ON USING SIRT METHOD FOR GRAVITY INVERSION DATA - Troinich, K. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
This paper proposes to use simultaneous iterative reconstruction technique (SIRT) for the gravity data inversion. SIRT is based on Kaczmarz method and allows to solve systems of linear algebraic equations via iterative update of parameters vector. Method gives a solution which fits the observed data vector and changed its first guess in the least squares sense. Relationship for the gravitational attraction of a cell could be split into two multipliers. First multiplier depends on density and second multiplier depends on observation point location against cell (geometrical factor). As a result gravity forward modeling could be described as multiplication of matrix by vector. A gravitational attraction vector is a multiplication of geometrical factors matrix by a densities vector. SIRT could be used for the inverse of this operation, in other words estimation of the densities vector is based on the gravitational attraction vector. From the math point of view it is a solving of a system of a linear equations. Because of geometrical factors decay with depth inversion solution often gives a model where all anomalous masses lay in a shallow part of investigated section or volume. In order to contradict reminded decay geometrical factors should be multiplied by a special power function of depth. By doing this we force anomalous masses to be disposed even along depth axis. Synthetic data inversion proved possibility of using SIRT for gravity data inversion. Better results could be earned using depth weighting of the geometrical factors. Further development of method could be found for the simultaneous inversion of seismic and gravity data as one system of linear equations.