Inversion Of Stratigraphic Quality Factor Through Full Waveform Inversion

During seismic wave propagation, part of the elastic energy transforms into heat. High frequency energy dispersion is weaker than low frequency dispersion, thus it produces amplitude attenuation, low-resolution seismic data, and waveform distortion, especially for medium to deep formation. The intrinstic attenuation of the formation reflects its inelastic properties. Furthemore, the formation quality factor Q is used to reflect the seismic wave attenuation and thus Q can be used for the description of tectonic distribution and the prediction of oil and gas. Presently, the methods of estimating Q value are classified into three categories. The first kind of methods is in the time domain, such as the pulse rise time,the amplitude attenuation, etc. The second category of methods is in the frequency domain, such as the spectral ratio, the centroid frequency shift, and the peak frequency shift, etc. The third class of methods is in the time-frequency domain, such as the energy attenuation. Among them, the methods of pulse rise time, centroid frequency shift, and the peak frequency shift are all based on seismic wave broadening, and the other methods such as the amplitude attenuation, the spectral ratio, and the wavelet-domain energy attenuation are all based on energy or amplitude attenuation. However, these methods have universal applicability because of the quality of seismic data. Full waveform inversion can be used to inverse physical parameters from the wave equation effectively, but most of full waveform inversion method which inverses physical parameters is given priority to with velocity parameter, and the other physical parameters are assumed known.This paper is the hypothesis that density and speed parameter are known, using full waveform inversion to inverse formation quality factor Q from 2D viscosity acoustic wave equation. Full waveform inversion based on L-BFGS algorithm is on the basis of the frequency domain. The advantage of 2D viscosity acoustic wave equation forward modeling in the frequency domain is that it is convenient to introduce parameter Q which reflects seismic wave attenuation.In this paper the observed wave field and the other wave field obtained by forward modeling construct an objective function, and then use L-BFGS algorithm to inverse updated model. Applying this method for simple abnormal body model and complex Marmousi model respectively under the condition of without noise and containing noise test. The result shows that the formation quality factor Q can be estimated well by full waveform inversion based on L-BFGS algorithm, and the inversion model is more stable under the condition of containing noise.To compare and to analyze the effectiveness between the method of Q inversion based on L-BFGS algorithm and the method of Q inversion based on other optimization algorithms. Firstly, set up a horizontal layerd medium model, and then apply the steepest descent method, conjugate gradient method and L-BFGS algorithm to horizontal layered meduim model respectively. Secondly, compare and analyze the relative error of the theoretical model and the inversion model and the calculation time. Finally, the result shows that comparing with other two kinds of optimization algorithm, in the same iteration update situation, the relative error between the theoretical model and the inversion model which calculated by Q inversion based on L-BFGS algorithm is smaller, the iterative update is faster. On this basis, the models are tested with and without noise data, the result shows that the inversion method based on L-BFGS algorithm is more noise resistance.