Scat-Cad: a Mathcad 2000 professional package to model the energy decay due to seismic attenuation

Abstract

An important taskin seismology is the estimation of attenuation parameters for the earth medium, as they permit the reconstruction of the source spectral shape. Further, knowledge of the attenuation adds information on the constitution of the earth’s interior. In particular, it allows the modeling at small scale of site effects which contribute to seismic hazard studies. Several methods are frequently used to obtain this information from seismological data. Most of them are based on the estimation of the spectral decay coefficient with hypocentral distance, which is proportional to the inverse of the total quality factor of the earth medium. The attenuation parameter estimated in this way contains the combined effects of intrinsic and scattering attenuation. Scattering attenuation is produced by interaction of the primary waves with the elastic heterogeneity (which can be viewed as space fluctuations of the elastic parameters like velocity, for example). This interaction produces a secondary radiation, which comes to the receiver later than the primary. In this way, the apparent energy of the primary waves is lost. The intrinsic dissipation is the real energy loss produced by the transformation of the energy into heat. It is not always easy to interpret the (total) attenuation results in terms of geological structures: a medium which contains high heterogeneity may in fact produce a high-energy decay as a function of source–receiver distance, in apparently the same way in which a uniform, but highly dissipative medium (as a magmatic reservoir for example) can do. So, it is necessary to model the seismic propagation in terms of both scattering and dissipative attenuation. To perform this taska scattering model is necessary. Hoshiba (1993) modeled the propagation in an earth medium filled by randomly but uniformly distributed heterogeneity by means of numerical simulations. He hypothesized isotropic scattering and included multiple scattering, providing as output a set of energy–distance curves evaluated as a function of total attenuation and seismic albedo (L � 1 e and B0; respectively). These two parameters are defined as a combination of intrinsic and scattering attenuation coefficients, or what is the same, of the intrinsic and scattering quality factors. B0 ¼ QT =QS; where QT and QS are, respectively, the total and the scattering quality factors; L � 1