The One

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.

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

10.1190/1.3627721 ◽

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

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Some Computational Aspects of the Time and Frequency Domain Formulations of Seismic Waveform Inversion

Modern Solvers for Helmholtz Problems - Geosystems Mathematics ◽

10.1007/978-3-319-28832-1_7 ◽

2017 ◽

pp. 159-187 ◽

Cited By ~ 2

Author(s):

René-Édouard Plessix

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Seismic Waveform ◽

Computational Aspects

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Full waveform inversion in time and frequency domain of velocity modeling in seismic imaging: FWISIMAT a Matlab code

Earth Sciences Research Journal ◽

10.15446/esrj.v22n4.59640 ◽

2018 ◽

Vol 22 (4) ◽

pp. 291-300

Author(s):

Sagar Singh ◽

Ali Ismet Kanli ◽

Sagarika Mukhopadhyay

Keyword(s):

Frequency Domain ◽

Seismic Imaging ◽

Waveform Inversion ◽

Velocity Model ◽

Full Waveform Inversion ◽

Initial Model ◽

Final Model ◽

Full Waveform ◽

True Model ◽

Starting Model

This paper investigates the capability of acoustic Full Waveform Inversion (FWI) in building Marmousi velocity model, in time and frequency domain. FWI is an iterative minimization of misfit between observed and calculated data which is generally solved in three segments: forward modeling, which numerically solves the wave equation with an initial model, gradient computation of the objective function, and updating the model parameters, with a valid optimization method. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented using the Marmousi velocity model as the true model. An initial model is obtained by smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive on the starting model. The final model is compared with the true model to review the number of recovered velocities. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented usingMarmousi velocity model astrue model. An initial model is derived from smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive onstarting model. The final model is compared with the true model to review theamount of recovered velocities.

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Anisotropic 3D full-waveform inversion

Geophysics ◽

10.1190/geo2012-0338.1 ◽

2013 ◽

Vol 78 (2) ◽

pp. R59-R80 ◽

Cited By ~ 233

Author(s):

Michael Warner ◽

Andrew Ratcliffe ◽

Tenice Nangoo ◽

Joanna Morgan ◽

Adrian Umpleby ◽

...

Keyword(s):

High Velocity ◽

Field Data ◽

Waveform Inversion ◽

Velocity Model ◽

Full Waveform Inversion ◽

Low Velocity ◽

Data Set ◽

Reflection Data ◽

Full Waveform ◽

Gas Cloud

We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.

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Combined traveltime and frequency-domain seismic waveform inversion: a case study on multi-offset ultrasonic data

Geophysical Journal International ◽

10.1046/j.1365-246x.2003.01956.x ◽

2003 ◽

Vol 154 (1) ◽

pp. 117-133 ◽

Cited By ~ 19

Author(s):

J.-X. Dessa ◽

G. Pascal

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Seismic Waveform

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Waveform inversion using a logarithmic wavefield

Geophysics ◽

10.1190/1.2194523 ◽

2006 ◽

Vol 71 (3) ◽

pp. R31-R42 ◽

Cited By ~ 215

Author(s):

Changsoo Shin ◽

Dong-Joo Min

Keyword(s):

Objective Function ◽

Field Data ◽

Velocity Structure ◽

Waveform Inversion ◽

Synthetic Data ◽

Velocity Model ◽

Matrix Formalism ◽

Inversion Algorithm ◽

Data Set ◽

Short Period

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

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A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Geophysics ◽

10.1190/geo2019-0584.1 ◽

2020 ◽

Vol 85 (6) ◽

pp. R447-R459 ◽

Cited By ~ 1

Author(s):

Chao Song ◽

Tariq Alkhalifah ◽

Yuanyuan Li

Keyword(s):

Frequency Domain ◽

Null Space ◽

Joint Inversion ◽

Waveform Inversion ◽

Significant Loss ◽

Model Parameters ◽

Trade Off ◽

Intrinsic Attenuation ◽

Highly Nonlinear ◽

Wavefield Inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly nonlinear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is sometimes crucial to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing parameter trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse because this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we have used an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex-valued in the viscoacoustic EWI. We evaluate a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, which we refer to as outer iterations, until the convergence is achieved. Because viscoacoustic EWI is able to recover an accurate velocity model, the velocity update leakage to the [Formula: see text] model is largely reduced. We determine the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further demonstrate the validity of our approach, we generate data in the time domain using a viscoelastic wave equation solver and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.

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