Frequency‐dependent phase coherence for noise suppression in seismic array data

Abstract

[1] We introduce a coherence measure for seismic signal enhancement through incoherent noise attenuation. Our processing tool is designed for densely spaced arrays and identifies signals by their coherent appearance. The approach is based on the determination of the lateral phase coherence as function of distance, time, frequency, and slowness. The coherence is derived from the local phases of neighboring stations which we obtain from analytic signals through the S-transform. The coherence is used to attenuate incoherent components in the time-frequency representations of the seismic records. No waveforms are averaged in our approach to maintain local amplitude information. This way we construct a data-adaptive filter which enhances coherent signals using the frequency-dependent and slowness-dependent phase coherence. We explain the method and show its abilities and limitations with theoretical test data. Furthermore, we have selected an ocean bottom seismometer (OBS) record section from NW-Spain and a teleseismic event registered at Spanish broadband stations to show the filter performance on real array data. Incoherent noise has been attenuated in all cases to enable a less ambiguous signal detection. In our last example, the filter also reveals weak conversions/reflections at the 410-km and 660-km discontinuities which are hardly visible in the unfiltered input data.Citation: Schimmel, M., and J. Gallart (2007), Frequency-dependent phase coherence for noise suppression in seismic array data,

Ambient Seismic Noise Tomography of a Loess High Bank at Dunaszekcső (Hungary)

“…3 Cross-correlation functions computed using di↵erent normalisation and stacking techniques. The gray line shows the correlograms obtained using one-bit normalisation, conventional cross-correlation, and linear stacking, while the overplotted black line shows the cross-correlation function of phase correlation and time-frequency phase weighted stacking (Schimmel and Gallart, 2007). Both correlograms are amplitude normalised.…”

“…Sabra et al, 2005a;Shapiro et al, 2005;Yang et al, 2007;Cho et al, 2007;Bensen et al, 2009) and 2) time-frequency phase weighted stacking (tf-PWS) described by Schimmel and Gallart (2007), which has been applied in some recent ambient seismic noise tomography studies (e.g. Ren et al, 2013;Dias et al, 2015).…”

Spectral balancing GPR data using time-variant bandwidth in the t-f domain

“…The time-variant absolute phase of the signal is calculated by the phasor e ‫מ‬i2 ft ͑Pinnegar and Mansinha, 2003;Schimmel and Gallart, 2007͒. The S-transform and the WT exhibit progressive resolution, whereas the resolution of the STFT is independent of time ͑Stockwell et al, 1996͒.…”

“…It is common practice to apply a band-pass filter to partially circumvent this problem. To achieve this, time-varying band-pass filtering is better performed in the t-f domain ͑Schimmel and Gallart, 2007;Parolai, 2009͒. Irving and Knight ͑2003͒ and Bradford ͑2007͒ use the S-transform ͑Stockwell et al, 1996͒ and short-time Fourier transform ͑STFT͒, respectively, to study the dominant frequency variation of GPR traces.…”

The S-Transform and Its Inverses: Side Effects of Discretizing and Filtering

“…For further practical examples of the filtering with the ST and its inverses, the reader can look at [12].…”