Multicomponent Seismic Data Reconstruction via a Biquaternion-Based Vector POCS Method

Multicomponent seismic exploration as a powerful geophysical technology has attracted more and more attention in seeking and identifying subtle oil and gas reservoirs. However, like traditional single-component acquisition, multicomponent seismic data acquisition also encounters sparse and irregular sampling problems. The conventional reconstruction methods treat multicomponent data as independent components and recover the missing traces in a component-by-component manner. These componentwise approaches ignore the internal mutual relationships among different components and damage the vector characteristics of the seismic wavefield. Quaternion algebra provides an effective vector representation tool for multicomponent data. Upon that, we present a new vector Projection Onto Convex Sets (POCS) method with biquaternion Fourier transform to reconstruct the irregularly missing traces of 3-D and three-component (3-D-3C) seismic data. Compared to the current real-valued quaternion reconstruction methods implemented in the time domain, the proposed method performed in the frequency domain can fully maintain the conjugate symmetry property of the biquaternion data and only reconstruct the positive or negative frequency slices of the observed 3-D-3C data. Besides, the new method can simultaneously interpolate the 3C or 4C data with different missing patterns. We compare the proposed vector POCS method with the scalar POCS method through experiments with a synthetic 3-D-3C dataset and a field 3-D-3C volume. Both experiments demonstrate the effectiveness and superiority of the proposed method.