Migration velocity analysis for anisotropic models

Anisotropic velocity models are poorly constrained by surface seismic data alone. Rock physics anisotropic modelling of shale compaction and digenesis provides information which can be used to constrain anisotropic velocity model building. We demonstrate this new anisotropic model building methodology which incorporates shale compaction model, check shot data and tomography to build a 3D spatially varying anisotropic velocity model in the North Sea. The initial rock model is built by analysing well log data, temperature gradient and additional geologic information. Tomography with checkshots (local tomography) which takes into account both residual moveout of surface seismic data and vertical traveltime from checkshot data was used to calibrate rock model to predict a similar anisotropy profile. After calibration a 3D anisotropic model is built to produce spatially varying anisotropic parameters consistent with both rock model and checkshot data.

A methodology for velocity estimation using reverse time migration (RTM) is described. An objective function is posed in the image domain that promotes image focusing and minimizes non-focused energy. We use the adjoint state method for the gradient calculation. The procedure of gradient calculation is similar to RTM. The inversion uses amplitude normalization to mitigate the effects of the amplitude fluctuation in image gathers. Synthetic data examples demonstrate that the method can recover long wave-length information as well as some of the finer-scale details in the velocity model. It is robust in that the convergence does not require a starting model that contains the low frequency velocity structure.

In this study we develop a practical method for the location of microseismic events in anisotropic media. The velocity anisotropy is taken into account in the additional step after the conventional location procedure. In this step, the isotropic velocity model and corresponding estimated locations serve as an initial model, and the anisotropy parameters as well as resulting location misfits are inverted simultaneously due to the coupling of velocity model and hypocenter parameters in calculation. After obtaining the anisotropic velocity model, one can relocate all the events around their isotropic velocity based locations. The method is ray theory based and only consider transversely isotropic layered model. The nonlinear inversion problem is solved by using Gauss-Newton method. The results of synthetic example closely fit with the true values and event depths are better determined than radial distances. Real data test shows that the estimated Thomsen parameters are consistent with previous study, and the isotropic velocity based locations are significantly corrected with large decrease of average misfit from 52m to 6m.

In an anisotropic model, traveltime can be determined approximately by numerical solution of the eikonal equation in terms of an anellipticity parameter η, using perturbation theory. However, its accuracy decreases under the effect of strong anisotropy at larger offsets. It becomes invalid for determining normal moveout velocity and anellipticity parameter in seismic processing. We propose a new approach using Levin T-transformation to transform the expanded traveltime in the transversely isotropic medium with vertical axis of symmetry (VTI) into rational form. The objective of this study is to provide a new traveltime approximation that is more accurate at larger offsets. In this study, we derive Levin algorithm and determine the optimal value of Levin parameters, which is a key step in achieving better accuracy. In a numerical experiment, we compare the accuracy between Levin T-transformation and second sequence of Shanks transformation in a homogeneous VTI medium. We also implement both approximations in a velocity analysis and stacking traces using synthetic common midpoint gathers on a multilayer earth model. The proposed method shows a superiority in accuracy to existing methods over a range of offsets with offset-to-depth ratio up to 6 and anellipticity parameter 0–0.5.

Wave-equation migration velocity analysis (WEMVA) is a non-linear optimization process that aims at estimating seismic velocities from reflection data using the wave equation. One important issue in Born-approximation-based WEMVA is preparation of an image perturbation free of cycle-skipping during each linear update. I show that this step can be accomplished by estimating the non-stationary slope of defocused events in subsurface offset gathers (ODCIG). The analysis also compares and unifies two popular WEMVA approaches, namely differential semblance optimization (DSO) and differential residual migration (DRM). The proposed method could be considered as an improved DSO implementation that overcomes some of its limitations by incorporating concepts from DRM.

Combining PP-waves with mode-converted PS reflections in migration velocity analysis (MVA) can help build more accurate VTI (transversely isotropic with a vertical symmetry axis) velocity models. To avoid problems caused by the moveout asymmetry of PS-waves and take advantage of efficient MVA algorithms designed for pure modes, here we generate pure SS-reflections from PP and PS data using the PP þ PS ¼ SS method. Then the residual moveout in both PP and SS common-image gathers is minimized during iterative velocity updates. The model is divided into square cells, and the VTI parameters VP0, VS0, e, and δ are defined at each grid point. The objective function also includes the differences between the migrated depths of the same reflectors on the PP and SS sections. Synthetic examples confirm that 2D MVA of PP- and PS-waves may be able to resolve all four relevant parameters of VTI media if reflectors with at least two distinct dips are available. The algorithm is also successfully applied to a 2D line from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. After the anisotropic velocity model has been estimated, accurate depth images can be obtained by migrating the recorded PP and PS data.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2001Anisotropic migration and model building for 4C seismic data: A case study from AlbaAuthors: Hengchang DaiXiang‐Yang LiHengchang DaiEdinburgh Anisotropy Project, British Geological Survey and Xiang‐Yang LiEdinburgh Anisotropy Project, British Geological Surveyhttps://doi.org/10.1190/1.1816753 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Permalink: https://doi.org/10.1190/1.1816753FiguresReferencesRelatedDetailsCited byLarge-offset P-wave traveltime in layered transversely isotropic mediaMohammad Mahdi Abedi and David Pardo11 March 2021 | GEOPHYSICS, Vol. 86, No. 3Reduced memory implementation of a local elastic finite-difference solverLigia Elena Jaimes-Osorio, Alison Malcolm, Polina Zheglova, Erik F. M. Koene, and Henrik R. Thomsen11 March 2021 | GEOPHYSICS, Vol. 86, No. 3Converted wave anisotropic correction technology based on azimuth scanningRuyi Zhang*, Qingfeng Kong, and Jianxin Shi19 August 2015Pre-stack time migration for PS-wave data in orthorhombic symmetry mediaZhong-Yu Huang* and Yu-Jing Wang5 August 2014An OpenCL Approach of Prestack Kirchhoff Time Migration Algorithm on General Purpose GPUComputing prestack Kirchhoff time migration on general purpose GPUComputers & Geosciences, Vol. 37, No. 10Four-parameter velocity analysis and its applications to the Ken-71 area converted-wave data13 May 2008 | Applied Geophysics, Vol. 5, No. 1Three‐component converted‐wave data processing and its application in a complicated areaGuo Xiangyu, Jiang Xiaosong, Zhang Guojuan, Hou Yan, Feng Xukui, and Tian Chengchun15 December 2008Converted-wave imaging in anisotropic media: theory and case studiesGeophysical Prospecting, Vol. 55, No. 3The effects of migration velocity errors on traveltime accuracy in prestack Kirchhoff time migration and the image of PS converted wavesHengchang Dai and Xiang-Yang Li6 March 2006 | GEOPHYSICS, Vol. 71, No. 2Parallel processing of Prestack Kirchhoff Time Migration on a PC ClusterComputers & Geosciences, Vol. 31, No. 7Converted‐wave imaging in anisotropic media: An overviewXiang‐Yang Li, Hengchang Dai, and Fabio Mancini3 January 2005 SEG Technical Program Expanded Abstracts 2001ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2001 Pages: 2135 publication data© 2001 Copyright © 2001 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 03 Jan 2005 CITATION INFORMATION Hengchang Dai and Xiang‐Yang Li, (2001), "Anisotropic migration and model building for 4C seismic data: A case study from Alba," SEG Technical Program Expanded Abstracts : 795-798. https://doi.org/10.1190/1.1816753 Plain-Language Summary PDF DownloadLoading ...

In this paper, we use a VTI two-way propagation engine to perform wave-equation migration velocity analysis. Using RTM, we have a chance to characterize the wavefields propagating at large angles and to image steeply dipping reflectors. By including VTI Thomson parameters, we can better describe the properties of the subsurface. Based on the framework developed for isotropic MVA, we first derive the MVA gradients for anisotropic parameters when using the first-order VTI twoway wave-equation. Then, we test our method on a synthetic VTI Marmousi model. The inversion results show that our method can resolve a better anisotropic model and a betterfocused subsurface image.

The paper describes a collaborative project between Total and WesternGeco on quantifying structural uncertainty in application to the development of the Hild field. The key motivation for the project was to improve the seismic uncertainty inputs into the workflows for assessing uncertainty for the gas reserves and risks associated with the development well placement. The main focus of this work was related to the anisotropy ambiguity analysis for more accurate quantifying the structural uncertainty of the BCU top. The workflow used a novel technology of uncertainty analysis in anisotropic model building based on eigen decomposition of the tomography operator and a null-space projection. The main lesson learned was that prior information about anisotropy should be defined thoroughly from the geologic and rock physics perspective and also to be calibrated with the available well data. Overall, the project turned out to be successful and the results enabled more confident decision making in the Hild field development.

It has been shown in the past that the interval-NMO velocity and the non-ellipticity parameter ν largely control the P-wave reflection time moveout of VTI media. To invert for these two parameters, one needs either reasonably large offsets, or some structure in the subsurface in combination with relatively mild lateral velocity variation. This paper deals with a simulation of an inversion approach, building on the assumption that accurately measured V NMO, as defined by small offset asymptotics for a particular reflector, were available. Instead of such measurements we take synthetically computed data. First, an isotropic model is constructed which explains these V NMO. Subsequently, residual moveout in common image gathers is modelled by ray tracing (replacing real data), along with its sensitivity for changes in the interval-NMO velocity and the non-ellipticity parameter under the constraint that V NMO is preserved. This enables iterative updating of the non-ellipticity parameter and the interval-NMO velocity in a layer that can be laterally inhomogeneous. This approach is successfully applied for a mildly dipping reflector at the bottom of a layer with laterally varying medium parameters. With the exact V NMO assumed to be given, lateral inhomogeneity and anisotropy can be distinguished for such a situation. However, for another example with a homogeneous VTI layer overlying a curved reflector with dip up to 30°, there appears to be an ambiguity which can be understood by theoretical analysis. Consistently with existing theory using the NMO-ellipse, the presented approach is successfully applied to the latter example if V NMO in the strike direction is combined with residual moveout in dip direction.

An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.

In areas of complex geology, migration-velocity analysis (MVA) should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. MVA by wavefield extrapolation has the ability to address these issues because it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization have prevented its routine industrial use. We overcome those limitations by using new wavefields: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the pre-stack exploding-reflector model. Cost of MVA by wavefield extrapolation is decreased because only a small number of image-space generalized wavefields are necessary to accurately describe the kinematics of velocity errors and because these wavefields can be easily used in a target-oriented way. Flexibility is naturally incorporated because modeling these wavefields have selected reflectors as the initial conditions, allowing the use of a horizon-based parametrization of the model space. In a 3D real data example, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of migration-velocity analysis by wavefield-extrapolation, while yielding a final accurate migration-velocity model evidenced by good quality and reliable depth images.

With complicated and huge salt bodies as in Gulf of Mexico, ray tomography reaches its limitation due to difficulties in performing raytracing. In this paper we investigate a strategy in which ray tomography and wave equation migration velocity analysis are integrated to construct velocity models for sub‐salt targets. We apply stereotomography to accurately estimate the background sediment velocity which is then used as the initial model for the wave equation migration velocity inversion (WVI) to refine, in particular, the sub‐salt images. Our results on the Sigsbee2B synthetic data show that we can significantly improve the quality of the sub‐salt images.

The Common Reflection Surface (CRS) method, introduced by Peter Hubral in 1997, is an alternative technique to the conventional CMP stacking. The CRS stack is able to provide not only improved simulated zero-offset sections, but also a set of parameters that convey more information of the propagating medium than the single NMO-velocity parameter of the classical CMP method. The objective of this work is to analyze the potential of the CRS method to produce seismic velocity models, analogously to the computation of the NMO velocities in the CMP method. We review the CMP and CRS methods, and compare their performances on illustrative synthetic and real data examples.

The estimation of anisotropic parameters is a critical step in the work flow for seismic anisotropic imaging. Walkaway(WVSP) or 3DVSP provides a valuable way to measure seismic anisotropy, as WVSP/3DVSP geometry is generally characterized by wide seismic ray angle coverage and well-determined vertical velocities and first break (FB) times. Most of the presently available anisotropic inversion methods are valid only for flat-layered or lateral homogenous velocity models. Anisotropic parameters in the presence of laterally inhomogeneous geological structures such as salt diapirs and faults often need to be estimated for accurate seismic imaging. Therefore, a new methodology was developed to estimate anisotropic parameters in lateral inhomogeneous velocity models. First, an anisotropic Eikonal solver (referred to as a fast marching scheme) is employed to efficiently and accurately calculate FB times in 2D or 3D grid-based inhomogeneous anisotropic velocity models. Then, a constrained global optimization algorithm known as simulated annealing is used to efficiently search and invert the anisotropic parameters based on the least square errors between calculated and observed FB times. Both numerical and field WVSP data examples are used to demonstrate the feasibility of this methodology in estimating anisotropic parameters in lateral inhomogeneous anisotropic models from WVSP or 3DVSP surveys.