The migration of GPR three dimension wave equation in wavelets domain

This paper elaborated on the standard and nonstandard forms of matrix multi-resolution analysis theory in detail, and taking Hilbert operator as an example, explained the compression result of operator with multi-resolution form. It laid a good theoretical foundation for migration algorithm of wavelets domain. Then, setting out from the three-dimension 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. Through equation splitting and multi-resolution wavelets theory, and solving the extrapolate matrix of wave field in the wavelets domain, we have also got the migration algorithm of GPR three-dimension wave equation in wavelets domain. Based on this, the authors developed the migration program of GPR three-dimension wave equation, and applied this program to three-dimensional forward modeling result of three spheric caverns and practical GPR data. Through comparing the radar data before and after the migration processing, it is known that this three-dimension 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.