«Tomographic transformation» of anomalous magnetic field using grid distribution of equivalent sources

Abstract

The article is devoted to the «tomographic» approach to the interpretation of geopotential fields. A brief excursus into the history of the development of interpretational (pseudo-) tomography is given. General issues concerning the creation of «effective» tomographic models are considered. Transformations based on the equivalent source technique are proposed as a key part of the tomography. This type of transformations permits the usage of elevation data of magnetic survey as input. When constructing an analytical approximation, usually a system of linear algebraic equations (SLAE) with an approximated right part is solved. Using a model example, some issues concerning the conditionality of SLAE for different depths of equivalent sources are studied. Two iterative methods for the solving of systems, the Seidel method and the quickest gradient descent, are compared. It is shown that the latter method makes it possible to achieve the required accuracy of the field approximation with a smaller number of iterations. The advantage in the calculation speed, when the matrix of coefficients of the transform operator (source function) is sparce, is emphasized. An example of using this approach to interpret magnetic field anomalies above the submarine volcano 3.18 within the Kuril Iceland arc is presented.

Keywords

• interpretation tomography
• effective model
• equivalent source approximation
• magnetic field