Douglas W. McCowan

A slant-stack procedure for point-source data

The proper implementation of the τ-p method for surface data excited by a point source requires a cylindrical slant stack. Usually the common (Cartesian) slant stack is computed instead as an approximation to the geometrically correct procedure. Here we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks; our cylindrical slant stack is computationally efficient to perform. We show how, although the usefulness of the slant stack is most easily seen with Cartesian coordinates, it can also be used with Fourier‐Bessel transforms. An example of the method shows results computed from data recorded on the West Florida Shelf. Severe edge‐effect noise which overwhelms the Cartesian slant stack is attenuated by the cylindrical slant‐stacking. Applications of the cylindrical slant stack to other seismological calculations, such as Lamb’s problem, are also discussed. In particular, we prove that the plane‐wave reflection coefficients apply exactly in the τ-p domain; hence...

Spherical divergence correction for seismic reflection data using slant stacks

We have developed a method for the spherical divergence correction of seismic reflection data based on normal moveout and stacking of cylindrical slant stacks. The method is illustrated on some Gulf of Mexico data. The results show that our method yields essentially the same traveltime information as does conventional processing. Our amplitudes, however, are more interpretable in terms of reflectivity than are those obtained by using an empirical spherical divergence correction.

Cartesian and Cylindrical Slant Stacks

The proper implementation of the τ-p method for surface data excited by a point source, requires the computation of a cylindrical slant stack. Usually, the common (Cartesian) slant stack is computed instead as an approximation to the geometrically-correct procedure. Here, we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks which is accurate for all slownesses and efficient to perform.

High-resolution group velocity analysis☆

Abstract A method is developed for group velocity dispersion analysis of seismic surface waves using the instantaneous frequency estimator of Griffiths (1975). The inverse of a data-adaptive prediction error spectrum is contoured to give a high-resolution estimate of the group arrival time of a compact waveform. The method is applied to two SRO long-period recordings. Results from the first, an NTS explosion recorded at Albuquerque, indicate a structure for the Colorado plateau exhibiting a 40 km thick crust and no low-velocity zone. Results from the second, a Southern Iran earthquake recorded at Mashad, indicate a standard continental structure for the Iran plateau with, however, an anomalously thick 55-km crust. Both events were approximately 1000 km away from the respective stations.

On: “Comparison of plane-wave decomposition and slant stacking of point-source seismic data; discussion and reply

Mithal and Vera give the impression that the correct cylindrically symmetric slant stack (e.g., Chapman, 1981; Harding, 1985; Brysk and McCowan, 1986a) needed to represent point‐source radiation in vertically stratified media is both expensive and unnecessary in ordinary data analysis.