Improving the seismic image in reverse time migration by analysis of wavefields via continuous wavelet transform
Paniagua Castrillón, Juan Guillermo
Doctor in Engineering
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During the last 50 years there has been a lot of effort to obtain subsurface structures on the oil and gas exploration. Some of them even if they are based on the mathematical formulation of the phenomenon, were not easily implemented due to the lack of computational power. Nevertheless, the problem is not only the algorithmic complexity but also, the uncertainty reduction of the scalar field that is obtained after the mathematical modeling and inversion procedures. Specifically, this thesis deals with the well known Reverse time migration (RTM) procedure, which is basically the two-way wave equation migration that is able to generate models with both great structural and velocity complexities, problems arise when the construction of subsurface models take into account seismic signals recorded on the surface. The data is mapped into the subsurface using the acoustic wave equation and the models obtained contain uncertainties that affect their subsequent interpretation. In order to reduce these uncertainties, we seek to improve the algorithm used in RTM before and after the generation of the final model looking for uncertainty reduction and improved scalar fields. We propose a set of strategies of extracting information from the seismic signals in order to obtain characteristics that allow a better and more refined representation of the subsurface structure model. Integral transforms are developed for this purpose. Inspired on the concept of information retrieval from data, we developed a signal procedure algorithm to determine in time-scale domain, the main features of the traveler wave in order to relate temporarily the inherent physics phenomena, locate complex structures by pointing the velocity field singularities due to the main changes on the frequency content revealed within the scalogram obtained by Gaussian wavelet family. Later on, a wavefield separation for the scalar field calculation is proposed based on the same principle and we called it Time Scale Wavefield Separation (TSWS). The space defined by Source wave propagation is decomposed on the subspaces and the analysis in time-domain time-scale of the subset of the wavefield is performed by selecting special features extracted by Wavelet Transform Modulus Maxima (WTMM) and a numerical algorithm is introduced for massive data . Consequently, a Depth Scale Wavefield Separation (DSWS) is developed to the Receiver Wavefield separation by extracting the depth-domain scale-domain features of the relevant information of the reverse traveler wave . Finally and taking into account the need for the proper structure definition for drilling purposes, we introduced the Laguerre Gauss Transform as final part of the Zero lag cross correlation imaging condition (ZL-CC-IC-LG) and provide a useful transformation of the final real scalar field into a complex scalar field with properties of spatial features enhancement.