SS: The Future of Seismic Imaging; Reverse Time Migration an Full Wavefield Inversion - Wave equation based model building and imaging in complex settings
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Abstract In complex geological environments encountered in today's exploration practice there is a need for model building and imaging schemes based on an as accurate a description as possible of wave propagation in the earth. In this paper we discuss the most advanced members of a family of wave equation based imaging and model building schemes, namely Reverse Time Migration and Full Waveform Inversion. We illustrate the potential of these schemes by results obtained on an OBS survey in the Gulf of Mexico. Introduction Seismic imaging consists of two steps. One starts by building a subsurface velocity model and follows this by creating the actual reflection image by a depth migration in this velocity model. Of these two steps depth migration is well understood. It is based on a single scattering description of wave propagation in the earth. This description provides a linear relationship between the reflectivity in the subsurface and the reflection data measured at the surface of the earth. Depth migration boils down to constructing the inverse of this relationship on the reflection data and thus constructs an image of the reflectivity in the subsurface. Obviously, because of the single scattering assumption, this does not deal with multiple reflections, which therefore have to be attenuated before migration. The most advanced depth migration algorithm in use today is Reverse Time Migration. The velocity model building problem is much harder, as it is inherently a non-linear problem. The standard approach is to exploit the redundancy in the seismic data, for example the offset between source and receiver. One migrates subsets of the data with fixed values of the redundant coordinates (" minimal datasets??) and requires that at each horizontal location (x,y) the depth of an imaged reflector does not vary with the redundant coordinate. If it does, the variations are used to update the velocity model iteratively. This leads to a family of well known reflection tomography schemes, which go under the name of migration velocity analysis. Although most of them are based on some form of raytracing, these methods do have a natural generalization towards the wave equation domain, see e.g. Symes 2008. It is important to stress that they are based on primary reflections only. These methods therefore all rely on effective multiple attenuation and/or interpreter based identification of the primaries. The latter is still one of the most important bottlenecks of migration velocity analysis, especially in poor signal to noise situations, such as subsalt. Full Waveform Inversion is another, completely different method for estimating the velocity model. In this approach one tries to find the model by requiring that the data calculated by solving the wave equation in this model optimally resemble the measured data in a seismic survey. The great advantage of this formulation is that it should work for all wave types, not only for primary reflections. In this paper we will take a closer look at Reverse Time Migration and Full Waveform Inversion.Keywords:
Seismic migration
Geophysical Imaging
Reflection
Model building
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Salt movement often results in steeply-dipping complex structures, which pose significant challenges for model building and migration. In recent years, advances in seismic imaging algorithms have permitted imaging of steep structures by exploiting the two-way wave equation via the introduction of reverse time migration (RTM). With such imaging algorithms, double bounces and turning wave reflections can be imaged, thereby enabling the imaging of vertical and overturned salt flanks. However, despite advances in the migration algorithms, the derivation of a suitable earth model incorporating the anisotropic behaviour of the velocity field remains a significant challenge, requiring tight integration of geological interpretation, and geophysical skills.
Geophysical Imaging
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Summary We applied the time-domain pseudospectral method on the classic acoustic wave equation (with S-wave artefact) and the new acoustic wave equation (without S-wave artefact) for vertical transversely isotropic media. Both were employed to simulate the wavefield in simple and complex media. Reverse time migration (RTM) by the two equations were tested for the VTI Marmousi model. It is shown that both equations generate similar images in RTM but the new qP-wave equation is better regarding the computational performance.
Transverse isotropy
Seismic migration
Acoustic wave equation
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We derive a new time-domain complex-valued wave equation for viscoacoustic modeling and imaging. Starting from the frequency-domain viscoacoustic wave equation, we use a second-order polynomial to approximate the dispersion term and a pseudo-differential operator to approximate the dissipation term. With these two approximations, we transform the frequency-domain viscoacoustic wave equation to the time domain. Due to the introduction of an imaginary unit in the dispersion approximation, the new wave equation is complex-valued, which is similar to the time-dependent Schrödinger equation. The advantages of the proposed viscoacoustic wave equation include (1) dispersion and dissipation effects are separated naturally, (2) quality factor Q is explicitly incorporated in the wave equation, and (3) it can be solved using time matching and avoids solving a large linear system as the frequency-domain approaches. By flipping the sign of the dissipation term, the phase dispersion and amplitude loss can be corrected during wave-field back-propagation, which is important to image sub-surface reflectors with accurate kinematic and dynamic information. Since both source and receiver wavefields are analytical functions, we can explicitly separate the extrapolated wavefields into up- and down-going components, and apply a causal cross-correlation imaging condition to produce reflectivity images.
Seismic migration
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Prestack reverse time migration(RTM) is an accurate imaging method of subsurface media. The viscoacoustic prestack RTM is of practical significance because it considers the viscosity of the subsurface media. One of the steps of RTM is solving the wave equation and extrapolating the wave field forward and backward; therefore, solving accurately and efficiently the wave equation affects the imaging results and the efficiency of RTM. In this study, we use the optimal time–space domain dispersion high-order finitedifference(FD) method to solve the viscoacoustic wave equation. Dispersion analysis and numerical simulations show that the optimal time–space domain FD method is more accurate and suppresses the numerical dispersion. We use hybrid absorbing boundary conditions to handle the boundary reflection. We also use source-normalized cross-correlation imaging conditions for migration and apply Laplace filtering to remove the low-frequency noise. Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imaging resolution than the acoustic wave equation RTM when the viscosity of the subsurface is considered. In addition, for the wave field extrapolation, we use the adaptive variable-length FD operator to calculate the spatial derivatives and improve the computational efficiency without compromising the accuracy of the numerical solution.
Seismic migration
Acoustic wave equation
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Both vertical well seismic imaging and deviated well seismic imaging are needed in oilfield development.At the same time,it is not possible for us to obtain detailed reservoirs and interlayers with high resolution when only surface seismic data are used.In this research,we investigated cross well staggered-grid finite-difference reverse-time migration algorithm and absorbing boundary conditions.In the end,we obtained reverse-time migration image from the theory model and field seismic data.The result shows that the migration algorithm is correct,and the signal-to-noise ratio and resolution ratio of reverse-time migration imaging profile are higher than that of surface seismic imaging profile.What is more,for the reverse-time imaging profile,the details of layers are clearer,and it coincides well with the actual strata,which makes it much more credible.This means we can use the above method to get detailed reservoirs and interlayers with high resolution.
Seismic migration
Geophysical Imaging
Seismic exploration
SIGNAL (programming language)
Passive seismic
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Cross-well seismic is a geophysical exploration method, where the seismic source is triggered in one well and the data are accepted in another well, in order to obtain the geological structure between the two wells. In this paper, we mainly study the algorithm of elastic wave reverse time migration imaging with cross-well seismic models. The forward simulations, pre-processing of received data, and reverse time migration imaging are presented. To overcome the problem of large amounts of memory costs in reverse time migration, we develop a saving boundary scheme into cross-well seismic to reduce the memory consumption. The feasibility of our algorithm is verified by a horizontally layered model.
Seismic migration
Geophysical Imaging
Seismic exploration
Vertical seismic profile
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In the seismic migration, Kirchhoff and reverse time migration are used in general. In the reverse time migration using wave equation, two-way and one-way wave equation are applied. The approach of one-way wave equation uses approximately computed downward continuation extrapolator, it need tess amounts of calculations and core memory in compared to that of two-way wave equation. In this paper, we applied one-way wave equation to pre-stack reverse time migration. In the frequency-space domain, forward propagation of source wavefield and back propagration of measured wavefield were executed by using monochromatic one-way wave equation, and zero-lag cross correlation of two wavefield resulted in the image of subsurface. We had implemented prestack migration on a massively parallel processors (MPP) CRAYT3E, and knew the algorithm studied here is efficiently applied to the prestck migration due to its suitability for parallelization.
Seismic migration
Prestack
Acoustic wave equation
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Seismic migration
Acoustic wave equation
Finite difference
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VSP reverse-time migration is a well adaptable wave equation migration method. Its control equation not only describes all-direction propagation of seismic wave but also removes interbed multiples. Clearbout's image principle is generalized to determine image conditions, real VSP data are used to determine boundary condition, and two way reflection-free wave equation is solved by making reverse-time extrapolation. In each step of extrapolation, the migration value at relevant image point is obtained by using the image condition. The complete migration of a seismic section is achieved when reverse-time extrapolation reaches the minimum image time. In this paper it is proved theoretically and practically that this method is applicable to any velocity variation and makes the migrated section have both good resolution and high S/N ratio. Besides, this method results in high processing efficiency.
Seismic migration
Reflection
Section (typography)
Multiple
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Pre-stack reverse-time migration shows great superiority in dealing with steep dip angle structures and complex velocity models,but the low frequency noise seriously affects the quality of imaging. The reflect angle can be calculated by the Poynting vector,the direction of which indicates that of the propagation of seismic wave, and meanwhile seismic wave field can be separated into up-going one and down-going one.This paper proposes a new imaging condition,by using which the imaging noise caused by the cross-correlation of the up-going wavefield and the down-going one in the same direction,as well as wide angle noise can be well suppressed. Compared with the conventional crosscorrelation imaging conditions,the new imaging condition is easy to realize,the extra calculation and storage are both very small.The new imaging condition is applied in Marmousi model and the migration results shows that the low frequency noise is well suppressed.
Seismic migration
Geophysical Imaging
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