The Implementation of Desirable Transformations of the Registered Seismic Waves

Abstract

A critical phase in seismic research is the transformation of the recorded seismic waves into new ones, more suitable for further interpretation or processing. When the propagation of the recorded and desired after the transformation waves can be described by analytical functions, the use of the method of stationary-phase transformations of seismic data proposed by the authors earlier seems justified and appropriate. This method relies on a unified mathematical approach (finding the envelope of a family of functions), is fairly versatile, and is relatively simple to apply. Nearly 30 years of experience in its application, the creation, and the use of 16 procedures aimed at implementing the desired transformations of waves recorded as a result of seismic observations. These procedures include: poststack time and depth migrations using average velocities; transformation waves with hyperbolic traveltime curves into waves with linear curves without information about velocities; prestack and poststack time migrations using stacking velocities; prestack time and depth migrations utilizing average velocities; transformation of input data into time sections employing average velocities; poststack depth migration using a depth-linear velocity function; transformation of VSP data into time sections, time migrated sections, and depth migrated sections with using average velocities; transformation refracted waves (headwaves) into time sections, time migrated sections, and depth migrated sections applying average velocities; transformation of input data into “floating” time sections simultaneously with obtaining information on the average velocities of waves propagation. Many of these procedures have no analogues, and those that do differ from them significantly in dynamic features. The procedures mentioned above were developed using the stationary-phase transformations method and are undoubtedly beneficial for broadening the potential of seismic research. Moreover, this method itself serves as an impactful and promising tool for addressing numerous ongoing and future challenges in seismic exploration.