The ambient seismic field
The signal that is sometimes regarded as noise, the ambient seismic field, has recently been shown to provide important
information about Earth's structure. By looking at the spatially coherent signals between seismic stations (and under certain
conditions) we are able to extract the Green's function of the medium, as if one station behaved like a source and the
others record the response of the Eartth's crust and upper mantle. In my research I have been focusing in additional
information observed in the amplitudes of these Green's functions, both in time and frequency domains.
Earthquake source scaling
A major question in seismology is whether the earthquake process is self-similar. Is a M = 8.0
earthquake simply a M = 2.0 earthquake scaled by a large factor or is the physics of the two
processes different? There is continuing interest in the question of earthquake scaling and
there is currently a debate regarding the self-similarity of the earthquake rupture
over their entire size range. Seismologists use some parameters (such as seismic moment, stress drop, and radiated seismic
energy) to describe the earthquake rupture. The behavior of some of this parameters as a
function of the earthquake size provides information about the physics of the rupture process.
Error analysis
Part of the difficulty in studying earthquake source scaling is the accurate estimation
of the source parameters, accounting for seismic attenuation, path effects, etc. These
factors lead to considerable uncertainties in the estimation of stress drop or radiated
seismic energy. What is often missing in many studies is these measurements of uncertainty,
which are of key importance when comparing two results, or when comparing different
methods of analysis.
Multitaper analysis
The are multiple applications in geophysics (e.g., seismology, climate, electromagnetics),
engineering (e.g., structural engeneering) and even the social sciences (e.g., economics)
where relevant information may be extracted from the frequency content of the spectrum.
In 1982 David J. Thomson introduced the multitaper spectrum algorithm which has been widely
used since. In my analysis of the earthquakes I have used the multitaper method extensively. I wrote a
Fortran 90/95 Library (mwlib.html) with many more features than
other available codes. The algorithm allows for the estimation of the power spectra of a
signal, confidence intervals, phase information, correlations, coherency, deconvolution, etc..