Synthetic seismograms in a spherical Earth using exact flattening transformation

Abstract

In a layered spherical earth, we take inhomogeneity in each shell such that the solutions of equation of motion are obtained in terms of exponential functions. In this case, the propagator matrix becomes similar to that in a flat earth. We call such transformation as ‘exact flattening transformation’. This transformation allows us to study wave propagation using the rich algorithms of a flat earth and to achieve similar accuracy and efficiency as in a flat earth. Here we generate synthetic seismograms in a spherical earth through exact flattening transformation using the corresponding computer code of a flat layered earth. Comparison of vertical, radial and transverse components of waveforms with approximate flattening transformation has been made for epicentral distances between 20 deg and 60 deg; comparisons show that the body waves fairly agree in both transformations but disagree mainly in Rayleigh wave part; the disagreement increases with the increase of epicentral distance.