A Study On "Sompi" Cepstrum Methods For Accurately Controlled Routinely Operated Signal System

Accurately Controlled Routinely Operated Signal System,shorted as ACROSS,is a technique developed in the world since 1990's. It is a new tool to detect and observe the structure and status of underground media by accurately measuring its transfer function through sinusoidal elastic wave accurately controlled in frequency and stable in phase. It consists of three parts:accurately controlled signal source,time signal stacker and "sompi" cepstrum method. The accurately controlled signal source generates sinusoidal elastic wave accurately controlled in frequency and stable in phase to "illustrate" underground media. Time signal stacker receive signal by stacking and doing FFT to measure the transfer function of media. "Sompi" cepstrum method retrieve group velocity travel times and decayed factors of wave element from observational data of transfer function in a limited frequency window. The thesis mainly deals with the third part of ACROSS:"sompi" cepstrum methods. The principle and system structure of ACROSS are first introduced. The propagation of wave in media is simply studied and its transfer function in frequency domain is modeled as superimposed damped exponential sinusoids,each damped exponential sinusoid is called as a wave element and its exponential index part consists of two factors:group velocity travel time and decayed factor. The model of transfer function is further generalized into mathematical one,on the basis of which the algorithm and realization of many kinds of "sompi" cepstrum methods are discussed and their performances are fully compared by means of numerical .simulation. Finally a computation efficient method with good performance is selected as the to-be-used one. The compact Cramer-Rao Bound for estimated parameters is derived. How the proficiency of estimation is affected is analyzed .How to choose optimal number of observations and how to determine the order of model are also studied and practical method is presented for each. The selected "sompi" cepstrum method and the presented order determination method are tested with synthesized data. The selected "sompi" cepstrum method also processed experimental data of sample machine of ACROSS and the reasonableness of the result is proven by comparing with those from classical method.