The Migration of GPR Three Dimension Wave Equation in Wavelets Domain

Abstract

AbstractThis paper expounds on the standard and nonstandard forms of multi‐resolution matrix analysis. Taking Hilbert operator as an example, we explained the compression result of the operator with multi‐resolution form. It laid a good theoretical foundation for migration algorithm of wavelets domain. Then, setting out from the three‐dimensional radar wave equation, and making use of the bursting reflection theory and floating coordinate transform, we have deduced the finite difference format of GPR three‐dimension wave equation. Utilizing the equation splitting and multi‐resolution algorithm of wavelet theory and solving the extrapolation matrix of wave field in the wavelet domain, we have also got the three‐dimensional wave equation migration algorithm of GPR data in wavelet domain. Based on this, the authors developed the computer program of GPR migration, and used this program on the synthetic data of a three‐spherical cavern model and practical GPR data. Through comparing the radar data before and after the migration processing, it is known that this three‐dimensional migration algorithm could make the reflection wave return to original position, and make the diffraction wave converge in the three‐dimension sections. The lateral resolution of radar sections could be highly enhanced, and the migration algorithm could make the radar three‐dimension detection more reliable and precise, which is propitious to the geology explanation of GPR data.