Remove Wavelet Dispersion In GPR Data By Using Inverse-Q Filter

Ground penetrating radar (GPR) is a high resolution geophysicalexploration method and is widely applied in engineering task. Thecapability of GPR has been proved. The characteristic of GPR waveis similar with seismic wave. At present, most of the processing ofGPR data is as same as seismic method, include filer, stack and so on.In fact, GPR wave is different to seismic wave. High frequencycomponents decay seriously in GPR method. With increase of time,dispersion is a common occurrence, and displayed in the radar imageas blurriness that increases with depth. The resolution reducedseriously. Removal of dispersion is a necessary step before applyingother methods, such as migration and spiking deconvolution, whichare based upon the assumption of a stationary wavelet.Some scholars raised accounting for dispersion in GPR data, butit was proved to be so difficult.The research of Turner and Siggins proved that over thebandwidth of a GPR pulses, the attenuation of some earth materialscould be characterized using a parameter known as Q *, which isclosely related to the seismic quality factor Q. The impulse responseof the transfer function for a given value of Q * differs from that ofthe same value of Q only in total amplitude.Spectral ratio and Q scanning methods are usually used inestimating parameter Q in seismic method. To the GPR data, they arecompletely valid in theory, but some troubles in actual work.Irving and Knight propose a technique for the estimation ofsubsurface Q from GPR data that builds on the frequency shiftmethod of Quan and Harris. The principle of frequency shift methodis that attenuation increases with frequency, and the high frequencycomponents of the signal are attenuated more rapidly than the lowfrequency components as waves propagate. As a result, the centroidof the signal's spectrum experiences a downshift during propagation.The downshift is proportional to a path integral through theattenuation distribution. The frequency shift method is relativelyinsensitive to geometric spreading, reflection and transmission effectsand the method is convenient.In time-frequency analysis, Fourier transform is a generaltechnique. As long as according with Dirichlet conditions, a functioncan be expanded by Fourier serials. But non-stationary signal cannotbe analyzed by Fourier transform.Short-time Fourier transform (STFT) is able to analyze a signalin a time-window context, but the width of time-window is stationary.So the STFT is not well-suited to the analysis of signals that containdifferent-scale features. Using wavelet transform (WT) is aconvenient way to acquire local-spectrum. However, a "motherwavelet" function is difficult to choose.The S transform can be regarded as a hybrid of the WT andSTFT, which is based on a moving and scalable localizing Gaussianwindow. This method is unique that it provides frequency-dependentresolution while maintaining a direct relationship with the Fourierspectrum.The receving-signal is a convolution result with source-pulseand reflectivity series. Using parameter Q constructs a time-varyingtransfer function. Based on the deconvolution theory, we use thedamped-least-squares inverse filter.After numerical simulation and the actual data processing, wethink the processing can enhance the resolution of the GPR image.