Diving Wave Q Tomography for Compensating Absorption and Dispersion of Shallow Gas Cloud

Gas clouds in the overburden can significantly distort seismic waves due to the absorption effects, pose severe imaging problems to the structures underneath. Q tomographic inversion has been developed to estimate absorption model which can be used to compensate for absorption effects during the process of migration. However, it is challenging to estimate absorption model at near surface by reflection based Q tomographic inversion due to limited available offset information at shallow. In this paper we propose a new approach for Q tomographic inversion using dissipation time information measured from first arrivals of diving wave to address this challenge.

We propose to compute the average instantaneous frequencies of the first arrival events and measure the dissipation time of these events. The measured dissipation time will then be back-projected along ray path to reconstruct the attenuation distribution. Following the process of estimating the instantaneous frequency with maximum entropy method, we use discrete Wigner-Ville distribution to estimate the instantaneous frequency of the event in time domain. When the instantaneous frequency of the source wavelet and the instantaneous frequency of the received seismic waveform are computed respectively, the shift of the instantaneous frequency can be generated. For a given dissipation time, we can precisely predict the instantaneous frequency shift of a source wavelet through applying absorption filter, thus we can build a frequency shift table indexed by the dissipation time. The absorption effect is determined solely by the dissipation time, independent of the actual path the seismic wave has propagated, which allows us to pre-compute and map the measured frequency shift to the tabulated dissipation time. In short, we propose the following flow for Q tomography using diving wave: firstly, pick the first arrivals of seismic data in shot domain; secondly, estimate the instantaneous frequencies and measure the dissipation time associated with the picked events; finally, estimate the inverse Q model through tomographic inversion. We will demonstrate how our approach can accurately estimate a near surface Q model and can be included in the Q compensation process to fully account for the frequency dependent attenuation effects observed on seismic data.