Extended Hilbert Transform and Application for Seismic Attributes

Abstract

Abstract The Hilbert transform (HT) has been widely used in seismic data processing and interpretation. However, HT results exhibit lower noise robustness and resolution. This paper extends HT by introducing three orders greater than or equal to 0 and the sign function in frequency domain and propose an extended Hilbert transform (EHT) which has many advantages over the HT—particularly noise robustness, resolution, and a variety of applications. The output of EHT depends on the choice of the three orders and the sign function. Analysis of synthetic cosine signal and hypothetical channel model shows that EHT helps to retain the desired characteristics of HT while overcoming its shortcomings and exhibits better noise robustness and higher resolution than HT. Analysis of real 3‐D seismic data application demonstrates that EHT shows a very desirable ability to capture subtle geologic features and can be well used for seismic attributes and other fields involving digital data processing.

Keywords

• Hilbert transform
• noise robustness
• resolution
• sign function
• extended Hilbert transform
• generalized Hilbert transform