Differential Monte Carlo method for computing seismogram envelopes and their partial derivatives
We present an efficient method that is applicable to waveform inversions of seismogram envelopes for structural parameters describing scattering properties in the Earth. We developed a differential Monte Carlo method that can simultaneously compute synthetic envelopes and their partial derivatives with respect to structural parameters, which greatly reduces the required CPU time. Our method has no theoretical limitations to apply to the problems with anisotropic scattering in a heterogeneous background medium. The effects of S wave polarity directions and phase differences between SH and SV components are taken into account. Several numerical examples are presented to show that the intrinsic and scattering attenuation at the depth range of the asthenosphere have different impacts on the observed seismogram envelopes, thus suggesting that our method can potentially be applied to inversions for scattering properties in the deep Earth.