Modelling the teleseismic P coda envelope: depth dependent scattering and deterministic structure

Abstract

The P-coda of teleseismic events contains information on the small-scale random structure of the near-receiver lithosphere. Various scattering theories have been suggested to model the time and frequency dependence of the coda envelopes for a given random structure. A specially simple model is the energy-flux model that describes P-coda excitation in terms of scattering attenuation of the direct P-wave front without dealing with the details of the scattering process. It is based on energy conservation and is valid for both weak and strong scattering cases. Here, the energy-flux model is extended to include a depth-dependence of the scattering structure. A variation of the depth range of the random medium manifests itself mainly in different decay rates of the coda, whereas the coda amplitudes at small lapse times behind the direct arrival are sensitive to the scattering strength of the shallow structure. Strongly heterogeneous layers at greater depths yield more complicated coda shapes which cannot be fully described by parameters like decay rate or coda Q . Full waveform simulations in random structures superimposed onto a deterministic layered model show that (1) the energy-flux model yields reliable results, and (2) the effects of deterministic layering on the coda envelopes are relatively small for waves with small incidence angles and realistic scattering strength and therefore may be neglected in coda inversions for teleseismic waves.