Research On Crosshole Radar Traveltime Tomography

Electromagnetic tomography technique is a commonly used interpretation method forcrosshole radar data. The theory of electromagnetic tomography is based on the Radontransform and inverse Radon transform, which inverse the distribution of the physicalparameters in the abnormal body according certain physical and mathematical relationship,and then the distribution of the physical parameters will be displayed by the computer in theform of image. According to the different observation data and inversion purposes,tomography technique can be divided into two types which are traveltime tomography andattenuation tomography, respectively. Traveltime tomography inverses the distribution ofvelocity between two boreholes using the first arrival data of direct wave. Attenuationtomography inverses the distribution of attenuation between two boreholes using theamplitude or centorid frequency data of direct wave.Tomography method can identify the subsurface structure (i.e., bedding, fracture andburied utilities) that induce significant physical property contrasts (dielectric permittivity,electrical conductivity, or magnetic permeability). For medium with low dielectric loss, thedielectric permittivity can be considered only concerned with electromagnetic wave velocity,and has nothing to do with the attenuation coefficient; dielectric permittivity can be obtainedthrough the traveltime tomography alone. And for the high dielectric loss medium, thedielectric permittivity is decided by both the electromagnetic wave velocity and theattenuation coefficient. Another reason for attenuation tomography is to obtain theconductivity structure of the detecting medium through the attenuation coefficient. The jointcrosshole radar traveltime and attenuation tomography can study the effects of permittivityand conductivity on the propagation of electromagnetic wave separately, which can greatlyimprove the understanding to the detection medium.The huge amount of computation and antenna characteristics limit the applications ofthe full wave form tomography techniques. The inversion process of attenuation tomographymay be effect by radiation patterns, geometric spreading and other factors which lead to a badresult. Traveltime tomography use the first arrival data of direct wave to inverse the velocityfield, which are not related with the radiation patterns, antenna characteristics, and so on. Andthe computational efficiency of traveltime tomography is much higher than full waveforminversion methods. Therefore, in this paper, we mainly studied the theory of crosshole radartraveltime tomography. Straight rays may be adequate if a medium is characterized by smooth and negligiblysmall velocity variations. At this time, the equation of traveltime is linear, and the traveltimetomography based on straight raytracing may be realized through a least squares linearizednon-iteratively inversion scheme. During the inversion, the observation data of traveltimescan be obtained by the first arrival extraction, and the Jacobi matrix can be constructed byusing the straight raytracing technique. In case of strong variations, using curved rays isnecessary to obtain accurate results. At this time, the equation of traveltime is non-linear, andthe traveltime tomography based on curved raytracing may be realized through a leastsquares linearized iteratively inversion scheme. During the inversion, we should extract thefirst arrival time firstly to get the observation data of traveltime. In each iteration, thecalculated data of traveltime can be calculated using the MSFM algorithm, and the Jacobimatrix can be constructed by using the curved raytracing technique based on the MSFMalgorithm and the steepest descent technique. The traveltime tomography without raytracingmay be realized through a least squares linearized iteratively inversion scheme which are thesame as the one used in curved raytracing traveltime tomography. During the inversion, theobservation data of traveltimes can be obtained by the first arrival extraction. In eachiteration, the calculated data of traveltime can be calculated using the MSFM algorithm andthe Jacobi matrix can be constructed by using the finite difference approximate.In the attenuation tomography based on amplitude ratio, amplitudes are easilycontaminated by factors such as scattering, geometric spreading, source and receivercoupling, radiation patterns, and transmission and reflection effects. It can be difficult toobtain reliable attenuation estimates from time-domain data. In the attenuation tomographyusing the centroid frequency downshift method, the frequency shift or pulse broadening of anEM pulse is not affected by far-field geometrical spreading or reflection losses, appears to bemore reliable than the time-domain amplitude-decay methods, and can be easily implementedby a tomography algorithm. The attenuation tomography can be realized through a leastsquares linearized iteratively inversion scheme which are the same as the one used intraveltime tomography.The fast marching method (FMM) uses a first-order approximation to solve the eikonalequation, which makes the FMM algorithm having a low accuracy. The higher accuracy fastmarching method (HAFMM) which solves the eikonal equation using a second orderapproximation which can improve the accuracy of FMM. However, both FMM and HAFMMignore the information provided by diagonal points and may suffer from a large numericalerror along the diagonal direction. The multistencils fast marching method (MSFM) computes the solution at each grid point by solving the eikonal equation along two stencilsthat cover its entire neighbor points and then picks the solution that satisfies the upwindcondition, which can improve the accuracy of FMM and HAFMM greatly.We presented a ray-based iteratively traveltime tomography algorithm for crossholeradar direct-arrival data using the multistencils fast marching method (MSFM) and thesteepest descent technique. The proposed scheme used MSFM to compute the traveltimesolution at each grid point by solving the traveltime eikonal equation along several stencilsand picked the solution that satisfies the upwind condition. In contrast to classical fastmarching method (FMM) and the higher accuracy fast marching method (HAFMM), MSFMis highly accurate for forward modeling of traveltime. Curved raypaths, which were neededfor the construction of the Jacobi matrix during inversion, were generated by following thesteepest descent direction through a computed traveltime field from each receiver back to thesource using the steepest descent technique. In order to verify the accuracy and efficiency ofthe new ray tracing method, we test the proposed scheme on three synthetic velocity models,and we compared our results with the one obtained by a FMM based and a HAFMM basedsteepest descend ray tracing methods. This comparison indicated that the suggested raytracing technique is efficiency and can achieve much better results both on accuracy andefficiency compared to the FMM based and the HAFMM based steepest descend ray tracingmethods.Digital image segmentation is an accurate extraction method for first arrival times whichwas first used in refracted seismic data. Digital image segmentation method extracts firstarrival times by segment the color image of the energy ratio based on the projection ontoconvex sets (POCS). We first applied the digital image segmentation method into crossholeradar first arrival extraction. We employed three synthetic data sets to test the digital imagesegmentation method and the traditional signal to noise ratio method and correlation method.The contrast indicated that the digital image segmentation method is more accurate withsmaller residual which can provide more effective help for the traveltime tomography.The comparison of synthetic data set and field data set inversion results using threetypes of traveltime tomography algorithms indicate that the traveltime tomography algorithmwithout raytracing is able to generate a solution as good as the one resulting from a curvedraytracing scheme.In traveltime tomography, inversion results are easily affected by factors such asweighting operator, weighting matrix, traveltime calculation methods, first arrival extractionmethods, least square inversion algorithms, inversion grid size, antenna stepping, ray coverage angle, and so on.The L-curve approach can be used to obtain an optimal value for the weighting factorwhich can also lead to a good misfit between the data space and model space during thetraveltime tomography. When considering both the reconstruction result and residual, theLaplace operator is the most suitable weighting operator for crosshole radar traveltimetomography.The accuracy for the extracted first arrival using the digital image segmentation methodis higher than the one using the max signal-to-noise ratio method and the cross-correlationmethod, and the inversion result based on the extracted first arrival using the digital imagesegmentation method is the best during the three first arrival extraction methods. Theaccuracy for both traveltime calculating and traveltime tomography using the MSFMalgorithm is higher than the FMM and HAFMM algorithms. In crosshole traveltimetomography, the three kinds of least square algorithm (LSQR, GMRES and BICGSTAB) canget very good reconstructed velocity field.Reducing inversion grid spacing can improve the retrieval accuracy, but the inversionaccuracy is achieved at the expense of computing time. However, in the two-dimensionaltraveltime tomography algorithm based on curved raytracing, the increase of the computingtime is acceptable. Therefore, we can improve the inversion accuracy by reducing the size ofthe inversion grid spacing. By reducing the moving step of antenna, we can get more numberof rays (observed data), which can improve the accuracy of inversion; but at the same time, itwill also introduce more high angle rays which can affect the inversion effect. When we bothreduce the antenna moving step and only using the small angle rays for inversion, we can notonly improve the inversion precision, but also obtain better inversion results.