Traveltime signature of 3-D edge diffractions exemplified by triple-square-root moveout

TL;DR

This paper introduces a new traveltime formula for 3-D edge diffractions, called the triple-square-root moveout, which helps identify and analyze edge diffractions in seismic data more effectively.

Contribution

It derives an exact traveltime formula for 3-D edge diffractions and demonstrates its application through comparison with standard moveouts and wave modeling.

Findings

The triple-square-root moveout accurately models edge diffractions.

Mixed source-receiver derivatives identify diffractions at arbitrary offsets.

The method enables sorting data into focused fragments on edges.

Abstract

Various underground anomalies, both natural and artificial, cause diffraction of high-frequency seismic and electromagnetic pulses emitted from the earth's surface. Backscattered, they are registered by seismic sensors and ground-penetrating radars. Most of these signals can be categorized as either point or edge diffraction. Despite the abundance of linear structures in geological formations and among buried anthropogenic objects, diffraction processing often relies on the idea of point diffraction. However, 3-D edge diffractions have unique properties that need to be exploited. We show that the mixed source-receiver traveltime derivatives, available from data, identify edge diffractions at arbitrary offsets. Additionally, they constitute a system of ordinary differential equations describing finite-offset focusing curves on the acquisition surface. Such curves enable sorting of the data into fragments that focus on specific points on the edge. To confirm and demonstrate these properties, we derive an exact traveltime formula for a straight diffractor in a homogeneous medium. We refer to it as the triple-square-root moveout in analogy to the double-square-root moveout of 2-D diffractions. Since it represents a potentially useful approximation, we compare it with standard moveouts and wave modeling.