Spectral Inversion Method Analysis Based On The Union Of LSQR And Simulated Annealing

This paper first explains the seismic record convolution model, then does the researchthat whether the odd even decomposition of reflection coefficient sequences can improve ourresolution, this is the critical-new point of John P. Castagna proposed the spectral inversion.Through the wedge model analysis, we know that peak frequency and peak amplitude as afunction of thickness for the even component, the odd component, and the total.Interestingly,below the tuning thicknessλ/4(is the seismic wave length),the evencomponent’s peak frequency and peak amplitude show significant and continuous changingdown to zero thickness.In the second place, this paper derives the objective function of spectral inversion,establishs the matrix equations of spectral inversion. And we perfect the objective function bychanging plural division to plural multiplication, eliminate the denominator close to zerovalue unstable situation of plural division,and so forth,enhance the stability of spectralinversion. Analysis the multiple solutions, uncertainty and stability of the spectral inversion.For the optimization algorithm of spectral inversion,we do some research on theSimulated Annealing(SA) algorithm and Least Squares QR algorithm(LSQR). Throughnumerical example,we proved the global optimization characteristic of simulated annealing.Applying the least squares QR algorithm to solve the spectral inversion objective functionequations is a bold attempt and innovation, also get the ideal inversion results. Also this ismore superior to John P. Castagna’s the least squares conjugate gradient (LSCG) algorithm.On convergence speed and precision of solution,LSQR algorithm is better than the randomoptimization method,such as monte carlo algorithm and so on.The next,we do some model analysis of the spectral inversion, first and foremost is non-sparse spectral inversion. Verify the correctness of the spectral inversion’s objectivefunction. Through the single trace theory model analysis, verify that the spectral inversionprecisely get the position,the size and the polarity of reflection the coefficient sequence. Showthat spectral inversion wipe out the seismic wavelet influence from the seismic records,thenget the reflection coefficient sequence. Reveals the spectral inversion compensation the lostedhigh frequency component of seismic records spectrum without changing the low-middlefrequency components of seismic records spectrum. Through several different wedge modelsanalysis, confirmed that the spectral inversion can identify the thin layers whose thicknessbelow the tunning thickness. Through the Marmousi model analysis, undulating surfacemodel analysis, Sigsbee2A model analysis and so on,we come to the conclusion that thespectral inversion has the ability of recovering complex geological model, it is very suitablefor exploring complex structure-subtle oil and gas reservoirs resources.Finally,we do some research on the sparse spectral inversion method analysis. In the caseof inversion initial model including the real layer boundary surface location and In someextent wavelet is accurate, sparse spectral inversion get the purpose of “cast out the false andretain the true”. Sparse spectral inversion has the powerful ability of anti-noise. In the partsection inversion, sparse spectral inversion get little influence of signal truncation andinformation missing. Spectral inversion method,which based on the union of LSQR andsimulated annealing alogrithm, also get the ideal perfect result. For the sparse spectralinversion,we do some real practical seismic data test.In the end,wo point out the next researchdirection and the emergency problems of the Spectral Inversion.