High Frequency Electromagnetic Modeling And Inversion

High frequency electromagnetic technique is a new kind of electromagnetic surveys, of which the frequency is between the traditional EM and ground penetrating ground (GPR). It is necessary to take into account both the effects of conduct current and displacement current in the high frequency EM. Using the characteristics of wideband and multi-frequency, the technique which can detecte both resistivity and dielectric permittivity differences, has a large potential in applied geophysics at shallow depth, and can overcome the limitations of the tradition EM, so there are great prospects in application to hydrology and engineering geology surveys, army exploration and other fileds.The main purpose of this paper is to investigate the features of high frequency EM more detailed based on the study of forward modeling and inversion algorithms, and set the foundation for interpretation and application. Because of some special features of the high frequency EM, The algorithms existed for the traditional EM may be invalid, so some improvements or optimizations need to be made. In the end of paper, we also investigate the time domain EM in the corresponding frequency range. The following four parts will be involved:1) Modeling Algorithm.The equations for calculating EM response are kinds of Hankel integration. There are many numerical solutions for computation, but the linear filtering and Chave's Gauss integration are often used. The linear filtering has advantages of efficiency and accuracy in the low frequency range, but it will cause significant errors in our high frequency range. The Chave's Gauss integration can solve the above problem, and the convergence will be expedited using fractional formula, but the computation has a very low efficiency. In our paper, the linear filtering with high density sampling from the Johansen's algorithm, of which the sampling density is increased by the value of ln10/100, is used for computing filtering coefficients. After that, the coefficients then are applied into Hankel integration. By contrast to other algorithms, the high density sampling algorithm has more advantages. The algorithm solves the problem of losing accuracy by the traditional filtering, and also avoids the problem of losing efficiency by the Chave's Gauss integration.2) Quantitative InversionIn this paper, a nonlinear least-squares integrated with Monte Carlo method is adopt, using high density sampling linear filtering algorithm for forward modeling which is an order-of-magnitude faster than direct numerical integration such as Chave's(1983)in speed of calculation. By contrast to the Anderson's approximate inversion solution, it increases the accuracy greatly in inversion results at the deep layer parameters. For the multi-layer earth, because the response function of polarization ellipticity is very nonlinear, the measurement data usually can't involve the enough information for inversion, so the Monte Carlo method is introduced into improve convergence. The Monte Carlo method is used to initial selection for the least-squares method and reduce the solution space before going into the least-squares inversion. The result of illustrated cases indicates that the method presented avoids the local minimum of the objective function. By selecting the measurement configuration with suitable combinations of frequency range and coils offsets, the wideband high frequency EM could show a high resolution in detecting layer models in the shallow depth less than 5m and the thin overlay with low resistivity. The inverse results consist with the analysis of sensitivity matrix.3) Approximate InversionThe Phase Vector Graphics method is often used for interpretation of helicopter-borne EM and constructed with the normalized in phase and quadrature components. Analogically, we construct a phase diagram using polarization ellipticity and tilt angle components, and then the dielectric permittivity and conductivity of a half-space earth are obtained by transforming from measurement data of polarization tilt angle and ellipticity using a 2-D interpolation scheme, but for the multi-layer earth, the inverse result can be regarded as apparent paramenters. The method could be used for real-time interpretation, helpful to geology mapping and initial selection for least-squares method. It is an important supplement tool to quantitative inversion.4) VETEM and GPR modelingVery early transient EM (VETEM) is a shallow detection survey, and makes a large development recently, but it is tough to implement forward modeling efficiently due to the existent displacement current. Two methods exited are usually used to transform EM from frequency to time domain, including linear filtering algorithm (cosine transform) and fast Fourier transform algorithm (FFT). In our paper, the linear filtering algorithm using high density sampling is applied to calculating cosine transform and the very early transient electromagnetic responses in a layered earth. Compared to the result of closed-form analytic expressions, the numerical algorithm is proved to be valid. In the second part, the fast Fourier transform algorithm is applied to modeling single trace and common shot point gather of ground penetrating radar in different frequencies. Both the very early transient electromagnetic and low-frequency ground penetrating radar operate over the intermedial frequencies between the traditional transient electromagnetic and ground penetrating radar, so our research is order to find out valid forwarding algorithms and analysis the time EM features in such frequencies through some cases. The forward modeling algorithms which could calculate for each single frequency are also convenient to apply into dispersive media.To sum up, in this paper, we analyze the characteristics of high frequency EM in detail, and develop the program package to implement 1D modeling and inversion. The application of filtering algorithm with high density sampling and least-squares integrated with Monte Carol method, the construction of phase diagram in approximate inversion, the 1D modeling of VETEM and some others are all important creative ideas, which will break a new path for domestic development and application in high frequency EM. Although these studies are focused on one dimension subsurface earth, some conclusions may be also suitable to two or three dimension earth. In view of computer performance and computation complexity, the 2D or 3D modeling and inversion will not be within the scope of the studies in this paper.