| Transient Electromagnetic Method(TEM)is an important time domain electromagnetic exploration method,and has widely used in various fields of geophysical exploration.Although a lot of achievements have been made in the study of TEM 3D forward and inversion,3D TEM forward is time-consuming and 3D TEM inversion is inefficien due to the complexity of TEM field.In contrast,a remarkable progress has been achieved in 3D inversion in frequency-domain electromagnetic methods(FEMs),and 3D inversion has been effectively applied in the interpretation of actual data of FEMs.And then,it is worth studying to transform the TEM data in time domain to frequency domain and carry out 3D inversion in frequency domain.One dimensional(1D)inversion is the main method of transient electromagnetic data inversion in present,but it encounters the problem of poor continuity along the inversion section,also the 1D inversion efficiency is still low for large fixed loop,shift loop configurations,etc.Based on the above,this paper is devoted to the research of 3D inversion based on the time–frequency transform(T2F)of TEM data to improve the efficiency of the 3D inversion of TEM data and fast spatial constrained inversion method of TEM data.The main achievements are as follows:(1)A high-precision 3-D forward algorithm for loop source TEM based on frequency-time transform is realized.Aiming at the purpose of 3D inversion of TEM data in frequency domain,the 3D forward algorithm for loop source TEM based on frequency-time transform is studied.To overcome the singularity of the source and ensure the stabality of the numerical calculations,the anomaly field method is used for the 3D forward in frequency domain.The background field is calculated from the analytical formula,and the vector finite element method is used to calculate the anomaly field.In order to improve the accuracy of background field,the concise analytical formulas of background field in half space excited by loop source are obtained based on the decomposition of "current term" and "grounding term" of electromagnetic field formula of electric dipole.The idea of "flow through" isintroduced into the digital filter algorithm to calculate Hankel transform and sine/cosine transform,then the efficiency of the calculation of background field and the transform of frequency domain to time domain are significantly improved.The double curl equation of the anomaly electric field is used as the control equation in the solution of the vector finite element method.The Bi CGSTAB(l)algorithm with the duplex preconditioners of Jacobian and SSOR is used to solve the forward equation,and the equation solver based on direct decomposition is used to solve the multi-source excitation forward equations efficiently.The 3D forward algorithm is verified by comparing with the previous calculation results and 1D analytical formula calculation,the verification results show that the 3D forward algorithm is correct and has high accuracy.Based on the forward modeling,TEM response characteristics on the ground and underground of the low resistance and high resistance bodies are analyzed,which is worth for the design of TEM exploration and data interpretation.2.The 3D inversion based on T2 F of TEM data is realized effectively.The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current.A transform matrix based on the digital filtering calculation for the sine transform is established,and then the frequency domain projection of the TEM data can be determined from the linear transformation system using the smoothing constrained least squares inversion method,in which only the imaginary part is used to maintain the TEM data transformation equivalence in the bidirectional projection.Thus,the time-domain TEM inversion problem can be indirectly and effectively solved in the frequency domain.Based on the analysis of the computation cost,storage requirement and convergence property of the common optimization methods,the limited-memory quasi Newton method(L-BFGS)is used for the 3D inversion in frequency domain,and a restart strategy is used to adjust the regularization parameter when the algorithm tends to a local minimum.In addition,the key step of 3D inversion – to efficiently calculate the gradient of inversion objective function of single source and mutli-sources is studied in detail.Synthetic data inversion tests show that the 3D inversion of the transformed frequency-domain data is stable and can effectively recover the real resistivity model.The 3D inversion test with the real TEM data also is carried out,which shows stable iteration,good convergence,and reasonable inversion model.The synthetic data and real data tests show the 3D inversion based on T2 F is feasible,and worth to further research to improve the algorithm.Based on the 3D inversion method based on T2 F,the inversion effect ofmulti-coverage data of multi-sources is deeply analyzed.Compared with single source data,the inversion effect of multi-coverage data of multi-source is obviously improved,which shows that the exploration method of multi-coverage of multi-sources is an effective means to improve the exploration effect of TEM.3.The author proposed an efficient calculation method of the 1D TEM response of any measuring point of the rectangular loop,and a distance-weighted adjacent stations' spatially constrainted quasi-3D inversion is constructed.By referring to the equivalence calculation of 1D TEM forward by replacing rectangular center loop with circular center loop(R2C,rectangular loop to circular loop),the author proposed a efficient calculation method of the TEM response of any measuring point of the rectangular loop by being equivalent to the stack of the responses of several of circular center loops(R2SC,rectangular loop to stacked circular loops),which can greatly improve the 1D TEM forward speed of large fixed loop,shift loop configurations,etc.Compared with the electric dipole integration method,the speed of R2 SC can increase several times to more than 20 times.The accuracy of R2 SC is also more than that of R2 C.In addition,the model forward tests shows R2 C is only suitable for the later time,but not for the early time.The principle of lateral constraint is introduced into the TEM 1D inversion of 2D line survey and 3D grid survey;on considering the 3D survey grid is not strictly regular,a distance-weighted adjacent stations' spatially constrainted quasi-3D inversion is constructed.The Gauss Newton method is used to solve the minimum of the inversion objective function;and the Jacobian matrix is calculated efficiently by semi analytical method.The synthetic data and actual field tests had verified the effectiveness of the spatially constraned inversion with R2 SC.Because the spatially constraned inversion is a 1D inversion with lateral constrain of multi-directions,it is more suitable for areas with obvious layered electrical characteristics. |
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