Generalized Pattern Search Algorithm for Crustal Modeling

Mulugeta Dugda,Farzad Moazzami

doi:10.3390/computation8040105

Abstract

In computational seismology, receiver functions represent the impulse response for the earth structure beneath a seismic station and, in general, these are functionals that show several seismic phases in the time-domain related to discontinuities within the crust and the upper mantle. This paper introduces a new technique called generalized pattern search (GPS) for inverting receiver functions to obtain the depth of the crust–mantle discontinuity, i.e., the crustal thickness H, and the ratio of crustal P-wave velocity Vp to S-wave velocity Vs. In particular, the GPS technique, which is a direct search method, does not need derivative or directional vector information. Moreover, the technique allows simultaneous determination of the weights needed for the converted and reverberated phases. Compared to previously introduced variable weights approaches for inverting H-κ stacking of receiver functions, with κ = Vp/Vs, the GPS technique has some advantages in terms of saving computational time and also suitability for simultaneous determination of crustal parameters and associated weights. Finally, the technique is tested using seismic data from the East Africa Rift System and it provides results that are consistent with previously published studies.

Highlights

Receiver functions are time series determined by the deconvolution of vertical component seismograms from radial component seismograms [1]
In the few sections, we provide the method making use of receiver functions inversion and H-κ stacking algorithm followed by the generalized pattern search (GPS) technique
We developed a technique to solve the problem of inverting receiver functions to find optimal crustal parameters and optimal weights using a generalized pattern search (GPS) by setting up the problem as an optimization problem

Summary

Introduction

Receiver functions are time series determined by the deconvolution of vertical component seismograms from radial component seismograms [1]. Receiver functions consist of a number of seismic phases, the arrival times of which are correlated to discontinuities in the crust and upper mantle. Receiver functions represent the impulse response of the structure of the earth beneath the seismic station [2]. H-κ stacking has been applied in many crustal structure studies (e.g., [4,5,6]). In some of these studies, the values of weights, which are necessary components for the H-κ stacking procedure, have been assigned through assumptions or using the Monte Carlo simulation technique (e.g., [3,7]) or by using genetic algorithms (GA) [8]. The main objective of this paper is to harness the generalized pattern search (GPS) technique to simultaneously determine optimal or near optimal values of weights along with H and κ values

Objectives

Methods

Discussion

Conclusion