Interpreting cross-correlations of one-bit filtered seismic noise

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 non-stationary Gaussian and a very broad range of 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.

Generalized interferometry – I: theory for interstation correlations

“…The dashed curve of the forward modelling error is mostly hidden by the curve for the processed correlations. [ER] Capdeville 2010;Cupillard et al 2011;Hanasoge & Branicki 2013). Therefore, this special case constitutes a successful test of the effective forward modelling theory developed in the previous sections.…”

Reflecting boundary conditions for interferometry by multidimensional deconvolution

“…We acknowledge, however, that for such applications, specific preprocessing of the field data will be required. 46,47 In general, frequent interruption of the stream of ambient seismic noise by earthquakes and other (anthropogenic) events complicate the application of interferometric methods. 30 Additionally, the assumption of a single-mode surface wave overwhelming other surface-wave modes may in practice not always be valid, 48 requiring different surface-wave modes to be separated prior to application of MDD.…”

Passive seismic monitoring with nonstationary noise sources

“…We deliberately do not apply non-linear processing techniques, such as spectral whitening or one-bit normalization (Bensen et al, 2007;Groos et al, 2012), even though the latter has been shown to not add a systematic bias to the measurement in the case of Gaussian wavefield statistics and for a variety of other distributions (Hanasoge and Branicki, 2013;Fichtner et al, 2016). We deliberately do not apply non-linear processing techniques, such as spectral whitening or one-bit normalization (Bensen et al, 2007;Groos et al, 2012), even though the latter has been shown to not add a systematic bias to the measurement in the case of Gaussian wavefield statistics and for a variety of other distributions (Hanasoge and Branicki, 2013;Fichtner et al, 2016).…”