超参数控制下的波阻抗约束反演

The seismic survey is the most effective geophysical method during exploration and development of oil/gas. As a main means in processing and interpreting seismic data, impedance inversion takes up a special position in seismic survey. This is because the impedance parameter is a ligament which connects seismic data with well-logging and geological information, while it is also essential in predicting reservoir properties and sand-body. In fact, the result of traditional impedance inversion is not ideal. This is because the mathematical inverse problem of impedance is poor-pose so that the inverse result has instability and multi-result, so it is necessary to introduce regularization. Most simple regularizations are presented in existent literature, there is a premise that the image(or model) is globally smooth. In fact, as an actual geological model, it not only has made of smooth region but also be separated by the obvious edge, the edge is very important attribute of geological model. It's difficult to preserve these characteristics of the model and to avoid an edge too smooth to clear. Thereby, in this paper, we propose a impedance inverse method controlled by hyperparameters with edge-preserving regularization, the inverse convergence speed and result would be improved. In order to preserve the edge, the potential function of regularization should satisfy nine conditions such as basic assumptions edge preservation and convergence assumptions etc. Eventually, a model with clear background and edge-abnormity can be acquired. The several potential functions and the corresponding weight functions are presented in this paper. The potential functionφLφHL andφGM can meet the need of inverse precision by calculating the models. For the local constant planar and quadric models, we respectively present the neighborhood system of Markov random field corresponding to the regularization term. We linearity nonlinear regularization by using half-quadratic regularization, it not only preserve the edge, and but also simplify the inversion, and can use some linear methods. We introduced two regularization parameters (or hyperparameters) λ2 and δ in the regularization term. λ2 is used to balance the influence between the data term and the transcendental term; δ is a calibrating parameter used to adjust the gradient value at the discontinuous position(or formation interface). Meanwhile, in the inverse procedure, it is important to select the initial value of hyperparameters and to change hyperparameters, these will then have influence on convergence speed and inverse effect. In this paper, we roughly give the initial value of hyperparameters by using a trend- curve of φ-(λ2, δ) and by a method of calculating the upper limit value of hyperparameters. At one time, we change hyperparameters by using a certain coefficient or Maximum Likelihood method, this can be simultaneously fulfilled with the inverse procedure. Actually, we used the Fast Simulated Annealing algorithm in the inverse procedure. This method overcame restrictions from the local extremum without depending on the initial value, and got a global optimal result. Meanwhile, we expound in detail the convergence condition of FSA, the metropolis receiving probability form Metropolis-Hasting, the thermal procession based on the Gibbs sample and other methods integrated with FSA. These content can help us to understand and improve FSA. Through calculating in the theoretic model and applying it to the field data, it is proved that the impedance inverse method in this paper has the advantage of high precision practicability and obvious effect.

f-x-y域去除随机噪音方法研究

The seismic survey is the most effective prospecting geophysical method during exploration and development of oil/gas. The structure and the lithology of the geological body become increasingly complex now. So it must assure that the seismic section own upper resolution if we need accurately describe the targets. High signal/noise ratio is the precondition of high-resolution. For the sake of improving signal/noise ratio, we put forward four methods for eliminating random noise on the basis of detailed analysis of the technique for noise elimination using prediction filtering in f-x-y domain. The four methods are put forward for settling different problems, which are in the technique for noise elimination using prediction filtering in f-x-y domain. For weak noise and large filters, the response of the noise to the filter is little. For strong noise and short filters, the response of the noise to the filter is important. For the response of the noise, the predicting operators are inaccurate. The inaccurate operators result in incorrect results. So we put forward the method using prediction filtering by inversion in f-x-y domain. The method makes the assumption that the seismic signal comprises predictable proportion and unpredictable proportion. The transcendental information about predicting operator is introduced in the function. The method eliminates the response of the noise to filtering operator, and assures that the filtering operators are accurate. The filtering results are effectively improved by the method. When the dip of the stratum is very complex, we generally divide the data into rectangular patches in order to obtain the predicting operators using prediction filtering in f-x-y domain. These patches usually need to have significant overlap in order to get a good result. The overlap causes that the data is repeatedly used. It effectively increases the size of the data. The computational cost increases with the size of the data. The computational efficiency is depressed. The predicting operators, which are obtained by general prediction filtering in f-x-y domain, can not describe the change of the dip when the dip of the stratum is very complex. It causes that the filtering results are aliased. And each patch is an independent problem. In order to settle these problems, we put forward the method for eliminating noise using space varying prediction filtering in f-x-y domain. The predicting operators accordingly change with space varying in this method. Therefore it eliminates the false event in the result. The transcendental information about predicting operator is introduced into the function. To obtain the predicting operators of each patch is no longer independent problem, but related problem. Thus it avoids that the data is repeatedly used, and improves computational efficiency. The random noise that is eliminated by prediction filtering in f-x-y domain is Gaussian noise. The general method can't effectively eliminate non-Gaussian noise. The prediction filtering method using lp norm (especially p=l) can effectively eliminate non-Gaussian noise in f-x-y domain. The method is described in this paper. Considering the dip of stratum can be accurately obtained, we put forward the method for eliminating noise using prediction filtering under the restriction of the dip in f-x-y domain. The method can effectively increase computational efficiency and improve the result. Through calculating in the theoretic model and applying it to the field data, it is proved that the four methods in this paper can effectively solve these different problems in the general method. Their practicability is very better. And the effect is very obvious.