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- Volume 56, Issue 6, 2008
Geophysical Prospecting - Volume 56, Issue 6, 2008
Volume 56, Issue 6, 2008
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Migration velocity analysis and waveform inversion
More LessABSTRACTLeast‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.
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Velocity analysis based on data correlation
Authors T. Van Leeuwen and W.A. MulderABSTRACTSeveral methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band‐limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least‐squares sense by using a gradient‐based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model.
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Quantitative imaging of the Permo‐Mesozoic complex and its basement by frequency domain waveform tomography of wide‐aperture seismic data from the Polish Basin
Authors Michal Malinowski and Stéphane OpertoABSTRACTIn this study we present the workflow and results of 2D frequency domain waveform tomography applied to the global‐offset seismic data acquired in central Poland along a 50‐km long profile during the GRUNDY 2003 experiment. The waveform tomography method allows full exploitation of the wide‐aperture content of these data and produces in a semi‐automatic way both the detailed P‐wave velocity model and the structural image (i.e., perturbations in respect to the starting model). Thirteen frequencies ranging from 4 to 16 Hz were inverted sequentially, gradually introducing higher wavenumbers and more details into the velocity models. Although the data were characterised by relatively large shot spacings (1.5 km), we obtained clear images both of the Mesozoic and Permian sedimentary cover. Velocity patterns indicated facies changes within the Jurassic and Zechstein strata. A high velocity layer (ca. 5500 m/s) was found near the base of Triassic (Scythian), which made the imaging of a deeper layer difficult. Nevertheless, we were able to delineate the base of the Permian (i.e., base of the Rotliegend), which was not possible to derive from conventional common‐depth‐point processing, as well as some deeper events, attributed to the Carboniferous. The sub‐Permian events formed a syn‐form which favoured our previous interpretation of a depression filled with Upper Carboniferous molasse. The validity of the waveform tomography‐derived model was confirmed by well‐log data. Forward ray‐tracing modelling and synthetic seismograms calculations provided another justification for the key structures present in the waveform tomography model.
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Exploring some issues in acoustic full waveform inversion
Authors W.A. Mulder and R.‐E. PlessixABSTRACTThe least‐squares error measures the difference between observed and modelled seismic data. Because it suffers from local minima, a good initial velocity model is required to avoid convergence to the wrong model when using a gradient‐based minimization method. If a data set mainly contains reflection events, it is difficult to update the velocity model with the least‐squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum.
Several authors observed that the model could be updated by diving waves, requiring a wide‐angle or large‐offset data set. This full waveform tomography is limited to a maximum depth. Here, we use a linear velocity model to obtain estimates for the maximum depth. In addition, we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain. In the presence of noise, the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage.
We also considered acoustic inversion of a synthetic marine data set created by an elastic time‐domain finite‐difference code. This allowed us to validate the estimates made for the linear velocity model. The acoustic approximation leads to a number of problems when using long‐offset data. Nevertheless, we obtained reasonable results. The use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density.
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Elastic full waveform inversion of multi‐component OBC seismic data
Authors T.J. Sears, S.C. Singh and P.J. BartonABSTRACTElastic full waveform inversion of seismic reflection data represents a data‐driven form of analysis leading to quantification of sub‐surface parameters in depth. In previous studies attention has been given to P‐wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P‐waves and mode‐converted S‐waves in the marine environment in the inversion for both P‐ and S‐wave velocities by using wide‐angle, multi‐component, ocean‐bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode‐converted events. A series of one‐ and two‐dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P‐ and S‐wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P‐ and mode‐converted PS‐waves. Whilst P‐wave events are exploited for inversion for P‐wave velocity, examples show the contribution of both P‐ and PS‐waves to the successful recovery of S‐wave velocity.
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Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media
Authors Yunseok Choi, Dong‐Joo Min and Changsoo ShinABSTRACTIn order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.
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Investigation into the use of 2D elastic waveform inversion from look‐ahead walk‐away VSP surveys
Authors Mark A. Roberts, Satish Singh and Brian E. HornbyABSTRACTPore pressure in sediments beneath salt in the Gulf of Mexico varies widely creating a potentially dangerous and difficult drilling challenge. Estimating elastic parameters of sediments beneath salt is key to the prediction of pore pressure and reducing the drilling risk in exiting the base of the salt. In this paper we investigate the ability of 2D waveform inversion to recover the elastic parameters in the sedimentary layer beneath the salt from a walk‐away VSP (vertical seismic profile) carried out with the receivers in the salt, with the objective of estimating pore pressure at the base of the salt (to be estimated using traditional methods). We propose an effective method for performing the inversion and apply this method to a blind test of a large and realistic synthetic dataset. To facilitate the design of a VSP survey suitable to this type of inversion we also present an analysis into the effects of the receiver array receiver spacing. It is shown that the resulting velocity estimates are sufficiently accurate to predict the pore pressure within the limits required for drilling.
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Feasibility study for an anisotropic full waveform inversion of cross‐well seismic data
Authors Christophe Barnes, Marwan Charara and Terumitsu TsuchiyaABSTRACTAnisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data.
Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium.
The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient.
The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f−k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 18 (1970 - 2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 36 (1988)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 28 (1980)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 23 (1975)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 2 (1954)
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Volume 1 (1953)