Through the computer numerical experiment, it systematically studies the excitation and propagation properties of the head-wave in a borehole surrounded by a porous medium,and proves that the head-wave has the property of resonance and attenuation. However it is evidently different from the head-wave in an oil well surrounded by homogeneous medium. The attenuation of the resonance peak amplitude appears first insreasing and then decreasing when the resonance frequency increases. The reservoir parameters——porosity (φ) and permeability (κ) of the porous medium have few influence on resonance frequency. But they have an evident effect on resonance peak amplitude, Which decrease when the porosity (φ) and the permeability (κ) become larger.

By using the mathematical model of fractal insertion, an algorithm is given for auoustic logging curve based on similar logging data. When applying it to processing of the data of 7 similar logging in Dan Feng Chang, Sichuan and 3 similar logging in Nan Hai, the obtained fractal curve is very close to the real acoustic logging curve, with correlation coefficient greater than 70%. This method makes it possible to get the same message of logging curve from the CDP recording of the seismic prospecting.

In this paper, we give the two improved formulas of distance, which can be used in the G-P algorithm, and the corresponding recurrence formulas, which improves the G-P algorithm,We present a rule and a mathematical model to determine no-scale interval. Such a algorithm to solve the end points of the interval can be applied to the signal processing of the seismic prospecting. The no-scale interval and the fractaldimension of time data series of the seismic tunnel are computed as well in our work.