Fast computation of local dips using the one-lag correlation method

Abstract

We adapt the one-lag correlation (OLC) method to estimate the local dips of seismic events or velocity contrasts. The resulting local dips have extensive applications in exploration geophysics, including seismic inversion regularization, computation of seismic attributes like coherence-cube, and facilitating structural-oriented smoothing and extrapolation techniques. Compared to the widely adopted structure tensor (ST) method, the proposed OLC algorithm exhibits notable advantages. The OLC method is characterized by a recursive calculation process that yields significant computational efficiency, boasting an approximately 100 times faster performance for 3D scenarios. The fundamental principle of this novel approach lies in the computation of local dips by using the ratio of two inner products, i.e., OLC, performed on a 2D/3D array along the vertical and horizontal axes, respectively. Crucially, the elements of this array consist of complex numbers derived from the application of the Hilbert transform on the corresponding real-number inputs. Furthermore, the implementation of this algorithm is remarkably straightforward, as exemplified by the concise nature of the code, which comprises a mere ten lines of programming instructions. The OLC method excels in accuracy, surpassing the performance of the ST method, and exhibits superior resistance to random noise. Compelling demonstrations are provided herein to corroborate these desirable properties of the OLC approach, using both synthetic and field data examples.