Residence time of diffuse waves in the crust as a physical interpretation of coda Q: application to seismograms recorded in Mexico

We consider a simple model for elastic wave propagation in the Earth's lith osphere consisting of a heterogeneous and scattering crust overlying a homo geneous mantle; that is, we neglect backscattering from the upper mantle. T his rough condition is not strictly valid everywhere, but this model allows us to investigate the effects of variations of diffracting properties betw een crust and mantle on the coda decay. The free parameters describing the wave propagation are the mean free path of the waves and the intrinsic abso rption in the crust. In the framework of the radiative transfer theory, we treat, accurately, jumps in S-wave speed and the mean free path at the Moho . Without intrinsic absorption, this configuration yields a synthetic coda decay 1 / t exp(-2 pi ft/Q(c)*), a form similar to that proposed by Aki & C houet (1975) to parametrize the observations. The exponential decay in our purely elastic model is due to the partial leakage of diffuse energy into t he mantle. In order to test the applicability of our model, we have determined the cod a Q parameter (Q(c)) in the 1-15 Hz frequency band from data recorded at fo ur stations in Mexico. In the low-frequency regime (around 1 Hz), we sugges t that the energy leakage significantly affects coda Q, whilst at higher fr equencies (around 10 Hz), the anelastic attenuation dominates. A weak intri nsic absorption expressed by a frequency-independent parameter, Q(i), of ab out 1000 accounts satisfactorily for the observed Q(c) values in the whole frequency range. Our very simple model has only two free parameters and off ers an attractive alternative physical interpretation of coda Q. In Mexico, this model is sufficient to interpret the coda observations. According to our model, in regions where the mean free path is much larger than the crustal thickness (weakly heterogeneous crust), the leakage effect should be small, and the observed Q(c) will mainly be due to the intrinsic absorption. On the other hand, when the mean free path is of the order of the crustal thickness (strongly heterogeneous crust), we predict a strong s ensitivity of the decay rate of the coda to the crustal thickness. This dep endence may be important for the interpretation of the regional variations of coda Q. We propose introducing a new parameter, tau(d), the residence ti me of diffuse energy in the crust, which is physically more meaningful than a quality factor to quantify the leakage effect.