Numerical Solution Of Geophysical Inverse Problems

The study of inverse problems can involve many fields.For geophysical exploration,using elastic wave and electromagnetic wave are used to do the work of deep geophysical exploration and perception in China.For a long time,Learning from mature techniques in seismic exploration has been one of the development directions of exploration electromagnetic method.Transient electromagnetic method(TEM)is an important geophysical exploration method.If the TEM data can be converted into virtual seismic data,the data can be interpreted according to the methods in seismic exploration,and the interface imaging of underground targets can be realized by TEM.The thesis mainly studies the inverse problem optimization algorithm in data conversion from transient electromagnetic diffusion field to seismic virtual wave fieldBased on the specific ill-posed problem of wave field conversion equation,the thesis has done the works as follow:(1)Since satisfactory inversion results can't be obtained by a single regularized inversion or TSVD inversion,in the thesis,an improved weighted coefficient method is established to fuse the two inversion values based on the weighted average method.Dividing the time into two parts and using the concept of correlation,final date will be obtained by regularization inversion date and TSVD inversion date,then using simulation to illustrate the effectiveness of the algorithm.(2)A new numerical method-improved truncated singular value method,is proposed in the thesis.When the equation does not satisfy discrete Picard condition,the unstable solution obtained by SVD inversion and the inaccurate solution obtained by TSVD inversion are overcome.(3)Finally,the improved truncated singular value decomposition method is used to invert the data of a coal mine in Shanxi Province.The inversion results coincide with the known geological information and successfully distinguish the goaf interface.The correctness of the proposed method is verified.