Two‐layer earth model corrections to the MLTWA estimates of intrinsic‐ and scattering‐attenuation obtained in a uniform half‐space

SUMMARY Following the numerical scheme of Yoshimoto we synthesized seismogram envelopes in the multiple scattering framework. We supposed the earth model constituted by a inhomogeneous crust overlying a transparent mantle. In this model velocity is assumed depth‐dependent through a continuous function of the depth, v = v ( h ) ; Moho discontinuity is approximated by a sharp increase of the velocity around the crust–mantle boundary; inhomogeneity in the crust is parametrized through a depth‐dependent scattering coefficient (the inverse of mean free path) g = g 0 f ( h ) , with f ( h ) function of depth, and g 0 the scattering coefficient at zero depth; intrinsic attenuation is parametrized in terms of the intrinsic attenuation coefficient, η i , that is assumed independent of depth. Generating a suite of energy envelopes as a function of lapse time and distance, for reasonable values of B 0 , the seismic albedo and Le −1 , the extinction length inverse (which are functions of g 0 and η i ), we span a wide range including most of the measurements done through the world. Then, we apply the ordinary MLTWA technique to these synthetic envelopes. In this application, we assume a constant g and a constant velocity, v = < v ( h )> which equals the average of v ( h ) calculated in the depth range characteristic of the volume encompassed by the scattered waves. In this way, we obtain the estimates of B 0 , and Le −1 , for a constant half‐space. The relationship between the estimates of B 0 and Le −1 , obtained assuming half‐space, and the correspondent values used in the simulation, results to be well approximated by a second‐order polynomial. Then, evaluating the best fit polynomial coefficients, we obtain a correspondence map between attenuation parameters retrieved for a uniform model with those characteristic of a more realistic structure. This map is useful to reinterpret all the couples B 0 and Le −1 already calculated through the world in geological structures similar to the one adopted in our simulation. Results show that scattering and intrinsic‐attenuation coefficients estimated using MLTWA in the assumption of a uniform half‐space are always overestimated.