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Angle-domain common image gathers for anisotropic migration (ps.gz 1250K) (pdf 665K) (src 1259K)
Biondi B.
I present a general methodology for computing Angle-Domain Common Image Gathers (ADCIGs) in conjunction with anisotropic wavefield-continuation migration. The method is based on the transformation of the prestack image from the subsurface-offset domain to the angle domain by use of slant stacks. The processing sequence is the same as for the computation of ADCIGs for the isotropic case, though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles are more complex. I demonstrate that the slopes measured by performing slant stack along the subsurface-offset axis of the prestack image are a good approximation of the phase aperture angles, and that they are exactly equal to the phase aperture angles for flat reflectors in Vertical Transverse Isotropic (VTI) media. In the general case of dipping reflectors, the true aperture angles can be easily computed as a function of the reflector dip and anisotropic slowness at the reflector. I derive the relationships between phase angles and slopes measured in the prestack image from both a ``plane-wave'' viewpoint and a ``ray'' viewpoint. The two derivations are consistent with each other, as demonstrated by the fact that in the special case of flat reflectors they lead to exactly the same expression. The ray-theoretical derivation is based on a novel generalization of kinematic migration to the computation of prestack images as a function of the subsurface offset. This theoretical development leads to the linking of the kinematics in ADCIGs with migration-velocity errors, and thus it enables the use of ADCIGs for velocity estimation. I apply the proposed method to the computation of ADCIGs from the prestack image obtained by anisotropic migration of a 2-D line extracted from a Gulf of Mexico 3-D data set. The analysis of the error introduced by neglecting the difference between the true phase aperture angle and the angles computed through slant stack shows that these errors are negligible and can be safely ignored in realistic situations. On the contrary, group aperture angles can be quite different from phase aperture angles and thus ignoring the distinction between these two angles can be detrimental to practical applications of ADCIGs.
Residual moveout in anisotropic angle-domain common image gathers (ps.gz 1588K) (pdf 837K) (src 1633K)
Biondi B.
To enable the analysis of the Residual Moveout (RMO) in Angle-Domain Common Image Gathers (ADCIGs) after anisotropic wavefield-continuation migration, I develop the fundamental concepts for quantitatively relating perturbations in anisotropic parameters to the corresponding reflector movements in ADCIGs. I then apply the general methodology to the particular case of RMO analysis of reflections from flat reflectors in a Vertical Transverse Isotropic (VTI) medium. This analysis shows that the RMO in migrated ADCIGs is a function of both the phase aperture angle and the group aperture angle. Several numerical examples demonstrate the accuracy of the RMO curves predicted by my kinematic analysis. The synthetic examples also show that the approximation of the group angles by the phase angles may lead to substantial errors for events reflected at wide aperture angles. The results obtained by migrating a 2-D line extracted from a Gulf of Mexico 3-D data set confirm the accuracy of the proposed method. The RMO curves predicted by the theory exactly match the RMO function observed in the ADCIGs computed from the real data.
Wave-equation migration from topography: Imaging Husky (ps.gz 3362K) (pdf 741K) (src 330965K)
Shragge J.
Imaging land seismic data is wrought with many technical challenges that arise during different stages of seismic investigation: acquisition (e.g. irregular geometry), preprocessing (e.g. ground-roll suppression, statics), velocity estimation (e.g. near-surface complexity) and migration (e.g. rugged topography, uncertain velocities). Each of these complicating factors needs addressing before satisfactory final images are generated. Given the completion of each pre-migration processing step, one may choose from a variety of migration techniques; however, velocity profiles and geologic ...
Direct migration: The only way (ps.gz 1048K) (pdf 347K) (src 28188K)
Artman B.
Correlating transmission wavefields to produce reflection wavefields contains in its rigorous definition the mandate of processing data due to only a single source. If more than one source is contained in the wavefield, crosstalk between the sources will produce a data volume that is not the same as shot gathers with impulsive sources at each receiver location. When attempting to image the subsurface with the truly unknown ambient noisefield, parameterizing the field data by individual sources is impossible. For truly passive data, the source and time axis are inextricably combined, naturally and by processing. This changes direct migration to something more akin to planewave migration. Since the direct arrival from each source can not be expected to sum together with a common time-delay, the summation manufactures a source wavefront with temporal topography rather than a planewave. The Fourier transform of field data as a single wavefield provides insight into how sources are summed during correlation. Also, the transform simultaneously stacks away useless waiting periods between useful energy bursts and reduces the data volume. Previously, white, zero-phase source functions were invoked to avoid the summation problem. However, neither assumption is likely in the real environment of a long term experiment.
Nondestructive testing by migration (ps.gz 201K) (pdf 161K) (src 236168K)
Artman B. and Clapp R. G.
In the spring of 2005, engineers from Lawrence Livermore National Laboratories [*] contacted SEP to ask about the potential to use geophysical algorithms for nondestructive investigation of manufactured/machined parts. The conversation was sparked by emphasis from the LLNL management to search for existing solutions to their suite of current problems. Dr. Lehman presented SEP with a problem of investigating the interior ...


Wave-equation angle-domain Hessian (ps.gz 24K) (pdf 39K) (src 19K)
Valenciano A. A. and Biondi B.
A regularization in the reflection angle dimension (and, more generally in the reflection and azimuth angles) is necessary to stabilize the wave-equation inversion problem. The angle-domain Hessian can be computed from the subsurface-offset Hessian by an offset-to-angle transformation. This transformation can be done in the image space following the Sava and Fomel (2003) approach. To perform the inversion, the angle-domain Hessian matrix can be used explicitly, or implicitly as a chain of the offset-to-angle operator and the subsurface offset Hessian matrix.
Target-oriented wave-equation inversion: Sigsbee model (ps.gz 414K) (pdf 245K) (src 4612K)
Valenciano A. A., Biondi B., and Guitton A.
Sigsbee model is often used as a benchmark for migration/inversion algorithms due to its geological complexity. The data was modeled by simulating the geological setting found on the Sigsbee escarpment in the deep-water Gulf of Mexico. The model exhibits illumination problems due to the complex salt shape, with a rugose salt top. When the subsurface is complex, migration operators produce images with reflectors correctly positioned but biased amplitudes Kuehl and Sacchi (2001); Prucha et al. (2000). That is why an inversion formalism Tarantola (1987) needs to be used to account for that problem. In this paper, we apply the target-oriented wave-equation inversion idea presented in Valenciano et al. (2005) to the Sigsbee data. Due to the complex velocity structure and the limited acquisition cable length, the reflectors are not illuminated from all reflection angles. That highlights the need of a more sophisticated regularization in the angle domain Kuehl and Sacchi (2001); Prucha et al. (2000); Valenciano and Biondi (2005) than the simple damping proposed by Valenciano et al. (2005). ...
AMO inversion to a common azimuth dataset (ps.gz 2399K) (pdf 850K) (src 7741K)
Clapp R. G.
I cast 3-D data regularization as a least-squares inversion problem. The model space is a four-dimensional ($t,{cmp}_x, {cmp}_y, h_x$) hypercube. An interpolation operator maps to an irregular five dimensional space ($t,{cmp}_x, {cmp}_y,h_x,h_y$) which is then mapped back into a four dimensional space by applying Azimuth Move-Out (AMO). A regularization term minimizes the difference between various ($t, {cmp}_x, {cmp}_y$) cubes by applying a filter that acts along offset. AMO is used to transform the cubes to the same hx before applying the filter. The methodology is made efficient by Fourier-domain implementation and preconditioning of the problem. I apply the methodology on a simple synthetic and to a real marine dataset.
Iterative linearized migration and inversion (ps.gz 120K) (pdf 196K) (src 148K)
Wang H.
The objective of seismic imaging is to obtain an image of the subsurface reflectors, which is very important for estimating whether a reservoir is beneficial for oil/gas exploration or not. It can also provide the relative changes or absolute values of three elastic parameters: compressional wave velocity Vp, shear wave velocity Vs, and density $$. Two ways can achieve the objectives. In approach I, the angle reflectivity is given by prestack depth/time migration or linearized inversion, and the relative changes of the three elastic parameters are estimated from the angle reflectivity by AVO/AVA inversion. In, approach II, the relative changes (by linearized inversion) or absolute values (by nonlinear waveform inversion) are obtained directly. I compare non-iterative linearized migration/inversion imaging, iterative linearized migration/inversion imaging, and non-linear waveform inversion. All of these imaging methods can be considered as back-projection and back-scattering imaging. From backscattering imaging, we know that seismic wave illumination has a key influence on so-called true-amplitude imaging, and I give an analysis for the possibility of relative true-amplitude imaging. I also analyze the factors that affect the imaging quality. Finally, I point out that the Born approximation is not a good approximation for linearized migration/inversion imaging, and that the De Wolf approximation is a better choice.


Mapping of water-bottom and diffracted (ps.gz 622K) (pdf 585K) (src 791K)
Alvarez G.
Wave-equation migration with the velocity of the primaries maps non-diffracted water-bottom multiples to an hyperbola in subsurface-offset-domain-common-image-gathers. Furthermore, for positive surface offsets, the multiples are mapped to non-positive subsurface offsets if sediment velocity is faster than water. The larger the offset in the data space, the larger the subsurface offset and the shallower the image point. When migrated with the velocity of the water, the multiples are mapped to zero subsurface offset just as primaries migrated with the exact velocity. Diffracted multiples, on the other hand, map to positive or negative subsurface offsets depending on the relative position of the diffractor with respect to the common-midpoint. I present the equations of the image point coordinates in terms of the data space coordinates for diffracted and non-diffracted multiples from flat or dipping water-bottom in both subsurface-offset-domain common-image-gathers and angle-domain common-image-gathers. I illustrate the results with simple synthetic models.
Imaging primaries and multiples simultaneously with depth-focusing (ps.gz 20K) (pdf 30K) (src 150K)
Wang H.
Seismic imaging amplitudes are extracted with the imaging conditions t=0 and h=0, where t=0 means that the take-off time of the upward-coming wave is zero, and h=0, with h the half-offset between the source and receiver position, means that the downward-going and upward-coming waves meet together during the wavefield extrapolation. However, h=0 makes no sense for multiples imaging. This imaging condition is suitable for imaging the primary, where the source position must be known. I introduce an imaging condition for imaging primaries and multiples simultaneously. The imaging condition, in essence, states that the take-off time of the upcoming wave equals zero, and that the radius of curvature of the wavefront of the upcoming scattered wavefield equals zero. It is known that the primary and multiple scattered waves will be focused during the wavefield depth extrapolation, but the primary and multiple scattered waves at the same depth focus at different times; this is because the traveltimes from the source to the scattering point are different for the primaries and multiples, even for the same scattering point. The focused scattered wave can be picked out, and the image is formed at the focusing point. The advantages of the method are several: the primary and multiples can be imaged simultaneously, only the up-coming wave must be downward extrapolated, all the scattered wavefields in the different shot gathers can be added together and simultaneously extrapolated, and the source position needs not be known. Its disadvantage is that the imaging condition is much more difficult to use.

Rock Physics

Geomechanical analysis with rigorous error estimates for a double-porosity reservoir model (ps.gz 59K) (pdf 114K) (src 103K)
Berryman J. G.
A model of random polycrystals of porous laminates is introduced to provide a means for studying geomechanical properties of double-porosity reservoirs having one class of possible microstructures. Calculations on the resulting earth reservoir model can proceed semi-analytically for studies of either the poroelastic or transport coefficients, but the poroelastic coefficients are emphasized here. Rigorous bounds of the Hashin-Shtrikman type provide estimates of overall bulk and shear moduli, and thereby also provide rigorous error estimates for geomechanical constants obtained from up-scaling based on a self-consistent effective medium method. The influence of hidden (or presumed unknown) microstructure on the final results can then be evaluated quantitatively. Detailed descriptions of the use of the model and some numerical examples showing typical results for the double-porosity poroelastic coefficients for the type of heterogeneous reservoir being considered are presented.

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