Using the Sobel Operator to Improve the Spatial Resolution of the Cross Gradient Constraint
Cross-gradient; Joint Inversion; Sobel Operator; Smoothness Constraint; Total Variation constraint.
In order to improve the structural resolution in the joint inversion using the cross-gradient link, proposed by Gallardo and Meju, and to reduce the artifacts generated in the joint inversions, we suggest making changes both in the spatial formulation of the gradient calculation and in the of softness. In this work, this was done in two steps: in step E1, we replace both the cross gradient calculation and the finite difference calculation by the spatial formulation of the Sobel operator, in step E2, we replace the smoothness constraint, which is the stabilizer of the objective function with cross-gradient binding to be minimized, by the total variance binding. To demonstrate the effects suggested by steps E1 and E2, we made inversions using two synthetic 2D models.