KMAH index and separation of PSP-waves from streamer data

Abstract

The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The travel-time curve becomes multi-valued and the geometrical spreading correction factor tends to zero due to energy focusing. To select the regions of possible triplications (caustics) of travel-times, which can arise during the propagation of reflected seismic waves, we use the Keller–Maslov–Arnol’d-Hormander (KMAH) index. The identification of such regions improves the selection of signals associated with target reflecting horizons and their use in solving various inverse dynamic problems, including amplitude-versus-offset (AVO) and full-waveform inversions. The importance of the KMAH index increases in 4D surveys when the structure of the model is already known, and it is necessary to conduct a detailed analysis of the shapes of seismic signals with increasing accuracy when solving inverse seismic problems. In addition, this index can be valuable when solving various marine seismic problems associated with single and converted waves, in particular with PSP-waves. The present work is dedicated to the separation of signals associated with this type of wave using surface marine seismic data. However, the proposed algorithm has a wider application. It is based on: (i) a priori information on the medium under study; (ii) ray tracing method. The ray tracing method enables the identification of the corresponding signals and the determination of the time and space intervals, in which such signals are most accurately traced. These intervals are used in the selection of target signals, particularly signals related to PSP-waves. In order to select optimal areas of observation with higher amplitudes of target signals, we use the $$\tau -p$$ transform. To improve the stability of the signal separation, KMAH index is used. This approach allows the elimination of possible triplications (caustics) in the travel-time curve from the selected intervals.