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An effective estimate for selecting the regularization parameter in the 3D inversion of magnetotelluric data

Ghaedrahmati Reza, Moradzadeh Ali, Moradpouri Farzad

Acta Geophysica

2022

Vol. 70, no 2

609--621

The magnetotelluric (MT) inverse problem is a nonlinear and strongly ill-posed problem. Therefore, to avoid the problem of non-uniqueness of response, this problem is mainly solved by Tikhonov regularization method. The purpose of this study is to present a suitable method for selecting the regularization parameters in the 3D MT inverse problem, with regard to the accuracy and speed of the inversion. In this research, the regularization parameter is simply estimated in each iteration of inversion as the ratio of the data misfit to sum of the data misfit and model norm in the pre-iteration. This scheme is applied in the well-known 3D inversion algorithm, WSInv3DMT, instead of the discrepancy principle method. The accuracy of this scheme is assessed by performing the inversion on synthetic models and real data. Results from the inversion for the synthetic and real data indicate that the data misfit and the model norm are reduced with an acceptable rate during the inversion operation. The inverse model has been smoothly converged to an appropriate model and that unrealistic structures have not been included in the model. The results also show that estimation of the regularization parameter by the discrepancy principle method and continuing the inversion to achieve the target data misfit may lead to the production of a model with non-realistic structures, while in the proposed scheme the inversion has not encountered this problem and it converges to an appropriate model after fewer iterations of inversion. In addition, the results show that the time consumed for the inversion of a set of real data with 41 stations and 16 measurement frequencies would decrease up to 27 percent compared to the time devoted for inverting the same set of data by the discrepancy principle method. Also the inversion does not deviate toward unrealistic models and it closely converges to the model of real geological structures.

A new approach in reverse time migration for properly imaging complex geological media

Moradpouri Farzad

Acta Geophysica

2021

Vol. 69, no. 2

529--538

Reverse time migration (RTM) artifacts usually start to appear in large refection angles which include a wide-angle range. On the other hand, the only proposed starting refection angle for RTM artifacts is 60 degrees which is not based on a proven investigation and it seems to be just a suggestion based on trial and error. As an important issue, we determine a predominant starting refection angle (PSRA) for RTM artifacts which enables us to suppress artifacts properly. Therefore, frst we try to open and discuss some issues from a new fundamentally perspective about the number of cross-correlations (NOCC) and its relationship with RTM amplitude and artifacts at refection and nonrefection points. Second, the cross-correlation and its related NOCC at each subsurface position form a new approach to determine PSRA for RTM artifacts. Using NOCC values, the refection angle of 55 degrees was determined as PSAR at which the RTM artifacts often start to appear. Finally, a new imaging condition based on the down- and upgoing wave felds and a new weighting function were proposed to suppress RTM artifacts. The new imaging condition can maintain the desired information and suppress artifacts properly for the angle domain of 55° to 90°. A key point in the suppressing process is the direct relationship between refection angle and artifact production where each refection angle in the domain of 55° to 90° can produce a diferent amount of artifacts. Therefore, the proposed imaging condition is able to designate a suitable weight for each refection angle to properly maintain the desired amplitude and suppress artifacts.