Evaluating diffuse wavefield and its applications in seismic imaging

The cross-correlation of ambient seismic noise data can be utilized to image subsurface geological structures from ambient noise fields at local, regional, and global scales by extracting Green's functions between seismograph pairs. Precise extraction of empirical Green's functions from the cross-correlations of noise records requires that the seismic wavefield be fully diffuse. This requires the coefficients of the eigenfunction expansion of the seismic records to satisfy the statistical characteristics derived by Weaver and Lobkis (2004) in the time domain. Due to the complexities of the Earth media and noise sources, it is not feasible to obtain accurate eigenfunctions with the corresponding coefficients and adopt these statistical characteristics to evaluate actual seismic data. To resolve this issue, we derive the equivalent expressions in the frequency domain with dimensionless evaluation criteria without requiring the eigenfunctions. The evaluation of random noise, wind-induced vibrations, car- and air-traffic-excited ground motions, earthquakes, and continuous ambient seismic noise records confirms the validity of our evaluation method. We further apply the method to the widely used preprocessing procedures of ambient noise imaging techniques by examining time-domain normalization and spectral whitening operations of earthquake waveforms, thus quantitatively demonstrating how these procedures down-weight the non-diffuse component and improve the degree of waveform diffuseness (as shown in Figure 1). As an application, we select the coda wave signals generated by road traffic and earthquakes that satisfy the diffuse wavefield characteristics and extract the higher-order surface wave dispersion curves from 20-100 s seismic recordings without performing preprocessing procedures. Compared with the traditional surface wave processing process, our method is highly efficient, does not require long recording time and preprocessing such as normalization and whitening, and can be widely used in evaluating diffuse wavefield, imaging subsurface velocity and attenuation structures, and monitoring the temporal changes with high temporal resolution.