Blind inversion of multidimensional seismic data using sequential Tikhonov and total variation regularizations

Abstract

The acoustic impedance (AI) model is key data for seismic interpretation, usually obtained from its nonlinear relation with seismic reflectivity. Common approaches use initial geologic and seismic information to constrain the AI model estimation. When no accurate prior information is available, these approaches may dictate false results at some parts of the model. The regularization of ill-posed underdetermined problems requires some constraints to restrict the possible results. Available seismic inversion methods mostly use Tikhonov or total variation (TV) regularizations with some adjustments. Tikhonov regularization assumes smooth variation in the AI model, and it is incurious about the rapid changes in the model. TV allows rapid changes, and it is more stable in the presence of noisy data. In a detailed realistic earth model that AI changes gradually, TV creates a staircasing effect, which could lead to misinterpretation. This could be avoided by using TV and Tikhonov regularization sequentially in the alternating direction method of multipliers and creating the AI model. The result of implementing our algorithm, sequential Tikhonov and total variation regularizations (STTVR), on 2D synthetic and real seismic sections indicates that the smaller details in the lithologic variations are accounted for as well as the general trend. STTVR can calculate major AI variations without any additional low-frequency constraints. The temporal and spatial transition of the calculated AI in real seismic data is gradual and close to a real geologic setting.