Semi-blind Non-stationary Deconvolution - Joint Reflectivity and Q Estimation

Abstract

‎Source signature deconvolution and inverse Q-filtering are two challenging problems in seismic data analysis which are used for extending the temporal bandwidth of the data‎. An accurate estimate of the wavelet and the Q (quality factor) distribution are required in order to solve these ill-conditioned problems either separately or simultaneously via non-stationary deconvolution‎, while estimation of the Earth Q-model is very problematic‎. In order to circumvent the instability and uncertainty of the Q-model‎ ‎these problems are addressed in a unified formulation as a semi-blind non-stationary deconvolution (SeND) to decompose the observed trace into the least number of non-stationary wavelets selected from a dictionary via a basis pursuit algorithm‎. ‎The dictionary is constructed from the known source wavelet with different propagation times‎, ‎each attenuated with a range of possible Q values‎. ‎SeND is an extension of the conventional sparse spike deconvolution to its non-stationary form without requiring the Q-model and it provides the reflectivity and Q- models‎, ‎simultaneously‎. Numerical results from simulated data indicate that using SeND the original reflectivity and Q-model can be estimated‎ ‎with a high degree of accuracy‎. ‎the results show that more accurate Q values can be obtained by SeND compared to conventional spectral ratio technique‎.