Deterministic Searching Methods Of Prestack Seismic Inversion For Petrophysical Parameters

Seismic reflection data is comprehensive expression of underground stratigraphic information,such as geological structure,lithology and fluid.Through inversion of prestack seismic reflection data we can not only obtain elastic properties of the main subsurface structures,but also can estimate petrophysical parameters of the rocks and its saturated fluid.With the increasing difficulty of exploration and exploitation,elastic properties alone cannot meet the need for complex reservoir characterization.Estimating petrophysical parameters from the prestack seismic reflection data has long inspired the academia and industry.For the following three reasons,the suitability of prestack seismic inversion is greatly challenged:(1)due to earth filtering effect,the frequency of recorded seismic reflection data is band limited.(2)the seismic reflection data contain multiple types of noise,which usually has low signal to noise ratio.(3)due to our limited knowledge,a large number of approximate formulas and models are used in the seismic inversion process.Therefore,on the one hand,the solutions are inherently non-unique,since there are several earth models that all fit the data equally well.On the other hand,the transformation of seismic reflection data to petrophysical parameters is also an ill-posed inverse problem with roughness solutions,because minor differences in input data can lead to large errors in the solutions.Existing methods are mainly based stochastic searching techniques to solve the serious ill-posedness of seismic inversion.However,the main limitation of stochastic searching techniques is that the optimisation step can be computationally expensive in actual applications.Thus,it is difficult to fully meet the requirements of large-scale geophysical inversion.By considering the earth filtering effect,the approximate formulas and model errors as noise,we proposed to suppress the effect of noise in the inversion process to improve suitability.Only through this way can we obtain a strategy for the joint estimation of elastic and petrophysical parameters from prestack seismic data with deterministic optimisation techniques.The main research results and innovations can be summarized as follows:(1)We propose to develop a strategy under Bayesian theoretical framework for joint estimation of elastic and petrophysical parameters from prestack seismic data with deterministic optimization technique.This method first uses classical rock-physics models and AVO forward modeling model to establish the relationship between petrophysical parameters and prestack seismic reflection data.An objective function of prestack simultaneous inversion of elastic and petrophysical parameters is then established based on the Bayesian theory framework.To the problem of finding a solution for the nonlinear objective function,we propose to use Taylor polynomial to convert the original problem into a linear least squares problem.Synthetic model test and real data application show that the proposed method can combine with different types and scales of seismic,geological and logging data to constrain inversion process.In this way,it narrows the solution space of the inverse problem,so that the inversion results are closer to the real underground situation.Compared with the stochastic searching methods,the proposed method can obtain optimal solutions more quickly with the use of gradient information,so it meet the need of large-scale geophysical inversion.(2)Aiming at the issue that gaussian assumption in the above inversion method is not enough to describe the statistical characteristics of seismic noise,we propose to introduce a generalized gaussian distribution that can approximate arbitrary symmetric probability density.The kurtosis k of seismic noise is first used to approximate the morphological parameters p of the generalized Gaussian distribution.An adaptive -norm seismic data fitting term is then proposed to improve stability of the above simultaneous inversion method.Synthetic model test and real data application show that the proposed method can adaptively adjust norm type of seismic noise according to the kurtosis k of seismic noise,and the seismic noise suppression is obviously superior to the traditional -norm inversion method.(3)Aiming at the issue that gaussian assumption in the above inversion method is not enough to describe the statistical characteristics of rock-physics model noise,we propose to introduce Hampel three truncated distribution function to adaptively set a segmentated weighting function.Thus a regularization term of rock physical model based on weighted least squares is proposed to improve the stability of the above simultaneous inversion method.Synthetic model test and real data application show that the proposed method weights small residuals with -norm,and treats large residuals with -norm,making it a new rock-physcs model with no heteroskedasticity.As aresult,the rock physical model noise suppression is obviously superior to the traditional -norm inversion method.(4)Aiming at the issue that the band limited data error leads the inversion result not match the actual stratigraphic trend due,root mean square velocity is first introduced in the inversion process as a model constraint.A new objective function of prestack simultaneous inversion of elastic and petrophysical parameters is then established based on the Bayesian theory framework.Synthetic model test and real data application show that the proposed method can avoid the multi-solution problem caused by the initial model error.(5)Aiming at the issue that inversion result is over-smoothing or under-smoothing when the model regularization method is based on global smoothing or global sparseness.From the perspective of a hybrid model,we consider the prior subsurface stratum as a sum of two components: a piecewise constant component and a smooth component.In this way,a total variation regularization term is fisrt proposed for the piecewise constant component,and a Tikhonov regularization term is then proposed for the smooth component.Thus a hybrid model regularization term is proposed to protect the discontinuous boundary of the model and to penalize the smooth area of the model.Optimal solutions are obtained finally when variety of small goals on the basis of priori understanding have been reached.Synthetic model test and real data application show that the proposed method is better to reflect layer-like characteristics of subsurface strata.