Interpreting Cross-correlations of One-bit Filtered Seismic Noise

TL;DR

This paper demonstrates that one-bit filtering of seismic noise preserves the interpretability of cross-correlations even for non-stationary and non-Gaussian signals, offering a robust method for seismic data analysis.

Contribution

It extends the theoretical understanding of one-bit filtering to non-stationary and non-Gaussian seismic signals, validating its effectiveness for practical seismic noise analysis.

Findings

One-bit filtering maintains the relationship with raw correlations for non-Gaussian signals.

It performs at least as well as spectral whitening for certain Gaussian fluctuations.

The method is compatible with current theoretical frameworks and improves robustness against perturbations.

Abstract

Seismic noise, generated by oceanic microseisms and other sources, illuminates the crust in a manner different from tectonic sources, and therefore provides independent information. The primary measurable is the two-point cross-correlation, evaluated using traces recorded at a pair of seismometers over a finite-time interval. However, raw seismic traces contain intermittent large-amplitude perturbations arising from tectonic activity and instrumental errors, which may corrupt the estimated cross-correlations of microseismic fluctuations. In order to diminish the impact of these perturbations, the recorded traces are filtered using the nonlinear one-bit digitizer, which replaces the measurement by its sign. Previous theory shows that for stationary Gaussian-distributed seismic noise fluctuations one-bit and raw correlation functions are related by a simple invertible transformation. Here we extend this to show that the simple correspondence between these two correlation techniques remains valid for {\it non-stationary} Gaussian and a very broad range of {\it non-Gaussian} processes as well. For a limited range of stationary and non-stationary Gaussian fluctuations, we find that one-bit filtering performs at least as well as spectral whitening. We therefore recommend using one-bit filtering when processing terrestrial seismic noise, with the substantial benefit that the measurements are fully compatible with current theoretical interpretation (e.g., adjoint theory). Given that seismic records are non-stationary and comprise small-amplitude fluctuations and intermittent, large-amplitude tectonic/other perturbations, we outline an algorithm to accurately retrieve the correlation function of the small-amplitude signals.