GPR Forward Simulation And Migration Processing Research With Multi-resolution Of Wavelets

Ground penetrating radar is a geophysical exploration method whichdetects the underground structure and characteristics. Because of theadvantages such as high efficiency, quick speed, undamaged, highresolution, and strong anti-jamming features, it has been applied to everyaspect in engineering domain, and it has been a powerful tool of shallowlayer exploration. But nowadays, the technical of GPR also need to beimproved, because it exists apparently subjective, such as, the detectiontechnical of GPR is still detained in two-dimension moment, and theexplanation technical is also build on the experiences to identifyingradar image and blocking out radar anomalous body handful. Thoroughlyunderstanding electromagnetic wave propagation rules, and launching theresearch of GPR two or three-dimension forward simulation wouldreduce the probability of the wrong explanation to the data, and providethe reference to develop the three-dimensional GPR technical and theaccurate explanation to radar data. This paper could be divided into twoparts, whose first part introduces the GPR forward simulation, and secondpart introduces the GPR migration processing.In the GPR forward simulation, based on the basic wavelets theoriesand the characteristic of Daubechies wavelets, the author chooses theGalerkin method to discrete the two Maxwell rotation equations. And italso uses the K.S.Yee grid to deduce the MRTD algorithm based on theDB2 wavelets basis. At the same time, it deduces the GPR two orthree-dimension finite difference formula, numerical stability, dispersionrelation of this algorithm detailed. And then, through analysis, it isknown that compared to the normal FDTD algorithm, MRTD algorithmhas better dispersion relation which could reduce the grid number in radarsimulation calculation, save memory space, improve the efficiency ofGPR forward simulation. Based on this, the author explores MRTDforward simulation program of GPR, which could do the data simulationexperiment to the complex two or three radar models. This programbreaks the limitation which is only could forward simple and regulationradar model, at the same time, it conforms the validity of MRTD algorithm which is used to GPR forward simulation.In the research of GPR migration processing, the author firstlyanalyzes the traditional finite difference method has some disadvantages,such as obliquity limitation, lowly calculation efficiency, big migrationnoise of Kirchhoff's method of integration migration, seriouslyinterference of high frequency, and the F-K migration inadaptable withthe changeable of velocity. For better to realize the radar migration, theauthor systematically summarizes the relationship between waveletsmulti-resolution and GPR migration processing, and uses the wavelet tomulti-scale compress extrapolate matrix of radar wave field. Then theauthor deduces inverse time migration algorithm of GPR two-dimensionwave equation in wavelets domain, and takes the real example to explainthe concrete advantages of inverse time migration algorithm of GPRtwo-dimension wave equation in wavelets domain, such as smaller noisecomparing to Kirchhoff's method of integration migration, more accuracyof waveform returning to original position, highly adaptation to velocitymodel, no obliquity limitation and lowly requirement for Signal-to-Noiseof radar data. It could improve the migration algorithm velocity if setdomain data during the decompose course of radar wave fieldmulti-resolution, and it could also filtrate some high frequency noise.Secondly, setting from the three-dimension radar wave equation, usingthe bursting reflection theory and floating coordinate transform, withequation splitting and multi-resolution of wavelets theory, the authordeduces the migration algorithm of GPR three-dimension FD waveequation in wavelets domain. Then the author puts this algorithm tothree-dimension forward result of three sphere cavern. Through comparethe radar data before and after the migration processing, it is known thisthree-dimension migration algorithm could make the reflection wavereturn to original position, and make the diffraction wave converge in thethree-dimension sections. The lateral resolution of radar sections could behighly enhanced, and it can instruct the geology expiation of GPRsections better. At last, the author does the research of GPRthree-dimension field working method, data processing andthree-dimension expression in the program practice, and gets the goodeffect, which sets the base for three-dimension technology of GPR.