A. Kamel

On the construction and efficiency of staggered numerical differentiators for the wave equation

Finite‐difference (FD) techniques have established themselves as viable tools for the numerical modeling of wave propagation. The accuracy and the computational efficiency of numerical modeling can be enhanced by using high‐order spatial differential operators (Dablain,1986).

Seismic computations on the IBM 3090 vector multiprocessor

Computerized seismic prospecting is an echo-ranging technique usually targeted at accurate mapping of oil and gas reservoirs. In seismic surveys an impulsive source, often an explosive charge, located at the earths surface generates elastic waves which propagate in the subsurface; these waves are scattered by the earths geological discontinuities back to the surface, where an array of receivers registers the reflected signals. The data recorded are then processed in a complex sequence of steps. Among them, seismic migration and stacking velocity estimation represent two characteristic components of the process solving the inverse problem of recovering the structure and the physical parameters of the earths geologic layers from echo measurements. A complementary tool in relating seismic data to the earths inhomogeneities is provided by seismic numerical models, which assume a subsurface structure and compute the seismic data which would be collected in a field survey, by solving the direct problem of exploration geophysics. This paper describes a vectorized and parallelized implementation of a two-dimensional seismic elastic model on the IBM 3090 VF Vector Multiprocessor. An implementation of a parallel seismic migration algorithm is then described. The paper also reports performance data for a vector/parallel implementation on the IBM 3090 of some typical seismic velocity estimation algorithms. The three problems chosen are representative of a wide class of geophysical computations, and the results summarized in this paper show their suitability for efficient implementation on the IBM 3090 Vector Multiprocessor; combined vector/parallel speedups in the range 15–25 are in fact observed.

Large-scale computing on clustered vector multiprocessors

A two-level parallel implementation of a large-scale geophysical simulation code is presented. The software/hardware environment utilizes IBM Clustered Fortran, allowing a single application program to execute concurrently on two IBM 3090 computers (first level of parallelism) while exploiting the multiple vector processors of each 3090 system (second level of parallelism). The experiments reported show that the problem is characterized by large task granularity and small communication/computation ratio, thus leading to sustained parallel speed-ups of nearly ten on a cluster of two 3090 computers, totalling twelve vector processors.<<ETX>>

Cost-Effective Staggered Numerical Integration of the Wave Equation

Finite-difference (FD) schemes for the numerical integration of the wave equation are generally designed with one of two criteria: (a) maximize the numerical accuracy order (as in the case of conventional FD operators); (b) minimize the simulation error of some physical feature of wave propagation (e.g. the dispersion relation) within a spectral frequency band (as introduced recently by Hotberg). The analysis of cost-effectiveness for a required error bound of the second schemes has neglected the role played by time discretization in the overall accuracy.

Elastodynamics on clustered vector multiprocessors

We present the parallelization of an elastodynamic code on a firmly coupled configuration consisting of two IBM 3090-600 VF, a total of 12 processors, joined with a connection facility. The programming environment used is Clustered FORTRAN which is a facility for writing and executing parallel programs on two coupled IBM 3090 vector multiprocessors (VMP). Clustered FORTRAN provides extensions to FORTRAN so that a single application program can execute across multiple 3090 systems as well as across the processors of a single 3090 system. To exploit parallelism on each VMP, we used the parallel DO LOOP construct and to exploit parallelism across VMP we used the SCHEDULE statement allowing concurrent execution of subprograms. It is shown that such a problem, characterized by sufficiently large amounts of arithmetic operations within the parallel tasks, can be efficiently parallelized obtaining average speed-ups of more than five on one 3090-600 VF and nearly ten on a two 3090-600 VF cluster with a small programming effort.

Parallelism in Seismic Computing

This paper describes a vectorized and parallelized implementation of a two-dimensional pseudo-spectralseismic elastic model and of a (frequency-domain)seismic migration algorithm on the (tightly-coupled) vector multiprocessor IBM 3090 VF. Performance data of alternative parallel implementations on an LCAP (loosely coupled system of array processors FPS 164) are also given.The paper reports additionally performance data of a vector/parallel implementation on the IBM 3090 of some characteristicseismic velocity estimation algorithms. The three problems chosen are representative of a wide class of geophysical computations and the results summarized in this paper show their suitability to efficient implementation on the IBM 3090 vector multiprocessor: combined vector/parallel speedups in the range 15–30 are in fact observed.

Time‐domain behavior of wide‐angle one‐way wave equations

The constant‐coefficient inhomogeneous wave equation reads ∂2u(x,z,t)∂x2+∂2u(x,z,t)∂z2-1c2∂2u(x,z,t)∂t2=-δ(t)δ(r), Eq. (1) where t is the time; x, z are Cartesian coordinates; c is the sound speed; and δ(.) is the Dirac delta source function located at the origin. The solution to the wave equation could be synthesized in terms of plane waves traveling in all directions. In several applications it is desirable to replace equation (1) by a one‐way wave equation, an equation that allows wave processes in a 180‐degree range of angles only. This idea has become a standard tool in geophysics (Berkhout, 1981; Claerbout, 1985). A “wide‐angle” one‐way wave equation is designed to be accurate over nearly the whole 180‐degree range of permitted angles. Such formulas can be systematically constructed by drawing upon the connection with the mathematical field of approximation theory (Halpern and Trefethen, 1988).

Elastic Modeling on the IBM 3090 Vector Multiprocessor

Computerized seismic prospecting is an echo-ranging technique usually targeted at mapping accurately oil and gas reservoirs. In seismic surveys an impulsive source, often an explosive charge, located at the earth’s surface, generates elastic waves which propagate in the subsurface and are scattered by the earth’s geological discontinuities back to the surface where an array of receivers register the reflected signals. The subsurface imaging of the geological structures is obtained by means of complex mathematical inversion and modeling techniques amongst which the process of forward elastic modeling of the wave field plays a major role. The aim of this paper is to present formulations of pseudo-spectral as well as finite differences elastic models. Vector multiprocessor implementations of both formulations exploiting the IBM 3090 architecture together with its associated software are then described. Performance results are also reported. The results summarized in this paper show the suitability of this class of geophysical computations to efficient implementation on vector multiprocessors: combined vector/parallel speedups around 20–30 are in fact observed.