A Frequency Domain Methodology for Quantitative Evaluation of Diffuse Wavefield with Applications to Seismic Imaging

Ambient Noise Imaging (ANI) of subsurface structures relies on seismic interferometry of diffuse seismic wavefields. However, the lack of effective methods to quantify and identify highly diffuse waves hampers applications of ANI, particularly in evaluating seismic attenuation and monitoring structural changes with high temporal resolution. Conventional ANI approaches require data normalization, which effectively suppresses the non-diffuse component with large amplitude but also results in significant loss of amplitude and phase information in the continuous seismic records. In this study, we propose a frequency domain method to quantitatively evaluate the degree of diffuseness of seismic wavefields by analyzing their statistical characteristics of modal amplitudes for stationarity and randomness. Tests on synthetic waveform and field nodal records show that the proposed method can effectively distinguish between diffuse and non-diffuse waveforms for either single- or three-component data. As an application, we identify a 60-s-long diffuse coda of a local M 2.2 earthquake recorded by a dense nodal array on the San Jacinto Fault Zone, and successfully extract high-quality dispersion curve and Q-value without performing data normalization. These results are consistent with those obtained by conventional methods that assess the correlation between coherency and the Green's function, and by modeling ballistic waves generated by road traffic. Our proposed method can advance the imaging of subsurface velocity and attenuation structures as well as monitoring temporal changes for scientific studies and engineering applications. Earthquakes, explosions, and traffic events can generate seismic waves that travel through the Earth. As these direct waves encounter heterogeneous earth interior, they scatter and change direction, leading to more diffusive propagation. Fully diffuse waves can be used to image the subsurface structures. In this study, we develop a reliable and efficient method to measure how diffuse a seismic wavefield is at different frequencies. Tests on synthetic and field data show that the developed method can reliably differentiate between diffuse and non-diffuse waves. This method can improve our ability to use spread out wavefields for imaging and monitoring the Earth's interior. We present an efficient methodology to quantify seismic wavefield diffuseness based on stationarity and randomness in the frequency domain The method avoids waveform normalization and extracts reliable empirical Green's functions from interferometry using diffuse waveforms We validate the method by extracting dispersion curves and Q-values from the 60-s-long diffuse coda of a local M 2.2 earthquake