Open AccessExplicit SH transfer function of a layered crust by ray theory
Author(s) -
Wang Chengsung
Publication year - 1982
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1982.tb02786.x
Subject(s) - recursion (computer science) , transfer function , function (biology) , reflection (computer programming) , attenuation , inversion (geology) , dispersion (optics) , mathematical analysis , simplicity , geology , computer science , mathematics , physics , optics , algorithm , seismology , evolutionary biology , programming language , engineering , tectonics , electrical engineering , biology , quantum mechanics
Summary Previous theoretical studies on the transfer function of a horizontally layered crustal model for waves incident at its bottom have been based primarily on the application of recursion formulae in obtaining solutions to wave equations. In this application, except for some special cases, it is very difficult to express the transfer function in an explicit form, especially for an anelastic model. To show that this situation can be rectified by an alternative approach, the transfer function for SH ‐waves is derived in this paper by summing rays multiply‐reflected between interfaces with a suitable strategy of ray analysis. The derived function is related explicitly to some physical parameters such as wave travel times between interfaces, reflection coefficients at the interfaces and attenuation and dispersion of waves in each layer of the model; therefore it can be conveniently applied to different models and provides an advantageous position for the development of an explicit inversion method. Due to its mathematical simplicity and its easy application to a general anelastic model, the derived function is in some sense superior to those in the form of traditional recursion formulae.