Constant Q estimation from a seismic trace and its removal by non-stationary deconvloution

The visco-elasticity of the earth causes dissipation of the energy of seismic waves when traveling through a medium, a phenomenon referred to as seismic attenuation. The attenuation property of a medium is described by a quantity called quality factor, or Q, which describes the amount of energy loss. The quality factor is related to the frequency of the propagation wave. In seismic data processing, our knowledge about this quantity is used to enhance the quality of seismic data, as an increase in the temporal resolution of the data, via absorption compensation tools. An exact formulation of seismic attenuation and its effect on the recorded data are unknown but there are simple models for describing the attenuation behavior approximately. The constant Q model relates a single value for Q to all frequencies in a trace. An important step in dealing with absorption compensation is the estimation of Q value. There are some methods for estimation of Q. In this paper we formulate Q estimation as a non-linear inverse problem. The value of Q is found by the optimization over the sparsity of the reflectivity describing the trace with a given wavelet. Numerical tests using simulated and field data are presented showing high performance of the proposed method for Q estimation and high-resolution non-stationary deconvolution.