Truncated SVD Methods for MT Discrete Linear Ill-Posed Inverse Problems

Geophysics´ complexity and uncertainty, and interfering with a variety of humanities, which made the gaining first-hand information from the field in the process of data acquisition is often severely disrupted. The solution in the geophysical inversion would be many solutions or distortion, which is the geophysical ill-posed problem. Ill-posed problems could be attributed to the First Class of Operator Equations in normal. The TSVD regularized method is introduced for ill-posed problems in this paper. This method mainly is built on the Operator matrix´s singular value decomposition in the First Class of Operator Equations, and then in accordance with the characteristics of singular value to select the best regularization parameters. For TSVD method, by choosing an appropriate truncate parameter k, we truncated the small singular value after k which in the expression of least squares solution, because small singular values would affect the solution greatly when there are noises in data of the ill-posed problem. And then Filter Functions is also identified. GCV and L-Curve are adopted in determining the regularization parameter. Finally, one-dimensional magnetotelluric inversion is selected as an example to demonstrate the TSVD which is accuracy and practicality.