Alastair D. McAulay

Prestack inversion with plane-layer point source modeling

Prestack inversion with point-source plane-layer modeling has many advantages over poststack or normal incidence inversion. For example, it permits the determination of absolute compressional and shear velocities, density variations, and the accurate accounting of interbed and surface multiples. I neglect shear effects in this paper by assuming that they are adequately suppressed by velocity filtering. In the forward modeling step, a spherical wave expansion into plane waves is used to account for the point source. The plane-wave reflection response for a set of plane layers is extended to the nonnormal incidence case. I use a Hankel transform to account for cylindrical symmetry. Generalized linear inversion is used because the fast recursive approaches available for normal incidence inversion are no longer applicable. I provide the derivation for the required derivative matrix, and I take into account the band-limited nature of the data in frequency, time, and space. I demonstrate that moveout of events on realistic simulated prestack data enables the determination of absolute compressional velocity in the velocity-depth profile, even though the data are band-limited in frequency. I assume that preprocessing has adequately removed the shear and surface effects and that density is constant. Low frequencies in the velocity profile may be obtained more accurately than with velocity analysis used for stacking, because interbed multiples and other modeling phenomena are accounted for in the computation. Autoregressive modeling procedures that predict into the low frequencies of the velocity profile are also less accurate and cannot generate absolute velocity. I suggest future research leading to cost-effective inversion of real data.

Plane-layer prestack inversion in the presence of surface reverberation

Experiments with synthetic data have indicated that generalized linear inversion may be used to estimate compressional velocities as a function of depth with high resolution directly from band‐limited, unstacked data. The ocean surface was not included in these experiments. In the presence of strong surface multiples, inversion is expected to take longer and be less accurate, because events from multiple surface reflections overlie primary events and normally have differing moveout. Existing velocity‐analysis techniques rely on the ability of an observer to make the difficult distinction between multiples and primaries. Equations are provided for adding the surface to the inversion procedure. This involves adding the surface effects to the Jacobian matrix as well as to the forward modeling procedure. To speed computation, the addition of the surface effects to the Jacobian matrix is delayed until after the matrix has been multiplied by a vector in the linear‐equation solution. Absorption is added to the i...

Optical Crossbar Interconnected Digital Signal Processor With Basic Algorithms

A proposed high performance gigaflop signal processor is described in which 512 processors are interconnected with a 768 by 768 crossbar switch utilizing a spatial light modulator of the type presently under development at Texas Instruments. Optical fibers are used to provide high speed communication between the processors and the switch. The system, processor nodes, programming, and functional operation are described. The advantages are discussed for reconfigurability, optical crossbar switches, and programmed data flow. Efficient implementations are presented for a systolic filter, a fast Fourier transform, a correlator, and a matrix-vector multiplier. Preliminary performance estimates suggest that over one gigaflop performance is achievable for these algorithms on this processor.

Digital generation of accurate synthetic seismograms

A point source insonifies a one mile deep, 200 layer, compressional velocity earth model, and the backscattered response is computed at surface receiver elements. The computational method is based on a plane wave decomposition of the spherical wave emanating from the source. Cylindrical symmetry is assumed in computing the surface responses. Physical and numerical phenomena affecting accuracy are illustrated: aliasing, critical angle effects, absorption and a new phenomenon we call tunneling. The accuracy is demonstrated by comparison with real field seismograms for an area consistent with the computational assumptions. This research is directed toward improving accurate seismic inversion techniques for geophysical data.

Parallel AR computation with a reconfigurable signal processor

A proposed reconfigurable signal processor has hundreds of processors connected by optical fibers to an optical crossbar switch and uses static dataflow. The system, optical switch, programming methodology, and functional operation are described. Levinson-Durbin, Burg. and Schur algorithms for solving Toeplitz equations arising in optimal filters and AR modeling are reviewed. The implementation of these algorithms on the proposed processor are considered. Reconfigurability permits the most suitable algorithms to be selected and trade offs to be made between speed and efficiency.

Optimal Least Square Filtering With A Digital Optically Interconnected Processor

An optical crossbar interconnected signal processor, proposed previously, is reviewed. The ability to implement difficult-to-parallelize algorithms on this processor with reasonable efficiency is illustrated using optimal least square filtering. An inverse filter for removing the effects of a ringing source from reflected data is used as an example. A large number of Toeplitz matrix equations must be solved to determine the optimum inverse filter length and phase. Efficient parallel computation is required. Equations for Levinsons algorithm are provided and an implementation on the optical system is suggested. Performance estimates suggest that interleaving may he used to improve efficiency from 5% to approximately 30%.

Predictive deconvolution of seismic array data for inversion

Predictive deconvolution is used to remove the ringing source signature wavelet from seismic array data to enhance interpretation or to permit direct earth parameter estimation (inversion). For the latter it is important to know whether the procedure is removing information other than the source wavelet. Sets of synthetic marine data are generated for two plane layer solid earth models, including a minimum delay wavelet and with and without the ocean surface. Predictive deconvolution is applied with autocorrelation averaging across sensors to enhance the random earth assumption. The wavelet estimated during predictive deconvolution is close to the original wavelet except when surface ghosts are included. In this case it is close to the combined wavelet and ghosts.

Nearest Neighbor Hybrid Deformable Mirror Optical Computer

Deformable mirror and charge coupled devices are combined with parallel high speed electronics in order to produce a nearest neighbor computer in which the value at each point in a 2D array may be simultaneously updated based on values at the immediately surrounding points. The concept of such a machine is described together with its application to image processing and partial differential equation solution. Repeated iteration enables filtering which involves points at greater distance than the nearest neighbor. The problem is discussed of overcoming the limited dynamic range of the deformable mirror device for application to the solution of partial differential equations.

Optical Crossbar Signal Processor

A proposed high performance, many Gigaflop signal processor is described in which 512 processors are interconnected with a 768 by 768 crossbar switch utilizing a spatial light modulator of the type presently under development. Optical fibers are used to provide high speed communication between the processors and the switch. The system, processor nodes, programming and functional operation are described. The advantages are discussed for reconfigurability, optical crossbar switches and programmed data flow. Efficient implementations are presented for: a systolic filter, a fast Fourier transform, a correlator and a matrix-vector multiplier.

Deformable Mirror Nearest Neighbor Optical Digital Computer

Many problems are efficiently computed on nearest neighbor connected machines because they involve regular grids or grids that may be envisaged as distortions from regular. Examples include image processing and finite differences and finite elements that dominate engineering and scientific computation. Previously, I proposed an optical nearest neighbor machine concept with 5-bit accuracy. The simple design in this paper uses residue number arithmetic and two deformable mirror arrays of 1000 x 1000 elements to achieve 15 million operations per second with 32-bit accuracy. I assume that an array may be set in 8 ms. Duplication of equipment by 64 times enables one billion operations per second because perfect parallelism is achievable with residue numbers and nearest neighbor concepts. It is anticipated that the increased use of deformable mirror devices in computer peripherals will advance the technology to the point where designs such as that proposed will be practical. The proposed scheme appears to be superior to outer product and optical modulo schemes for nearest neighbor computation.