Phase Shift Plus Interpolation: a scheme for high performance echo-reconstructive imaging

Abstract

Echo-reconstruction techniques for non-intrusive imaging have wide application, from subsurface and underwater imaging to medical and industrial diagnostics. The techniques are based on experiments in which a collection of short acoustic or electromagnetic impulses, emitted at the surface, illuminate a certain volume and are backscattered by inhomogeneities of the medium. The inhomogeneities act as reecting surfaces or interfaces which cause signal echoing; the echoes are then recorded at the surface and processed through a "computational lens" defined by a propagation model to yield an image of the same inhomogeneities. The most sophisticated of these processing techniques involve simple acoustic imaging in seismic exploration, for which the huge data sets and stringent performance requirements make high performance computing essential. Migration, based on the scalar wave equation, is the standard imaging technique for seismic applications [1]. In the migration process, the recorded pressure waves are used as initial conditions for a wave field governed by the scalar wave equation in an inhomogeneous medium. Any migration technique begins with an a priori estimate of the velocity field obtained from well logs and an empirical analysis of seismic traces. By interpreting migrated data, comparing the imaged interfaces with the discontinuities of the estimated velocity model, insuficiencies of the velocity field can be detected and the estimate improved [2], allowing the next migration step to image more accurately. The iterative process (turnaround) of correcting to a velocity model consistent with the migrated data can last several computing weeks, and is particularly crucial for imaging complex geological structures, including those which are interesting for hydrocarbon prospecting. Subsurface depth imaging, being as it is the outcome of repeated steps of 3D seismic data migration, requires Gbytes of data which must be reduced, transformed, visualized and interpreted to obtain meaningful information. Severe performance requirements have led in the direction of high performance computing hardware and techniques. In addition, an enormous effort has historically gone into simplifying the migration model so as to reduce the cost of the operation while retaining the essential features of the wave propagation. The phase-shift-plus-interpolation (PSPI) algorithm can be an effective method for seismic migration using the "one-way" scalar wave equation; it is particularly well suited to data parallelism because of, among other things, its decoupling of the problem in the frequency domain.