On the use of P-wave seismograms to identify a double-couple source

Abstract

Abstract We examine the likelihood of observing different values of the relative amplitude of P, pP, and sP on an earthquake seismogram, given that the source is a point double couple at a known teleseismic distance, with an unknown orientation and every orientation equally likely. A display referred to as a compatibility plot is devised to show the probability density of seismogram types over the complete range of amplitude ratios and is computed for seismograms observed at selected source-receiver distances. These plots show in a quantitative way that the occurrence of seismograms from a double-couple source is highly nonuniform within the range of amplitude ratios and that, for many of the ratios, seismograms are not generated for any orientation. It is thereby concluded that individual teleseismic relative amplitude observations can provide powerful evidence for or against the validity of the double-couple assumption. Differences in, for example, source layer velocity and above-source velocity structure are shown to have only a limited effect, so that real data can provide valuable measurements, even when appropriately wide error bounds are placed on the relative amplitudes to allow for all sources of uncertainty. A pronounced linear concentration of probability density is identified on some compatibility plots, and its existence is verified analytically.