Calibrating Phase Delay Measurements and Comparison of 3-D Waveform Kernels with and without Near-field Terms

We present the calibration of an automated scheme to properly window the fundamental surface wave mode of an event record. Multi-taper fundamental mode phase delay measurements were made on a synthetic dataset. Measurement errors are reduced when minimal over tone energy is included in the window. The time window is calibrated by simply varying the minimum and maximum surface wave velocities used to determine the beginning and ending window times with source-receiver distance, as opposed to constant velocities. We compare phase delay measurements with and without calibration against measurements made manually. Manual window setting of a small representative subset of event seismograms are used to adjust these minimum and maximum surface wave velocities. The orthogonal 2.5π-prolate spheroidal wave function eigentapers (Slepian tapers) used in multi-taper methods reduce noise biasing, and can provide error estimates in phase delay measurements. Additionally, we examine the effects of excluding near-field terms in the calculation of 3-D finite-frequency waveform kernels for Rayleigh and Love waves on a synthetic dataset. Two methods of kernel calculation based on the single scatterer Born approximation are compared, that of Panning and Nolet (2008) and Zhao and Chevrot (2011). The Panning and Nolet (2008) method calculates the strain Green's tensors for the source-scatterer and scatterer-receiver paths by the summation of asymptotic surface wave modes, which is an inherently far-field approximation. Waveform kernels are then found by convolution (in the time domain) of these strain Green's tensors. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. The Zhao and Chevrot (2011) method creates a database of the set of strain Green's tensors for the source-scatterer (two-sided strain Green's tensor) and scatterer-receiver (one-sided strain Green's tensor) paths, and is calculated by normal mode summation. The full-wave waveform kernels are simple convolution (in time domain) of the two-sided and one-sided strain Green's tensors. These kernels are also formulated based on a hexagonal symmetry, but with a vertical or horizontal orientation. Kernels from the two methods are plotted as phase delay kernels and compared to determine the effects of the near-field terms on kernel shape. Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. A global input model with constant isotropic and anisotropic strength, and a constant direction of anisotropic symmetry axis was used.