3D Continuation Imaging Technology With A Synthetic Aperature Based On The Transient Electromagnetic Method

The paper is aimed at3-D interpretation of Transient Electromagneticmethod (TEM). By combining the TEM wave-field transformation andadopting the correlation superposition method for synthetic aperture process, Ihave based on the synthetic aperture radar method improved the resolution ofTEM. The3-D TEM imaging by continuation from surface to underground hasbeen realized by introducing the Kirchhoff integration.The TEM wave-field transformation is the first kind Fredholm integralequation, and the inverse transformation, from diffusion field to wave field, isa typical ill-posed problem. Besides, the dynamic time range of transientelectromagnetic sampling is so wide that it makes the ill-posed problem moreserious. To deal with this problem, Pre-conditioned Regularized ConjugateGradient Method (PRCG) has been proposed in this paper, so that the TEMfull-domain wave-field transformation could be executed. The over relaxationpre-conditioned process effectively reduces the condition number of thecoefficient matrix, while Regularized Conjugate Gradient Method(RCG) helpsrun the inverse transformation of wave-field in full time-domain. Thecomparison between the results of inverse transformation and the knownwave-field functions shows that the algorithm is stable and reliable. Comparison of the results with those of previously proposed sectionalizedregularization shows that the method in this paper is very effective. Combinedwith the algorithm of inverse transformation, I analyze the characteristics ofthe virtual wave-field for layered earth models and summarize its propagationproperties. The sensibility of virtual wave-field to resistivity difference isanalyzed quantitatively for G and D models, while for A,H,K,Q models, Istudy the resolution of virtual wave-field to layer thickness.The algorithm of TEM wave-field transformation makes it possible totransform the diffusing transient field to virtual wave-field. This creates thecondition for synthetic TEM aperture imaging. The synthetic TEM apertureimaging is based on the idea of synthetic aperture radar that utilizes therelative motion between airborne aperture transmitter and objectives, andmakes equivalent small-sized antenna apertures to a major transmitter via dataprocessing to improve the resolution and to strengthen the penetrations. Bothnumerical results and model experiments show that the reflections from thesame geological body at nearby points correlate well with each other, thusweighing functions are obtained based on the correlation coefficients ofdifferent positions. During the correlation superposition process, the signal inthe neighbor stations are weighed by weighting functions to enhance the signalof abnormal bodies. This improves the S/N ratio, strengthens weak abnormal signal, and increases the resolution and the exploration depth.Through numerous model analysis, it is found that the virtual wave-filedattenuates very quickly when propagating in dispersive earth. This causes thehigh-frequency signal be absorbed very quickly and is thus of little help to theimprovement of detection precision. In order to solve the problem withabsorption and broadening of virtual wave-field, the impulse deconvolutionmethod has been adopted from seismic and combined with minimum phasefiltering to realize the impulse compression of virtual wave-field. It ismanifested that the impulse compression method effectively improves thevertical precision through compressing the wavelets of the model.Based on the analysis of the algorithm from synthetic aperture radar andcombined with the TEM signal characteristics, the sampled signal is obtainedby correlated weighing to form the TEM synthetic aperture data. From theHuygens theory, the formula is built for surface continuation imaging andpractical algorithm of TEM virtual wave-field based on Kirchhoff integration.The3-D boundary-element method is adopted to improve the computationalefficiency. At the same time, an approximate velocity analysis based on themethod of equivalent conductive plane is assumed to carry out the downwardcontinuation over a curved surface.The practical use shows that the3-D TEM imaging by synthetic aperture continuation can image the3-D underground, and the resulted images matchwell with the drilling data. Both model experiments and practical use showthat3-D TEM imaging of the virtual wave-field continuation has the ability ofdistinguishing the underground resistivity distribution, and proves to be aneffective method in3-D data interpretation. The combination of impulsecompression and focusing synthetic aperture method can help improve theresolution of wave-field. This means that the imaging by wave-fieldcontinuation makes high-resolution TEM imaging possible. Moreover, themethod proposed in this paper can be used in both ground EM and airborneEM, this further implies that the TEM has the potential to explore finestructures in regions with complex surface conditions, such as in the mountainarea and over the sea.