Open AccessAutoregressive estimation of the splitting matrix of free‐oscillation multiplets
Author(s) -
Masters Guy,
Laske Gabi,
Gilbert Freeman
Publication year - 2000
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.2000.00058.x
Subject(s) - autoregressive model , oscillation (cell signaling) , matrix (chemical analysis) , computer science , coupling (piping) , geology , seismology , quality (philosophy) , current (fluid) , algorithm , statistical physics , physics , mathematics , econometrics , engineering , mechanical engineering , oceanography , quantum mechanics , genetics , materials science , composite material , biology
Summary Recent, large earthquakes, recorded by the rapidly growing global seismic networks, have produced a vast amount of high‐quality data. These new data allow us to develop new techniques to determine the coupling and splitting characteristics of multiplets, and hence determine the 3‐D structure of the Earth. Current techniques tend to be computationally intensive and non‐linear and require detailed models of earthquake sources (which might be unavailable for the large and often complicated events used in free‐oscillation research). Here, we introduce a new technique that allows us to solve for the most general form of the splitting matrix in a few steps without knowledge of the earthquake sources. The method takes advantage of the fact that certain linear combinations of seismograms for a single earthquake have an autoregressive property for which the propagator matrix is related to the exponentiated splitting matrix. To retrieve the propagator matrix, it is necessary to use only displacement scalars from a reference earth model and instrument calibrations to perform a two‐step linear inversion. Multiple events can (and, generally, must) be used to allow retrieval of the propagator matrix. It is straightforward to recover the splitting matrix from the propagator matrix and it is the elements of the splitting matrix that provide linear constraints on the 3‐D structure of the earth. We illustrate the technique by using nearly 900 vertical‐component recordings from 10 large earthquakes to recover the splitting matrices of a variety of multiplets. The results are presented as splitting functions, including some of the first robust anelastic splitting functions to be determined.