Evolution of the propagator matrix method and its implementation in seismology

TL;DR

This paper reviews the evolution and core features of the propagator matrix method in seismology, highlighting its theoretical foundations and providing Python implementations for calculating dispersion curves.

Contribution

It offers a comprehensive historical overview of the propagator matrix method and introduces Python code implementations for practical seismic analysis.

Findings

Clarified the theoretical basis of the propagator matrix method.

Provided Python implementations for dispersion curve calculations.

Enhanced understanding of the method's development in seismology.

Abstract

In this paper, we review development of an algorithm that is referred to in seismology as the Haskell matrix method, the Thomson-Haskell matrix method, or the propagator matrix method. The roots of this algorithm and main developments are examined to offer a better understanding of its essential features. The underlying theory is highlighted by removing specific expressions and manipulations that often shroud the common method involved. Also, I discuss implementations of the algorithm in Python, with a reference to source code. These implementations calculate dispersion curves for guided waves.