Prestack Migration Method For For Compensating Absorption GPR Data In Attenuation Medium

In prestack depth migration using explicit extrapolators, the attenuation of the electromagnetic wave for ground penetrating radar (GPR) has been almost neglected so far. Conventional migration techniques aim at processing common-offset data. This paper presents one method for multi offset data prestack depth migration with considering absorption effect in frequency-space domain. Migration can be realized separately from electromagnetic wave equation and wave equation. The two methods are both based on wave equation theory and consider medium absorption finite difference method and realize compensation to absorption attenuation in the course of wave extrapolation.The finite-difference time-domain (FDTD) scheme for wave field simulation can be derived from the Maxwell's curl equations. The size of a cell and the interval of time are determined by Courant condition that is a numerical stability condition. In order to eliminate the effects of boundaries, the perfectly matched layer (PML) absorption boundary condition is used in this paper. The absorption effect of the PML boundary is very nice.The electromagnetic wave equation in frequency field can be derived from Maxwell's curl equations and electromagnetic wave diffuse rule in attenuation medium can be obtained from analyzing the relationships of electromagnetic wave velocity and absorption attenuation and frequency by consulting conductance parameter. Upper frequency range can be easy to arrive at electromagnetic wave"flat domino effect"in condition of high frequency low conductance. If the condition can't be satisfied, the frequency dispersion can't be ignored. In zero absorbency and middle absorbency medium separately design simulated direct wave data system in medium bosom and discuss electromagnetic wave attenuation character in lateral direction.This paper derives finite difference wave field extrapolate operator from Maxwell equation with conduct current. Considering lateral velocity transformation design three step precision convolution operator which contain the function of absorption attenuation and complex velocity. Then obtain continuation wave field and vertical derivative inverse continuation matrix and realize not only finite difference prestack depth migration but also compensation to absorption attenuation by eliminating wave field propagation with inverse continuation.Under the condition without absorption, use electromagnetism wave equation migration for 3 kinds of synthetic data models. This method can also make diffraction body of lesser size accurate homing for not accurate speed structure and make horizontal layer result level smooth. For inclining diffraction energy of interface inflection point it also can well homing and this method has better and lateral and longitudinal resolution capacity. It discusses the advantage of double excitation for fully reflection medium lateral information. Under the condition that has absorption, for composing data, we carry out the migration without considering absorption attenuation and compensation absorption attenuation. It shows that this method can realize energy attenuation absorption arouses compensation, at the same time, it can improve longitudinal tension distortion resulting from absorption and it can eliminate up and down phenomenon of phase axis in some degree and complete the correct homing of data. The migration for data with stochastic noise shows that this method can be used in the course of inverse extrapolation and it is effective to use deconvolution for filtering noise and under the condition of very low signal-to-noise ratio it still has better effect and it embodies advantage of extrapolation in frequency field.The electromagnetism wave equation migration that compensates absorption attenuation for actual measurement data shows that this method can compensate weak layer position information and compensate according to the level of attenuation and improve phase axis in lateral continuity and increase longitudinal resolution while compensating energy. It discusses the effect of stack to suppressing for disturbing information and put forward the curve of frequency spectra ratio determines the reasonable compensation migration bandwidth.Based on the equation of sound wave, we analyze its approximation after substituting electromagnetic wave equation and give finite difference prestack migration with separate extrapolation wave field. The results of two methods contrast we discover that electromagnet wave equation can be recovered for the partial energies of greater deep attenuation, while the equation of sound wave without absorption and it can only strengthen amplitude and enhance differentiate to less attenuation information and the compensation ability is low for deep layer information.