Multi-trace nonstationary sparse inversion with structural constraints

Abstract

The recorded seismic signals are attenuated and spatially correlated due to their propagation through an elastic earth and the sedimentary rule of strata. This attenuation phenomenon is quantified by means of the earth quality factor (Q) or the attenuation factor (1∕Q). Nowadays, the related Q-compensation and multi-trace inversion for the seismic data are two challenging problems when used for enhancing the temporal resolution and preserving the spatial continuity. Separately estimating Q and reflectivity are difficult and produce the uncertainty or ill-condition problems. To overcome these limitations, we have developed a multi-trace nonstationary sparse inversion with structural constraint. Using prior dipping-angle information and reflectivity sparsity property, the proposed method simultaneously estimates equivalent-Q and reflectivity with structural constraint. Constructed by the source wavelet and different scanned equivalent-Q, a series of time-varying (nonstationary) wavelet matrices are provided for the forward-modeling schemes and the corresponding inversions. When the Q-model is infinitely close to the true attenuation mechanism, the corresponding inverted reflectivity is comparatively sparse and quantified as maximum sparsity or minimum sparse representation. A sparse representation function, such as l0.1-norm, is used for sparsity measurement of the inverted reflectivity corresponding to each scanned Q. Through optimizing these sparse representation values, a suitable equivalent-Q, as well as the corresponding inverted reflectivity with structural preservation and Q-attenuation, is determined. The synthetic and field examples both confirmed a substantial improvement on seismic records, especially for Q-estimation, structure preservation and Q-compensation.