# Master Thesis Chenwen XIANG

### A Geodetic Approach to Euler Deconvolution

Duration of the Thesis: 6 months
Completion: June 2010
Tutor: Prof. Dr.-Ing. N. Sneeuw
Examiner: Prof. Dr.-Ing. N. Sneeuw

### Abstract

In order to search for sources such as coal, oil, gas and other substances with economic value, the magnetic and gravity field of the earth are measured and interpreted by Euler deconvolution which can automatically estimate the location and depth of the source. In this MSc thesis, two methods (Gauss-Helmert model and Gauss-Markov model) to solve the Euler deconvolution are discussed and compared. Moreover, several ways of testing of the solution of the Euler deconvolution to distinguish the more reliable solutions are also discussed in the MSc thesis.

Euler deconvolution is a standard technique in geophysical exploration to determine the depth of a subsurface mass density or magnetic anomaly from surface measurements of the corresponding field. The Euler equation can be state as:

r • ∇f = –Nf

The comparison of Gauss-Helmert model and Gauss-Markov model is performed to 2D simulate data and 3D Full Tensor Gravity Gradiometery data which is measured by the Bell Geospace.

 Figure 1 - Euler Deconvolution of three point mass sources with window size 21, without noise

 Figure 2 - Solution of Euler deconvolution with two methods of line 54

The Euler deconvolution uses a sliding window to determine the location of the source. Each window will lead to a solution. For a huge set of solutions, not all of them are reliable and provide a proper location of the source. In this case, a discrimination technique is needed to distinguish more proper and reliable solution from the whole set of solutions. Three different types of test are expatiated with experiment test of simulated data as well as the 3D Full Tensor Gravity Gradiometery data. They are common sense test, mathematical test and statistical test.

Here are the testing results. For each figure, there are two main plots at left and right side which indicate to solution of the Gauss-Markov model and Gauss-Helmert model. In the first row, two plots of the solutions are displayed. The three rows of plots refer to the results of common sense test, geometric test and statistical test correspondingly.

 Figure 3 - Testing of solution of five point mass sources scenario

 Figure 4 - Testing of solution of data line 53