The Fast Hankel Transformation And Its Applications In Electrical Exploration Forward Calculations

:The forward modeling occupies a very important position in the geophysical data processing, it directly affect inversion effect. In the forward calculation of active source electrical exploration methods, usually encounter the problem of the bessel integral calculations, which the traditional method is complicated to solve. There are studies shows that the digital linear filtering method is very effective in solving Bessel integral, not only high accuracy, but high speed. The fast Hankel is one of the digital linear filtering methods, which is widely used. This paper is a research about the the fast Hankel theory and application in electrical exploration methods, purposing with the least amount of time to achieve high accuracy forward calculation results.Since fast Hankel transform being introduced in geophysical field,there have generated a lot of fast Hankel filter coefficients.Different coefficients have different lengths and accuracy. Five groups coefficients with high-precision are selected, to calculate a set of Bessel integral which have analytical solutions, then we can gain the relative error. Analysis of the accuracy of different filter coefficients, select a filter coefficients usually have a better performance. we make an adaptive truncation on the coefficients chosen, to calculate the integral of relate hankel transformation in EM problems. In this algorithm, it can be terminate the calculations when achieve the required accuracy, and also avoid the time-consuming of repetitive convolution calculations. It is possible to save time in the calculation of related hankel transforms, especially when the kernels are very complicated complex functions.The five sets of high-precision filter coefficients are also applied to the resistivity sounding method, frequency electromagnetic sounding method and transient electromagnetic sounding method, programming for many modles, and calculate the apparent resistivity curves. On the analysis of the difference between curves,we know that different filter coefficients in different exploration methods have different calculation accuracy. This is very complicated, we can not say, the longer coefficients, the higher accuracy. Consider both time consuming and accuracy performance,120JO and140J1most time have a better performance. Because it is difficult to give a quantitative conclusions, it is recommended that we should choose a filter which have a better performance for most conditions. In additon, a few tentative selection of filters are necessary.