Signal detection and enhancement for seismic crosscorrelation using the wavelet-domain Kalman filter

Abstract:

Abstract: Crosscorrelation is a classical signal-processing technique that plays an important role in exploration and earthquake geophysics. Seismic velocity estimation utilizes the crosscorrelation between observed and predicted seismic records in traveltime tomography. The crosscorrelation between two stations represents the Green’s functions retrieved from ambient noises in passive seismic interferometry. It can be used to estimate the subsurface velocity and amplitude information. The calculation of crosscorrelation usually assumes that the input data are stationary, however, the real seismic data are often non-stationary, due to the presence of multiple wave-modes. The seismic crosscorrelations often have low signal-to-noise ratio and frequently fail to provide correct information for subsequent processing. To address this problem, we develop a comprehensive technique to reduce contamination and improve the quality of crosscorrelation in the wavelet domain. The new procedure includes the forward wavelet transformation of raw records, the crosscorrelation between wavelet coefficients, image object detection, Kalman-filter object tracking, and inverse wavelet transformation to produce the new crosscorrelation gathers. We effectively remove the unwanted components associated with contaminated wave-modes as the proposed detection and tracking algorithm can accurately extract the target wave-mode. We validate the method for three datasets: a marine streamer survey, a borehole survey, and a broadband dataset from seismic stations. We demonstrate that the proposed method can significantly improve the signal-to-noise ratio of the seismic crosscorrelations, considerably enhancing the quality of the data for subsequent advanced crosscorrelation-based seismic processing.

1. Introduction

Crosscorrelation is a powerful signal-processing tool and extensively adopted in pattern recognition and signal detection among different industries, such as acoustics, medical applications, and geophysics. It projects one signal onto another is a means of measuring how much of the second signal is present in the first, so it can detect the presence of known signals as components of more complicated signals(Keane and Adrian 1992). Crosscorrelation of pressure transient and acoustic waves was applied for leak detection and location in the pipeline network of water authorities (Hafezi and Mirhosseini 2015). An active radar with omnidirectional sensors used crosscorrelation to measure the travel time difference between a forward signal, that was transmitted, and a received backscattered signal, to estimate the range of a radar target (Silvia 1987). In clinical ultrasounds, the crosscorrelation function between the transmissions and reflections recorded with ultrasound transducers coupled to the skin could measure the geometry of different tissues (Viola and Walker 2003).

The usage of crosscorrelated seismic waveforms plays an essential role in several stages in geophysics (Yilmaz 2001). For instance, in traveltime-based velocity building methods, the crosscorrelation between observed and calculated records (Luo and Schuster 1991) extracted phase shifts to constrain subsurface velocity models. When the compared waveforms were simple and similar, the traveltime difference between two traces was estimated by selecting the lag that corresponds to the peak of the crosscorrelation (Knapp and Carter 1976; Sun et al. 2016). Crosscorrelation methods usually assume that the input data is stationary, whereas this is not the case for most of the applications due to the presence of multi wave-modes. This argument is no longer valid in cases where inequivalent amplitude spectra associated with complex multi-wave modes (Van Der Hilst and De Hoop 2005). Another important geophysical application is seismic interferometry: a stack of crosscorrelations of traces recorded by two receivers over sources that were uniformly distributed in three-dimensional heterogeneous earth could retrieve the Green’s function activated at one receiver and received by the other (Curtis et al. 2009). This assertion applied to passive-source records in the ambient noise range from borehole microseismic (Grechka and Zhao 2012) to global seismology (Niu et al. 2008). The reconstructed Green’s function retrieved from crosscorrelations of ambient noises produced either P- or S-waves traveling between the receivers, which were then transferred to subsurface velocities at different scales. However, the assumptions of an enclosing boundary of sources behind seismic interferometry were often not satisfied in most acquisitions (Zhao and Li 2018a). It, therefore, produced a low signal-to-noise ratio (SNR) crosscorrelation gathers and unreliable Green’s functions. Interferometric data required advanced processing to restore the coverage in a way that crosscorrelation can still work effectively (Nakata et al. 2011).

Similar to crosscorrelation, the wavelet transform was widely used in acoustics, medical applications and geophysics areas (Mallat and Zhang 1993). It decomposes a signal into a series of time-scale wavelet coefficients. The scale measures, which are closely related to frequency, can be used to analyze and filter data (Diallo et al. 2006; Yu et al. 2007). Crosscorrelation was also computed in the wavelet domain (Li and Nozaki 1997) and was extensively applied in Earth’s science studies of river runoffs and global climatic index analysis(Labat 2005). In addition to this time series analysis, Kalman filtering can function as a powerful spatial algorithm for recursively updating a prediction of a system by processing a succession of measurements over distances. After each spatial measurement, a new offset prediction is produced by the filter’s measurement step (Bishop and Welch 2001). It uses a series of measurements containing statistical noise and other inaccuracies, so the algorithm can produce estimates of unknown variables that tend to be more accurate than those based on a single measurement alone. Kalman filters demonstrated its usefulness in various applications such as navigation satellite systems and computer graphics because of its relatively simple form and require small computational power (Kim and Bang 2018). Although some excellent geophysics works of literature employed the Kalman filter for seismic deconvolution(Crump 1974) and time-lapse seismic history matching(Emerick and Reynolds 2012), the industry was not fully taken advantage of these power algorithms, for example, by performing them into the multi-dimensional spatial, frequency and time domain. Specifically, the traveltime estimation in velocity estimation and passive seismic interferometry with large-offset acquisitions contains informative correlated wave-modes in all dimensions. The quality of the extracted signal depends on the extent to which crosscorrelated wave-modes are interrelated at different frequencies, and how these time-frequency quantities move along spatial locations.

Many geophysical applications can be adapted to this proposed workflow, but the scope of this paper limits to be traveltime-difference estimation and passive seismic interferometry. We develop a new method using crosscorrelation in the wavelet domain that exploits non-stationary variations to simplify the complexity of correlation gathers associated with multi-wave-mode contaminations. Specifically, the method maps data from the time-offset (TX) domain into the TF domain. The multi-modes non-stationary gathers are then decomposed into several simple, single-mode and stationary components. Kalman filter robustly detects and tracks the target wave-mode via a sequence of spatial locations from these correlated constituents. The new method consists of the following steps: (1) transforming seismic records to the wavelet domain before applying crosscorrelation; (2) crosscorrelating the wavelet coefficients; (3) detecting target wave-modes via image segmentation in the TF domain; (4) tracking target wave-modes via Kalman filtering in the time-frequency-offset (TFX) domain; (5) transforming the filtered wavelet coefficients back to the TX domain. This method allows effective measurements of target wave-modes, using image segmentation and Kalman filtering for the wavelet-domain correlation coefficients. Meanwhile, it effectively attenuates non-desired wave-modes, and produces much higher SNR crosscorrelation functions, leading to high-quality data for subsequent seismic velocity estimation at different scales.