Alexander M. Popovici

Prestack migration by split-step DSR

The double‐square‐root (DSR) prestack migration equation, though defined for depth variable velocity, can be used to image media with strong velocity variations using a phase‐shift plus interpolation (PSPI) or split‐step correction. The split‐step method is based on applying a phase‐shift correction to the extrapolated wavefield—a correction that attempts to compensate for the lateral velocity variations. I show how to extend DSR prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the Marmousi data set. The split‐step DSR migration is very fast and offers excellent imaging results.

Diffraction imaging of the Eagle Ford shale

Diffraction imaging is a novel technology that uses diffractions to image very small subsurface elements. Diffraction imaging may: (1) improve prospect characterization and pre-drill assessment of the local geology; (2) improve production and recovery efficiency; (3) reduce field development cost; and (4) decrease environmental impact. Field development may be accomplished with fewer wells to optimally produce the reservoir using high-resolution images of small-scale fractures in shale or carbonate intervals. Standard approaches to obtain high-resolution information, such as coherency analysis and structure-oriented filters, derive attributes from stacked, migrated images. Diffraction imaging, in comparison, acts on the pre-stack data, and has the potential to focus super-resolution structural information. Diffraction images can be used as a complement to the structural images produced by conventional reflection imaging techniques, by emphasizing small-scale structural elements that are difficult to interpret on a conventional depth image. An efficient way to obtain diffraction images is to first separate the migration events according to the value of the specularity angle, in a similar way to offset gathers, and subsequent post-stack processing. The high-resolution potential is demonstrated by the diffraction images from the Kenedy 3D survey over the Eagle Ford shale, which show much more detail than conventional depth migration or coherence.

Three-dimensional travel-time computation using the Fast marching method

We present a fast algorithm for solving the eikonal equation in three dimensions, based on the Fast Marching Method (FMM). The algorithm is of order O(N log N), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system, and globally constructs the solution to the eikonal equation for each point in the coordinate domain. The method is unconditionally stable, and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity. In addition, the method resolves any overturning propagation wavefronts. We begin with the mathematical foundation for solving the eikonal equation using the FMM, and follow with the numerical details. We show examples of traveltime propagation through the SEG/EAGE Salt Model, and the use of these first arrival traveltimes to image 3D prestack data.

Velocity model building by wavefield-continuation imaging in the deepwater Gulf of Mexico

Wavefield-continuation-based migration algorithms that downward extrapolate the 3D prestack wavefield (commonly known as “wave-equation migration”) have been recently shown to produce better imaging results than Kirchhoff migration in many synthetic and real data cases (Popovici, 2000). Wavefield-continuation methods are potentially more accurate and robust because they are based on the full wave equation and not on an asymptotic solution based on ray theory. In addition, wavefield-continuation methods handle multipathing naturally in contrast to Kirchhoff methods, focusing and defocusing effects of velocity variations are correctly modeled, antialiasing is handled implicitly, and amplitudes are consistent with the wave equation.

Fast Beam Migration using Plane Wave Destructor (PWD) Beam Forming

In some embodiments, input seismic data is decomposed into Gaussian beams using plane wave destructor (PWD) filters. The beams are used in a fast beam migration method to generate a seismic image of a subsurface volume of interest. PWD filters are applied to groups of neighboring traces to generate a field of dips/curvatures that fit the input trace data. Beam wavelets are then formed according to the dip/curvature field. Multiple dips (PWD slopes) may be determined at each location in time/space in order to handle intersecting reflection events. Exemplary methods allow an improvement in processing speed by more than an order of magnitude as compared to standard industry techniques such as Kirchhoff migration.

Three-dimensional subsalt semirecursive Kirchhoff migration

We obtain accurate images of complex subsalt structures by combining Kirchhoff datuming and Kirchhoff migration into a 3D semirecursive Kirchhoff migration. By datuming to the top of salt, or even through the salt, and then imaging below the salt, a greatly improved image is obtained.

Kinematics of prestack partial migration in variable velocity media

I present in thii paper an algorithm to construct the PSPM operator in variable velocity media aa a potentially efficient alternative to full prestack migration. The PSPM impulse response is computed using raytracing by considering the PSPM process ss the combination of full prestack migration followed by sero-offset modeling. The generalieed impulse response can be applied to the data ss an integral operator. The kinematics of the proposed PSPM operator and those of the constant velocity PSPM differ in some cases, such as in preeence of a low velocity layer; in other cases when velocity increses with depth, there is much similarity in the shapes of the two operators.

Interpretation value of diffractions and sub-specular reflections – applications on the Zhao Dong field

We provide an overview of integrated pre-stack depth migration and diffraction imaging for the Zhao Dong field, Bohai Bay, China. This field is highly compartmentalized by complex faulting and further characterized by channel systems, fractures and volcanic features. The objective of the diffraction imaging is to better define these small-scale features. Tools to facilitate interpretation include displays with pre-stack depth migration and diffraction images overlain in different colour scales, as well as a weighted blending of them into a single volume. An important concept is that of the sub-specular reflection, which is obtained alongside the pure diffraction image by applying ultra-weak specularity tapers. Tuning properties of elementary diffractor images together with sub-specular reflectors provide a decisive uplift of diffraction imaging for the interpreter.

Integrated Internet collaboration

The last four years have brought tremendous advances in software applications, software tools, and software systems for modernizing, consolidating, and coordinating an enterprises computer applications. Many companies have existing legacy applications and databases and want to continue to use them while adding or migrating to a new set of applications that exploit the Internet, e-commerce, Intranet, remote collaboration, independence from operating systems, and other new technologies. They should be able to do this because the new software tools have orders of magnitude more functionality than mid-1990s software applications that relied on Xwindows, some mathematical libraries, and a compiler. The built-in network communications, remote collaboration support, database support, and 3D and 2D graphic libraries give programmers the power to create industrial strength solutions that integrate all these new technologies in a specific application—for example, a data-processing or depth-imaging system.

Neutron microfocusing by double reflection on curved perfect crystals

The imaging of large area neutron sources into millimeter-size spots by focusing with two curved perfect crystals is examined. In the parallel (+,-) setting large demagnifications can be achieved only with crystals in strongly asymmetric reflection. The most promising configurations appear to be those with crystals in antiparallel (+,+) setting. The beam intensities for the parallel and antiparallel settings of bent crystals are comparable, the reflection efficiency being enhanced by the reflectivity curve broadening. The instrument Q-resolution can be kept reasonably good in a limited range by phase space focusing. Results of neutron optics computations are presented for a diffractometer for stress scanning measurements and for a small-angle scattering instrument with long neutron paths.