Research On Cross-Borehole Radar Tomography Using Full-Waveform Inversion Method

Full waveform inversion of crosshole radar is a kind of tomographicimaging technique,which use full-waveform information to obtain the electricparameters of the underground media between the boreholes. Most conventionaltomographic inversion is using ray tracing method, the velocity profile can beinversed by first-arrival wave, and attenuation profiles can be inversed bymaximum amplitude. In certain conditions, the velocity and attenuationinversion image can be converted into permittivity or conductivity images. Thepermittivity and conductivity are relate to many underground mediumparameters, such as porosity, moisture, salt content, mineral content and so on.There are many shortcomings of conventional method, the main reason is that itapplies only a small portion of the signal information. For example: ray tracingmethod can only solve anomalous bodies, which are bigger than the signalwavelength, and their resolutions are approximately the first Fresnel zone.What's more, it can not provide the stable low-velocity anomalies inversionresults. When just a little number of directions of the target are provided"lighting", the weaknesses as illustrated are especially obvious.For waveform inversion method, it can solve many problems, such asseismic technology exploration and development, medical imaging,nondestructive testing, tunnels and mine detection and so on. In recent decades,waveform inversion developed some accurate imaging method in order tohandle different wave field datas which include acoustic, elastic wave, radarwave, microwave, optical and X-ray waves. And much waveform estimationimaging inversion methods such as the Fresnel volume, the eikonal equation,scattering field, full waveform technology have been applied in seismic. Inaddition in the forward method, the traditional ways are the finite elementmethod and finite difference method in time domain or frequency domain.As a category of the full waveform inversion, full-waveform inversion ofcrosshole radar is still in the primary stage with high-speed development. Thefull-waveform inversion is able to provide a resolution shorter than the wavelength when the situation is ideally. The resolution can reach1/2to1/3ofthe wavelength. Compared with ray-based methods, full waveform inversionmethod can improve resolution by one order of content. As it consideres wholeinformation of the signals, it can get many different forms of abnormalities,which involving the missing information due to energy attenuation duringpropagation. Full-waveform inversion method can accurately reconstruct theindividual anomaly body's position, size and electromagnetic characteristics; Itcan determine subwavelength adjacent bodies' position, dimensions in thebackground field; It can show the interface between two layers with largecontrast's electromagnetic parameters. And it cans recoganize water fillingtunnel and subwavelength pipes' location, size and conductivity in nonhomogeneous layered model.This paper deduces the full waveform of crosshole radar tomographyinversion method, this method emploies radar amplitude and phase informationsto inverse high resolution of the permittivity and conductivity images. Thebackground medium can be a big contrast with objections. This papereffectively solves the massive data computation using distributed parallelalgorithm based on LAN. We present the full waveform crosshole tomographicimaging method in common computers, which were only run in supercomputers before.In this paper we firstly establish two-dimensional FDTD algorithm basedon the UPML absorbing boundary with TE mode. Because of transmittingantenna's and receiving antenna's polarization is Z direction whichperpendiculars to the surface in the crosshole radar measurement mode, theselection of FDTD algorithm requires TE model with Ex, Ez, and Hy.In this paper, the gradient method is used to solve the inversion algorithmusing the full wave field information. We should use forward field and residualbackforward field to receive gradient directions, and consider the length of stepsby optimization of goal function. As there is magnitude difference betweenpermittivity and conductivity, it is necessary to calculate them respectively toimprove the convergence speed, and they need to use different stability factors.The permittivity and conductivity use logarithm processing, and new gradientformulas are derived. That's because logarithmetics will be very good atimproving the convergence speed and stability, and widen parameter contrast between the anomaly and the surrounding medium.Duing the computation of the gradient, we need to storage the full-wavefield informations which contain the electric field and residual field with timedimension. It will take many G memory space and up to several hundred FDTDforward calculation. Foreign counterparts are using super computers to settle thesame category of full wave inversion. This paper establishes a small PC clusterbased on LAN, organizes more than20cores of CPU to sovle the computation.We realize non-supercomputers algorithm of crosshole full-wave inversion, sothat the method can benefit the general PC users.Through the full wave inversion of cylindrical body with the diameter of1m in uniform background, we can realize the morphology and characteristicsof measured data (synthesis data)'s waveform, inverse time residual fieldwaveform. And we analyse morphological characteristics of the gradient foreach stage of the components. We offer the stability factorκ εandκ σin thestep size calculation.In this paper, the points where the sources settled and five points around itat horizontal direction are set to the background values. And we smooth thevalues amang10points around the source, which is in order to resolvewaveform distortion caused by the 'jump' of permittivity around the source ininversion and to improve algorithm stability.Without reducing the resolution of the inversion, we use pumped dilutesolution to solve the demand of computer memory with large scale model, andthe datas are reduced to1/6of the original memory requirement.When we inversion with rectangular target models, we find that full waveinversion can accurately inverse rectangular object edge position, electricalparameters and so on. As for inclined or vertical abnormal body, it can inversebody's horizontal surfaces accurately, but cannot good imaging the verticaltarget interface. Through the analysis of the complex model with actual surfacemodel, we can realize that when we consider the effect of surface, the surfacelocation calculation should be added in inversion initial model. When the modeladded background noise, we can find the small scale noise in vertical directiondoes not affect the target body imaging. Through the establishment of randommedium model with different horizontal correlation length and verticalcorrelation length, we find that full wave inversion can recognize0.5m thick of horizontal thin layer anomaly, when using the100MHz antenna and withrelevant permittivity3-8. But with vertical thin layer anomaly, full waveinversion can not be very good.We combine crosshole and VRP measurement mode with full waveinversion. Then we analyze the different measurement methods, differentelectric field component of the wave field and the residual wave field. Throughthe establishment of complex model we find that the full wave inversion caneffectively improve the cylindrical object with horizontal resolution using acombination of crosshole and VRP observation system.When doing permittivity and conductivity simultaneous inversion, ourpaper use first-step forward permittivity inversion as the initial model, iteffectively solves the problem of slow convergence rate of simultaneousinversion. Through the test we find the inversion of the conductivity is betterthan the permittivity. In addition, when there are thin layer objects or anomalybodies, we should not use the combination with VRP measurement method,using VRP measurement will reduce recognition ability of horizontal thin layerwith crosshole measurement mode.In the numerical inversion, the source waveform is given, but actually thewaveform of antenna transmitting does not know, so wavelet waveformestimation is necessary. This paper introduces two ways to settle this problem.First of all, the source was considered as unknown quantity for inversion usingdirect estimation method; What's more, we can use frequency domaindeconvolution waveform estimation method. Then we use the deconvolutionmethod rapidly completed the wavelet estimation. Despite the wavelet phase isdifferent with the theoretical value, this wavelet estimation method caneffectively complete wave inversion imaging.