Widely linear denoising of multicomponent seismic data

Abstract

Seismic data processing is a challenging task, especially when dealing with vector‐valued datasets. These data are characterized by correlated components, where different levels of uncorrelated random noise corrupt each one of the components. Mitigating such noise while preserving the signal of interest is a primary goal in the seismic‐processing workflow. The frequency‐space deconvolution is a well‐known linear prediction technique, which is commonly used for random noise suppression. This paper represents vector‐field seismic data through quaternion arrays and shows how to mitigate random noise by proposing the extension of the frequency‐space deconvolution to its hypercomplex version, the quaternion frequency‐space deconvolution. It also shows how a widely linear prediction model exploits the correlation between data components of improper signals. The widely linear scheme, named widely‐linear quaternion frequency‐space deconvolution, produces longer prediction filters, which have enhanced signal preservation capabilities shown through synthetic and field vector‐valued data examples.

The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

“…Their usefulness lies in the fact that they operate in higher-dimensional spaces, and are thus able to explain the relationships between the dimensions. As an example, we can mention the use of hypercomplex domains in virtual reality [17,18], acoustic applications [19,20], communication [21,22], image processing [23,24], seismic phenomena [25,26], robotics [27,28], materials [29,30], avionics [31,32], etc.…”

Sinusoidal Seismic Noise Suppression Using Randomized Principal Component Analysis

“…Seismic denoising methods have been developed by many scholars. For random noise attenuation, prediction-based methods [2][3][4][5], sparse-transform-based methods [6,7], rankreduction-based methods [8][9][10], machine-learning-based methods [11][12][13][14] and orthogonalization [15] are most common used algorithms. For the removal of harmonic noise [16,17], there are also many different methods presented besides the analog notch filter.…”