Finite-Frequency Delay Times of Phase Segments for Body Waves

Abstract

ABSTRACT We propose a new way of measuring the delay times of body waves, based on the time differences between short segments of a phase. Using this proposed methodology, which we call the delay time of phase segments (DTPSs) method, we believe it is possible to (1) optimize the reduction mode that reduces finite-frequency kernels to ray-theoretical kernels, (2) reduce computation and memory storage costs by reducing the volume of finite-frequency sensitivity kernels, and (3) achieve greater linearity between delay times and velocity variations for larger velocity perturbations up to ±30%. The DTPS kernel can also be used in adjoint methods. Theory and our calculations indicate that the width of the DTPS kernel decreases as the length of the phase segment decreases from the length of the entire phase. The scattering caused by inhomogeneity is more likely to complicate the latter parts of a phase more than its beginning. For this reason, the DTPS method using a phase segment in the first quarter of a phase is robust for velocity perturbations up to ±30% from the initial model, whereas traditional methods using the entire phase are only robust for velocity perturbations up to ±10%. The DTPS method may reduce computation times by up to 70% because the size of the DTPS kernels is smaller than that of other methods by up to 70%. Synthetic tests indicate that the DTPS method produces inverse models nearly as accurate as generalized seismological data functionals.