Seismic Inversion for the Calculation of Velocities Using the Generalized Inverse Linear Matrix, the Wave Equation, and a Non-Reflective-Boundaries Condition

Abstract

Objective: this work presents the results obtained in the development of a seismic velocity inversion mo­del. The reference times recorded on the surface are taken and using the inversion model to obtain the initial reference model (hypocenters and velocities), starting from an unknown model.
 Methodology: A hypothetical reference model is pro­posed containing 64 blocks with interval velocity, 16 recording stations on the surface, and 64 earth­quakes in the center of each block. With this model, the reference arrival times are generated for each ear­thquake registered in each station. The inversion mo­del is made up of two parts: the direct model, which allows calculating the arrival times of the signal regis­tered on the surface according to the hypo-central lo­cation of the earthquake and the velocity of the P and S wave of the medium; and the inverse model, which estimates a model of the velocity of the environment and hypo-central locations of the earthquakes that are the input variables of the direct model. The direct model was developed with the wave equation, while the inverse model was developed by modifying the generalized inverse matrix by introducing a factor called “damping.”
 Results: The discretization model is based on the finite difference method.. When estimating the values of velocity and hypo-central location with the inverse algorithm, the propagation of the wave is simulated with the direct model, and they are compared with the data of reference times measured on the surface. Depending on the value of the mean square error, we proceed to modify the mean velocities and hypo­centers of the earthquakes. This process is repeated iteratively until the calculated error is less than a to­lerance of 2x10-3s2.
 Conclusions: It was found that the estimated values of velocity and hypo central locations coincide well for regions closer to the surface, while for deep regions the error is greater compared to the hypothetical re­ference model.

Inversion of Seismic Data to Modeling the Interval Velocity in an Oilfield of Sw Iran

“…Wavelet amplitude and phase spectra are estimated statistically from either the seismic data alone or from a combination of seismic data and well control using wells with available sonic and density curves. After the seismic wavelet is estimated, it is used to estimate seismic reflection coefficients in the seismic inversion (Conzález-Veloza et al, 2020;Fichtner & Trampert, 2011). When the estimated (constant) phase of the statistical wavelet is consistent with the final result, the wavelet estimation converges more quickly than when starting with a zero-phase assumption.…”