Research And Application Of Fast Matching Pursuit Method Based On Optimized Local Frequency

The frequency content of seismic will continue to change when it propagates in the medium of underground strata,and the different frequency can reveal important information of stratum,such as the different tectonic characteristics,lithology and fracture,thus,it is necessary to adaptively decompose the seismic signal to obtain the frequency components at different moments so as to extract the important information implieded in the seismic signal.Matching pursuit algorithm(MP)is just a kind of signal decomposition method with these advantages,which can effectively revealing the time-frequency structure of the non-stationary signal.Dynamic matching pursuit algorithm takes the instantaneous characteristics of the signal as a priori information for its adaptive greed decomposition,to reduce the computational complexity of redundant dictionary indexes and iterative loops.However,the instantaneous frequency obtained by Hilbert transform will exhibit "negative frequency" interference and we need to perform a global search of frequency properties for the negative frequency point,which will reduce the searching accuracy of instantaneous frequency and can’t be used in dynamic matching pursuit.The paper introduced the least squares inversion strategy of local frequency,overcoming the problem that the instantaneous frequency overly depends on the instantaneous value of signal data point position,which can avoid the calculation results appear negative anomalies.The local frequency has been widely used in various fields and can be better used to detect natural oil and gas reservoirs and describe sedimentary geological phenomena.In this paper,the local frequency was firstly proposed to replace the instantaneous frequency to verify the validity of the local frequency.The smoothing factor in the regularized regularization operator is transformed from a constant to a vector,which can smooth different data points at different scales.It overcomes the disturbance caused by the denominator too small to solve the solution and makes the local frequency calculation result more reasonable and avoids Over-smoothing phenomenon.Even if the signal to noise ratio is too low or part of the signal is missing,the local frequency also can be reasonably calculated.The improved fast matching pursuit algorithm has stronger anti-noise.We use multi-atom search strategy that each iteration process will search for multiple optimal time-frequency atoms,so the operation speed of the method is accelerated.Firstly,the paper studies strong reflection recognition and separation using fast matching pursuit method based on optimized local frequency.We construct a time-frequency atomic library to identify the atoms that best match strong reflections,weaken the strong reflections and highlight the weakly small reflections of the target reservoirs above and below the strong reflections;Secondly,we use the method to characterize the boundary of the deposits using Wigner-Ville distribution to realize the time-frequency characterization of the signal,then determine the tip point of sand body using instantaneous spectrum information;Finally,the paper developed the fast matching pursuit sparse inversion method based on optimized local frequency constraints.The improved matching pursuit algorithm is used to solve the inversion objective function,and using model constrains to improve the resolution of the inversion result to achieve accurate estimation of the reflection coefficient.