Matrix-free anisotropic slope tomography: Theory and application

Slope tomography uses traveltimes, source, and receiver slopes of locally coherent events to build subsurface velocity models. Locally coherent events by opposition to continuous reflections are suitable for semiautomatic and dense picking, which is conducive to better resolved tomographic models. These models can be further used as background/initial models for depth migration or full-waveform inversion. Slope tomography conventionally relies on ray tracing for traveltimes and slopes computation, where rays are traced from scatterers in depth to sources and receivers. The inverse problem relies on the explicit building of the sensitivity matrix to update the velocity model by local optimization. Alternatively, slope tomography can be implemented with eikonal solvers, which compute efficiently finely sampled traveltime maps from the sources and receivers, whereas slopes are estimated by finite differences of the traveltime maps. Moreover, a matrix-free inverse problem can be implemented with the adjoint-state method for the estimation of the data-misfit gradient. This new formulation of slope tomography is extended to tilted transverse isotropic (TTI) acoustic media, in which the model space is parameterized by four anisotropic parameters (e.g., vertical wavespeed, Thomson’s parameter [Formula: see text], [Formula: see text], and tilt angle) and the coordinates of the scatterers. A toy synthetic example allows for a first assessment of the crosstalk between anisotropic parameters and scatterer coordinates. A more realistic synthetic example indicates the feasibility of the joint update of the vertical wavespeed and [Formula: see text]. The slope tomography is finally applied to real broadband towed-streamer data to build the vertical velocity and the scatterers, while anisotropic parameters [Formula: see text] and [Formula: see text] are used as background parameters. The velocity model quality is assessed through common-image gathers computed by TTI Kirchhoff prestack-depth migration.

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Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽

10.1190/1.1444224 ◽

1997 ◽

Vol 62 (4) ◽

pp. 1226-1237 ◽

Cited By ~ 8

Author(s):

Irina Apostoiu‐Marin ◽

Andreas Ehinger

Keyword(s):

Signal To Noise Ratio ◽

Velocity Model ◽

Point Of View ◽

Prestack Depth Migration ◽

Depth Migration ◽

Velocity Models ◽

Time Domain Data ◽

And Migration ◽

Point To Point ◽

Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

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Full-waveform inversion for full-wavefield imaging: Decades in the making

The Leading Edge ◽

10.1190/tle40050324.1 ◽

2021 ◽

Vol 40 (5) ◽

pp. 324-334

Author(s):

Rongxin Huang ◽

Zhigang Zhang ◽

Zedong Wu ◽

Zhiyuan Wei ◽

Jiawei Mei ◽

...

Keyword(s):

Model Building ◽

Seismic Imaging ◽

Structural Information ◽

Waveform Inversion ◽

Velocity Model ◽

Data Sets ◽

Full Waveform Inversion ◽

Data Types ◽

Velocity Models ◽

Full Waveform

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

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Passive seismic event estimation using multiscattering waveform inversion

Geophysics ◽

10.1190/geo2018-0358.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. KS59-KS69 ◽

Cited By ~ 8

Author(s):

Chao Song ◽

Zedong Wu ◽

Tariq Alkhalifah

Keyword(s):

Seismic Data ◽

Waveform Inversion ◽

Velocity Model ◽

Source Image ◽

Time Inversion ◽

Multiple Sources ◽

Origin Time ◽

Secondary Sources ◽

Velocity Models ◽

Passive Seismic

Passive seismic monitoring has become an effective method to understand underground processes. Time-reversal-based methods are often used to locate passive seismic events directly. However, these kinds of methods are strongly dependent on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used on passive seismic data to invert the velocity model and source image, simultaneously. However, waveform inversion of passive seismic data uses mainly the transmission energy, which results in poor illumination and low resolution. We developed a waveform inversion using multiscattered energy for passive seismic to extract more information from the data than conventional FWI. Using transmission wavepath information from single- and double-scattering, computed from a predicted scatterer field acting as secondary sources, our method provides better illumination of the velocity model than conventional FWI. Using a new objective function, we optimized the source image and velocity model, including multiscattered energy, simultaneously. Because we conducted our method in the frequency domain with a complex source function including spatial and wavelet information, we mitigate the uncertainties of the source wavelet and source origin time. Inversion results from the Marmousi model indicate that by taking advantage of multiscattered energy and starting from a reasonably acceptable frequency (a single source at 3 Hz and multiple sources at 5 Hz), our method yields better inverted velocity models and source images compared with conventional FWI.

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The application of 3-D depth migration to the development of an Alaskan offshore oil field

Geophysics ◽

10.1190/1.1443544 ◽

1994 ◽

Vol 59 (10) ◽

pp. 1551-1560 ◽

Cited By ~ 2

Author(s):

David N. Whitcombe ◽

Eugene H. Murray ◽

Laurie A. St. Aubin ◽

Randall J. Carroll

Keyword(s):

Velocity Model ◽

Oil Field ◽

Northwestern Part ◽

Positioning Error ◽

Depth Migration ◽

Velocity Models ◽

Positioning Errors ◽

Ray Trace ◽

Offshore Oil ◽

Lateral Positioning

Inconsistencies in fault positioning between overlapping 3-D seismic surveys over the northwestern part of the Endicott Field highlighted lateral positioning errors of the order of 1000 ft (330 m) in the seismic images. This large uncertainty in fault positioning placed a high and often unacceptable risk on the placement of wells. To quantify and correct for the seismic positioning error, 3-D velocity models were developed for ray‐trace modeling. The lateral positioning error maps produced revealed significant variation in the mispositioning within the Endicott Field that were mainly caused by lateral variations in permafrost thickness. These maps have been used to correct the positions of mapped features and have enabled several wells to be successfully placed close to major faults. Prior to this analysis, these wells were considered too risky to place optimally. The seismic data were 3-D poststack depth migrated with the final velocity model, producing a repositioned image that was consistent with the ray‐trace predictions. Additionally, a general enhancement of data imaging improved the interpretability and enabled the remapping and subsequent successful development of the peripheral Sag Delta North accumulation.

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Optimal coding of blended seismic sources for 2D full waveform inversion in time

CT&F - Ciencia Tecnología y Futuro ◽

10.29047/01225383.78 ◽

2018 ◽

Vol 8 (2) ◽

Author(s):

Katherine Flórez ◽

Sergio Alberto Abreo Carrillo ◽

Ana Beatriz Ramírez Silva

Keyword(s):

Waveform Inversion ◽

Velocity Model ◽

Computational Time ◽

Inversion Method ◽

Single Shot ◽

Full Waveform Inversion ◽

Velocity Models ◽

Full Waveform ◽

Seismic Image ◽

Blended Data

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired. Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration. In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

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Improved imaging of gas hydrate reservoirs and their plumbing system using 2d elastic full waveform inversion

Interpretation ◽

10.1190/int-2020-0163.1 ◽

2021 ◽

pp. 1-61

Author(s):

Adnan Djeffal ◽

Ingo A. Pecher ◽

Satish C. Singh ◽

Gareth J. Crutchley ◽

Jari Kaipio

Keyword(s):

Gas Hydrate ◽

Waveform Inversion ◽

Hydrate Formation ◽

Velocity Model ◽

Plumbing System ◽

Low Velocity ◽

Velocity Models ◽

Full Waveform ◽

Hydrate Reservoirs ◽

Velocity Zone

Gas hydrates are ice-like crystalline materials that form under submarine environments of moderate pressure and low temperature. Another key factor to their formation is the abundance in gas supply from depth in addition to local biogenic gas. Detailed imaging and velocity analysis of the plumbing system of gas hydrates can provide confidence that amplitude anomalies in seismic data are related to gas hydrate accumulations. We have conducted 2D elastic full-waveform inversion (FWI) along a 14 km long segment of a 2D multichannel seismic profile to obtain a high-resolution velocity model of a hydrate system on the southern Hikurangi margin. We compare the FWI velocity model to previously published semblance- and tomography-based velocity models from the same data to explore how much more can be gained from the FWI. The FWI yielded a structurally more accurate velocity model that better delineated the low-velocity zone associated with free gas beneath the bottom simulating reflector (BSR) compared to the semblance- and tomography-based velocity models. Our results also find a lateral velocity inversion, that is, a narrow low-velocity zone surrounded by bands of higher velocities at a seaward-verging protothrust fault, which the two other methodologies failed to resolve. The FWI provides an improved lateral resolution making it an important tool when imaging the “plumbing” systems of gas hydrate reservoirs. In the southeastern limb of the anticline, our results find that the closely spaced landward-vergent protothrusts provide gas-charged fluids for hydrate formation above the BSR. Moreover, at the center of the anticline, our results find that a seaward-vergent protothrust fault appears to be acting as a conduit for gas-rich fluids into strata, although there is no accumulation of any significant hydrate above the BSR at the apex of the anticline. Our finding emphasizes the significance of densely spaced faults and fractures for providing gas for hydrate formation in the hydrate stability zone.

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Constrained Full Waveform Inversion for Borehole Multicomponent Seismic Data

Geosciences ◽

10.3390/geosciences9010045 ◽

2019 ◽

Vol 9 (1) ◽

pp. 45

Author(s):

Marwan Charara ◽

Christophe Barnes

Keyword(s):

Inverse Problem ◽

Spatial Correlation ◽

Seismic Data ◽

Waveform Inversion ◽

Synthetic Data ◽

Model Space ◽

Elastic Model ◽

Full Waveform Inversion ◽

Spatial Correlations ◽

Full Waveform

Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.

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Incorporating geologic information into reflection tomography

Geophysics ◽

10.1190/1.1707073 ◽

2004 ◽

Vol 69 (2) ◽

pp. 533-546 ◽

Cited By ~ 98

Author(s):

Robert G. Clapp ◽

Biondo L. Biondi ◽

Jon F. Claerbout

Keyword(s):

Velocity Structure ◽

Null Space ◽

Velocity Model ◽

Prestack Depth Migration ◽

Depth Migration ◽

Interval Velocity ◽

Velocity Models ◽

Regularized Inversion ◽

Symmetric Operators ◽

Reflection Tomography

In areas of complex geology, prestack depth migration is often necessary if we are to produce an accurate image of the subsurface. Prestack depth migration requires an accurate interval velocity model. With few exceptions, the subsurface velocities are not known beforehand and should be estimated. When the velocity structure is complex, with significant lateral variations, reflection‐tomography methods are often an effective tool for improving the velocity estimate. Unfortunately, reflection tomography often converges slowly, to a model that is geologically unreasonable, or it does not converge at all. The large null space of reflection‐tomography problems often forces us to add a sparse parameterization of the model and/or regularization criteria to the estimation. Standard tomography schemes tend to create isotropic features in velocity models that are inconsistent with geology. These isotropic features result, in large part, from using symmetric regularization operators or from choosing a poor model parameterization. If we replace the symmetric operators with nonstationary operators that tend to spread information along structural dips, the tomography will produce velocity models that are geologically more reasonable. In addition, by forming the operators in helical 1D space and performing polynomial division, we apply the inverse of these space‐varying anisotropic operators. The inverse operators can be used as a preconditioner to a standard tomography problem, thereby significantly improving the speed of convergence compared with the typical regularized inversion problem. Results from 2D synthetic and 2D field data are shown. In each case, the velocity obtained improves the focusing of the migrated image.

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Practical aspects and applications of 2D stereotomography

Geophysics ◽

10.1190/1.1581072 ◽

2003 ◽

Vol 68 (3) ◽

pp. 1008-1021 ◽

Cited By ~ 93

Author(s):

Frederic Billette ◽

Soazig Le Bégat ◽

Pascal Podvin ◽

Gilles Lambaré

Keyword(s):

Estimation Method ◽

Synthetic Data ◽

Velocity Model ◽

Velocity Estimation ◽

Common Source ◽

Depth Migration ◽

Reflection Seismic ◽

Velocity Models ◽

Automatic Picking ◽

Iterative Inversion

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on synthetic data and on a 2D line extracted from a 3D towed streamer survey shot in West Africa for TotalFinaElf. The examples demonstrate that the method requires only minor human intervention and rapidly converges to a geologically plausible velocity model in these two very different and complex velocity regimes. The quality of the velocity models is verified by prestack depth migration results.

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Fast and accurate dynamic raytracing in heterogeneous media

Bulletin of the Seismological Society of America ◽

10.1785/bssa0800051284 ◽

1990 ◽

Vol 80 (5) ◽

pp. 1284-1296

Author(s):

Claude F. Lafond ◽

Alan R. Levander

Keyword(s):

Shooting Method ◽

Heterogeneous Media ◽

Velocity Model ◽

Travel Times ◽

Complex Velocity ◽

Geometrical Spreading ◽

Imaging Condition ◽

Depth Migration ◽

Velocity Models ◽

Complex Velocity Model

Abstract We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step. We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver. The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.

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