A data-driven transdimensional inversion approach to include lateral constraints into target-oriented AVA inversion

The inclusion of lateral constraints into the inversion framework is the most popular strategy devoted at attenuating the ill-conditioning of the seismic inversion. The Tikhonov approach is by far the most popular regularization approach even if it has several disadvantages, for example this method often leads to unfocused layer transitions. Other more advanced regularization strategies exist, such as the inclusion of geostatistical constraints in the form of isotropic model correlation functions (Buland et al. 2003), or stratigraphic constraints (Tetyukhina et al. 2010). The main limit of all these approaches is that they rely on an a-priori structural knowledge of the investigated area and force the recovered model to honor such a-priori constraint. These are essentially model-driven regularization strategies that could provide biased model parameter estimations in case of erroneous a-priori assumptions. To overcome these issues more advanced, adaptive, regularization strategies have been proposed (e.g. Aleardi et al. 2018). The goal of these approaches is to locally adapt the structural constraint to the local structural characteristics of the subsurface model that can be iteratively inferred form the local characteristics (i.e. variability) of the observed data. On the line of these data-driven approaches, we present a transdimensional reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm for target-oriented amplitude versus angle (AVA) inversion. In our case target-oriented means that only the AVA responses of the target layer are inverted, and these AVA responses are extracted for each considered CDP position. The results are 2D maps representing the lateral variability of the elastic contrasts along the considered reflecting interface. The AVA inversion is a severely ill-conditioned problem highly affected by noise contamination in which it is crucial adopting a reliable regularization strategy to retrieve reliable and stable results. In a transdimensional inversion the number of model parameters (that codes the optimal subsurface model parameterization) is considered unknown and is estimated using a probabilistic sampling. In our case the inverted 2D horizon is divided into Voronoi cells, whose number and shape are automatically determined by the rjMCMC sampling. The algorithm autonomously partitions the considered 2D horizon on the basis of the spatial variability of data, producing subsurface 2D models discretized in Voronoi polygons each one enclosing CDP positions with similar AVA responses. This also means that the CDPs falling within the same cell also share similar elastic properties and for this reason the same elastic property values are assigned to these CDPs. These values are computed by averaging the model properties pertaining to the CDPs falling within each cell. Similarly, the observed data for each polygon is computed by averaging the AVA responses of the CDPs falling within each Voronoi cell. From the one hand, this strategy constitutes a data-driven approach to include lateral constraints into the AVA inversion because these constraints are automatically inferred from the lateral variability of the data and not arbitrarily infused into the inversion framework. From the other hand, the averaging of the AVA responses pertaining to CDPs falling within the same cell inherently increases the signal-to-noise (S/N) ratio of the observed data. These two aspects revealed to be of crucial importance for stabilizing the inversion even in case of severely noise-contaminated data. For the lack of field data, we test the implemented rjMCMC algorithm performing synthetic inversions with different S/N ratios. The proposed method is benchmarked against a more standard Bayesian AVA inversion without lateral constraints.