Subsalt event regularization with steering filters
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Prucha M. L. and Biondi B. L.
The difficulties of imaging beneath salt bodies where illumination is poor are well known. In this paper, we present an angle-domain least-squares inversion scheme that regularizes the seismic image, tending to smooth along specified dips. This smoothing is accomplished using steering filters. We show the results of using the regularized inversion with smoothing along the angle axis and along both the angle and common midpoint axes. Additionally, the ramifications of specifying incorrect dips to smooth along will be examined. The results show that this regularized least-squares inversion does produce a cleaner, more continuous result under salt bodies. The inversion will reject incorrectly chosen dips used for the regularization.
Shot-profile migration of multiple reflections
Least-squares joint imaging of primaries and multiples
Converted wave dip moveout
Converted wave azimuth moveout
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Rosales D. and Biondi B.
Accurate prestack partial migration operators are important in seismic exploration. The development of different technologies, like the use of PS converted wave data, suggests the extension of applications of already successful operators and techniques for PP data. Azimuth moveout (AMO) is a partial migration operator that transforms prestack data into equivalent data with arbitrary offset and azimuth. We introduce a new, more accurate prestack partial migration operator for converted wave data. This operator has promising future applications in the regularization of ocean bottom seismic data.
Multidimensional imaging condition for shot profile migration
Wave-equation migration velocity analysis beyond the Born approximation
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Sava P. and Fomel S.
The Born approximation is based on the assumption of small slowness perturbation. We investigate the limits of the Born approximation when applied to wave-equation migration velocity analysis and propose two new schemes which allow for larger slowness anomalies, while improving accuracy and increasing stability. The new schemes are based on linearizations of exponential functions using bilinear and implicit approximations, rather than the (Born) explicit approximation. We demonstrate the feasibility of our new operators on a synthetic example with highly variable background and strong slowness anomalies.
Matching dips in velocity estimation
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Clapp R. G.
The proposed method for constraining reflector dip in tomography worked well on the complex North Sea synthetic. The estimated velocity model was more accurate with the dip constraint. The migrated image showed overall better image quality and the selected reflector was more continuous and better positioned. I would like to thank BP for the synthetic data used in this paper. ...
Velocity estimation for seismic data exhibiting focusing-effect AVO
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Vlad I. and Biondi B.
Transmission anomalies sometimes create AVO effects by focusing the reflected seismic wavefields, which impedes AVO analysis. The AVO anomalies caused by focusing are distinguishable by surface consistent patterns. We analyze the previous efforts to define, describe and eliminate spurious AVO anomalies. We also propose using wave equation migration velocity analysis to build an accurate velocity model. The transmission-related AVO can then be eliminated by downward continuation through this velocity model.
Time reverse imaging
Prestack imaging of overturned and prismatic reflections by reverse time migration
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I present a simple method for computing angle-domain Common Image Gather (CIG) using prestack reverse time migration. The proposed method is an extension of the method proposed by Rickett and Sava (2001) to compute CIGs by downward-continuation shot-profile migration. I demonstrate with a synthetic example the use of the CIG gathers for migration velocity updating. A challenge for imaging both overturned and prismatic reflections is the discrimination of the reflection generated on either side of interfaces. I show how the propagation direction of the reflections can be easily determined by evaluating the crosscorrelation of the source wavefield with the receiver wavefield at time lags different than zero. Reflections can be easily separated once their direction of propagation is determined. I demonstrate the method by imaging overturned events generated by a segment of dipping reflector immersed in a vertically layered medium. The example shows that for overturned reflections velocity errors cause asymmetric residual moveouts. This observation suggests that for updating the velocity from overturned reflections, the migrated CIGs should be scanned using a different family of residual moveouts than the standard parabolic moveouts used for non-overturned events. The migration of a synthetic example containing prismatic reflection shows that the CIGs computed using only horizontal subsurface offset are not useful, and that the vertical subsurface offset should be also used.
Statistical stability and time-reversal imaging in random media
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Berryman J. G., Borcea L., Papanicolaou G. C., and Tsogka C.
Localization of targets imbedded in a heterogeneous background medium is a common problem in seismic, ultrasonic, and electromagnetic imaging problems. The best imaging techniques make direct use of the eigenfunctions and eigenvalues of the array response matrix, as recent work on time-reversal acoustics has shown. Of the various imaging functionals studied, one that is representative of a preferred class is a time-domain generalization of MUSIC (MUltiple SIgnal Classification), which is a well-known linear subspace method normally applied only in the frequency domain. Since statistical stability is not characteristic of the frequency domain, a transform back to the time domain after first diagonalizing the array data in the frequency domain takes optimum advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.
Reverse time migration in midpoint-offset coordinates
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Reverse-time migration Baysal et al. (1984) has some potential advantages with respect to downward-continuation migration. It can migrate overturned and prismatic reflections even in the presence of strong lateral velocity variations Biondi (2002). It also models the amplitude ...
Adaptive subtraction of multiples with the -norm
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Guitton A. and Verschuur E.
The estimation of shaping filters with the -norm as opposed to the -norm leads to a proper attenuation of multiples when significant amplitude discrepancies exist between multiples and primaries. The actual method implemented is the fairly standard iteratively re-weighted least-squares method which is an excellent approximation to . Synthetic and field data results illustrate the advantages of the -norm.
A hybrid adaptive subtraction method
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A hybrid adaptive subtraction scheme is proposed. This hybrid scheme uses prediction-error filters as covariance operators within the filter-estimation step. This methods proves to be the most efficient when the noise and signal interfere. Although prediction-error filters are utilized, this technique is not a pattern-recognition technique: it simply tries to remove the correlated signal information to unbias the estimation of the matched-filters. Tests on synthetic and real data for a multiple attenuation problem illustrate the efficiency of the proposed scheme.
Removal of coherent noise from electroseismic data
Theoretical aspects of noise attenuation
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In Guitton (2001) I presented an efficient algorithm that attenuates coherent noise based on the spatial predictability of noise and signal. I called this algorithm the subtraction method. In this paper I show that the subtraction approach is closely related to another described method, the filtering method Brown and Clapp (2000); Clapp and Brown (2000); Soubaras (1994); Spitz (1999) if I use a preconditioning strategy Claerbout and Fomel (2001). ...
Removing velocity stack artifacts
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The Prediction Error Filter (PEF) is a widely used tool in various geophysical applications such as signal-noise separation and interpolation of missing data. Over the years, SEP has developed tools to estimate non-stationary Prediction Error Filters. Non-stationary PEFs are successfully used for multiple removal, ground-roll attenuation, and in other geophysical problems. I apply a non-stationary PEF to a velocity stack to remove artifacts caused by a limited offset of the data. My first goal is to create an artifact-free model in which individual reflections are easier to identify. To do this I create a simple model of the artifacts in the space. This ``noise'' model is data-independent and relies only on the geometry of the data acquisition and parameters of the velocity stack. Then I estimate a non-stationary PEF on this ``noise'' model and use it to improve the velocity stack. In the second part of the paper, I test the possibility of using the described PEF as a preconditioner for a velocity stack least-squares inversion.
Modeling and migration computational issues
Reference velocity selection by a generalized Lloyd method
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Clapp R. G.
Selecting reference velocities can be thought of as a non-linear problem. Choosing a reference velocity to use at a given location is a function of which reference velocity is actually closest to the given velocity, which makes posing the problem in a traditional linear framework difficult. When compressing signals, electrical engineers face a similar problem. They try to describe a signal with as few bytes as possible. To do this they develop a codebook. Each member of the codebook represents a region described by a single value. ...
One-way wave equation absorbing boundary condition
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In modeling and migration based on wave equation, the wavefield has to be extrapolated in a finite domain due to the limitations of our survey and computers. Absorbing boundary conditions must be introduced, otherwise some reflections will occur at the artificial grid boundary. In this paper, I will introduce an absorbing boundary condition based on the one-way wave equation, with some numerical examples.
Speeding up wave equation migration
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Clapp R. G.
When doing downward continuation in the offset domain, we begin by organizing our data cube as a function of midpoint x, offset h, and frequency f. We then apply the double square root (DSR) equation to move the wavefield down one depth step Claerbout (1995). We apply an imaging condition, ...
Finite-difference -x migration of unregularized seismic data
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Wavefield downward continuation does not need to be done on a structured spatial mesh. Semistructured meshes have advantages (no need for regularization before migration) but they sometimes produce artifacts. There are at least two acquisition settings which will not result in artifacts. The implementation is simple. I present a 2D zero-offset -x semistructured mesh migration (SMM) of a synthetic dataset. Its outputs are compared with those of -x migration on a regular grid, with zero traces inserted in the place of missing data. There are several potential ways of removing the artifacts. Extension to 3D is also possible.
Amplitudes and rock properties
Effect of velocity uncertainty on amplitude information
An extension of poroelastic analysis to double-porosity materials:
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Berryman J. G.
Double-porosity materials were introduced as models for oil and gas reservoirs having both storage and transport porosities, and were at first usually treated as static mechanical systems in order to study the flow patterns of fluids during reservoir pump-down. Because fluid withdrawal normally increases the effective stress acting on the reservoir, it also turns out to be important to study the geomechanics of the reservoir and how changing fluid pressure affects the solid compaction and fluid permeability of these systems. At the microscale, the mechanical properties of the solid constituents and their distribution in space determine the overall macromechanics of the reservoir system. For systems containing two porosities and two types of solid constituents, exact results for all but one (which may be taken as the overall drained bulk modulus of the system) of the mechanical constants can be derived when the constituents' properties are known using methods developed in this paper. For multi-porosity systems, closure of the system of equations remains an open question, although it is clear that the system can always be closed by the addition of further macroscale measurements.
Amplitude inversion for three reflectivities
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Prucha M. L. and Herkenhoff E. F.
Seismic amplitudes can provide information about rock properties if the amplitudes can be properly processed Backus (1983); Castagna and Backus (1993). This is very difficult to do given the nonlinearity of the Zoeppritz equation. The linearized Bortfeld approximation Bortfeld (1961) allows us to invert the data to obtain the reflectivities of events. Unfortunately, most ...
Filtering and inversion
Fault contours from seismic
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Fault contours are created by mapping the slip distribution along a fault surface. Fault contours have many useful applications in geophysics and geology including rock stress analysis, interpretation, and processing. Therefore, automatic calculation of fault contours from 3D data would be very valuable. As the first step in that direction, displacement is calculated from a simple 2D model of faulted seismic data. Making a stationary assumption, the displacement is calculated by fitting a smooth line to a cross-correlagram. The cross-correlagram is created by windowed cross-correlation across the fault. To fit this line, I use a non-linear optimization method that has similarities to Simulated Annealing. This removes most of the displacement which will later allow other methods to solve the non-stationary problem.
Toward subsurface illumination-based seismic survey design
Non-stationary, multi-scale prediction-error filters and irregularly sampled data
Madagascar satellite data: an inversion test case
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The Madagascar satellite data set provides images of a spreading ridge off the coast of Madagascar. This data set has two regions: the southern half is densely sampled and the northern half is sparsely sampled. This data set is an excellent test case for inversion methods. It presents several challenges that geophysicists face in generating seismic maps in general. The data is acquired in swaths that follow irregular paths(tracks), similar in some respects to irregular 3D acquisition geometries. Inversion allows us to combine these different data paths into one image. Shifts between tracks are removed by taking the derivative along the tracks in the inversion fitting goals. By looking at the residual in data-space, we were able to see errors in the weighting operator. The sparsely sampled region presents a missing data problem. In the future, we intend to estimate 2D prediction error filters (PEFs) on these sparse tracks and use them to fill in the missing data. I have tested one method on a simple 1D model, in which I estimate a PEF and missing data simultaneously while throwing out fitting equations where the leading 1 coefficient of the PEF lands on unknown data. Thus, this data will give us an opportunity to test different methods of estimating PEFs on sparse and irregular data. Also, preconditioning on the helix greatly speeds convergence.
Implementing non-stationary filtering in time and in
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Non-stationary filtering of seismic data can be accomplished in time or in Fourier domain by the theory of non-stationary convolution Margrave (1998). Here I show the results of implementing this theory for time-variant filtering of seismic data with an arbitrary number of filters and for forward and inverse NMO correction in the frequency domain. In the first case I show that the filters may be made to change sample-by-sample down the trace without artifacts being introduced and in the second case that the accuracy of the implied fractional sample interpolation can be controlled as an input parameter.
A return to passive seismic imaging
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Rekindling the passive seismic imaging effort at Stanford, I have acquired grants with Simon Klemperer of the Stanford Crustal Research Group from both the Petroleum Research Fund and the National Science Foundation to pursue two- and three-dimensional imaging efforts of the subsurface in a passive listening methodology. Utilizing the outstanding SEP hardware and software infrastructure and expertise, I have begun to build the resources necessary to manipulate the massive datasets toward producing an image. Efforts to acquire several existing datasets that seem to fit the requirements of this method are presently underway, while 180 Gbytes of the Santa Clara Valley Seismic Experiment from 1998 arrived in house on the first of March.
Is 2D possible?
Coherent noise in the passive imaging experiment
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Inherent in the passive seismic imaging experiment is the troublesome coexistence of the direct source phase and its excited ghost reflections that image the subsurface. Akin to the multiple problem in conventional seismic, I propose to attack the direct waves as noise in the framework outlined by Guitton et al. (2001). Whereas his methodology is effective at separation of signal and noise models, building an appropriate noise model is often the most limiting aspect of the technique. I propose a method to reconstruct the parameters of the ...
WEI: Wave-Equation Imaging Library
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Sava P. and Clapp R. G.
This paper introduces WEI, a new library in the SEP library of programs (SEPlib). The WEI library implements a Fortran90 imaging engine for mixed-domain downward-continuation operators. The main imaging operators are broken into functional operators which can be modified by the user without explicit contact with I/O, parallelization etc. The code is parallelized using a combination of the Open MP and MPI standards, and can run on both shared-memory and cluster computers.
Displaying seismic data with VTK
Cluster building and running at SEP
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Clapp R. G. and Sava P.
When we first decided that we wanted to buy a new cluster we got quotes from several different vendors. These quotes varied up to 50% for the same configuration based upon the add-on features that each company provided. However, even the lowest figure was 30% more than what we calculated if we built the cluster ourselves. Once we decided that the 30% cost differential was significant enough to make building it ourselves worthwhile, we had to determine what exactly we wanted to build.
- Artman, B., 2002, Is 2d possible?: SEP-111, 371-379.
- Guitton, A., Brown, M., Rickett, J., and Clapp, R., 2001, A pattern-based technique for ground-roll and multiple attenuation: SEP-108, 249-274.
- Kennet, B. L. N., 1991, The removal of free surface interactions from 3-component seismograms: [Geophys]ics [J]ournal [I]nternational, 104, 153-163.