CONSTRUCTION OF ILLUMINATION MAPS AND UNCERTAINTY ESTIMATION OF THE P-WAVE VELOCITY MODELS OBTAINED BY FULL-WAVEFORM INVERSION
Subsurface imaging is an important topic in geophysics and a topic of great economic interest. Several techniques have been used in the construction of geological models with precise information on their physical properties and can be applied from environmental studies to oil and gas exploration. One of the most powerful techniques is based on the use of the wave equation and is known in the literature as Full Waveform Inversion - FWI. The FWI is a technique formulated as an optimization method in which it aims to find the physical properties of the subsurface, which leads to the smallest differences between data observed in the field and computationally simulated data.
This technique has great potential, as it takes into account all the phenomena suffered by the wave when it propagates in the environment in which it crosses, such as, for example, reflections, refractions, diffractions, attenuation, etc. However, the FWI is an inverse problem in the Hadamard sense, this means that several velocity models can be a solution to the problem. In other words, the resulting velocity model may not match the actual model. Thus, there is a need to assess the reliability of the results provided by the FWI. Seismic illumination can be a good tool in controlling inversion quality and there are different ways to calculate it, such as ray tracing, or using the wave equation. Another alternative is to use formulations from Bayesian statistics, in which it is possible to incorporate prior information about the region under study, through the uncertainties related to the velocities of the initial model and later obtain uncertainties associated with the obtained velocity models. Since there are techniques that help in the quality control of the investment, together with the industry's need for these types of studies, the present work aims to compare methods that aim to quantify how well this investment has occurred and what its levels of correlation are. The methods used are: Illumination based on the point spread function - PSF, Illumination based on the energy of the source, and the calculation of uncertainties later based on Bayesian statistics. these relationships, three inversions were obtained for the same velocity model (Buja2019) and called BUJA I, II, and III. The illumination maps showed a result consistent with that obtained in the inversion, for the BUJA I and II cases, however, for the BUJA III case it was not possible to visualize this relationship. For the three cases, the calculation of final uncertainties was consistent, but the decay of final uncertainties in relation to the initial uncertainties was very low, always less than 17 \% for the three cases.