Testing the Amplitude of the Deconvolution‐Based Ambient Field Green's Functions by 3‐D Simulations of Elastic Wave Propagation in Sedimentary Basins

We test the amplitude of deconvolution‐based ambient field Green's functions in 3‐D numerical simulations of seismic wave propagation. We first simulate strongly scattered waves in a hypothetical 3‐D sedimentary basin with small‐scale heterogeneities, which provides an ideally random environment to test various approaches of extracting the amplitude of Green's functions, as the deterministic station‐to‐station Green's functions can be computed in the given velocity structure. Our second model computes the station‐to‐station Green's functions in the Community Velocity Model (S4.26) for Southern California and compares them with the Green's functions extracted from 1 year of ambient noise data. In both models, remarkable waveform similarity among different Green's functions is obtained. In the hypothetical basin model where the wavefield is nearly random, both the correlation‐ and deconvolution‐based Green's functions contain robust amplitude information. However, large‐amplitude biases are observed in the Green's functions extracted from ambient noise in Southern California, showing a strong azimuthal dependence. The deconvolution approach in general overestimates the amplitude along the direction of noise propagation but underestimates it in other azimuths. The correlation approach with temporal normalization and spectral whitening generates similar amplitude to the deconvolution in a wide azimuthal range. Our results corroborate that the inhomogeneous distribution of noise sources biases the amplitude of Green's functions. Carefully reducing these biases is necessary to use these ambient field Green's functions in the virtual earthquake approach.