Research On Local Optimization Inversion Method Based On Partial Differential Equation Constraint

The method of inverting the physical properties of the earth’s medium based on the seismic signal is called the seismic inversion method;the scientific research of an inverse problem mainly has three aspects:(1)model parameterization;(2)forward modleing;(3)inversion.Each of these three problems is very complicated,and it is exactly the theoretical problem to be solved in the whole exploration seismology.Judging from the reality of oil and gas exploration and development,traditional migration imaging and modeling methods have been difficult to adapt to the actual needs of oil and gas exploration.In western China,the geological conditions are extremely complicated.On the surface,it involves landforms such as deserts,and mountains;in the shallow layers,mountain seismic exploration has a low signal-to-noise ratio and broken velocity structure,and the shallow absorption attenuation in desert areas is quite serious;in the deep layers,in addition to being severely restricted by the surface and shallow layers.In addition to the conditions,it also faces the problems of low seismic resolution and insufficient angle information.Various seismic exploration methods based on simple geophysical models have also approached the upper limit of their capabilities in this case.This thesis re-examines the problems of migration methods and velocity modeling from the theoretical height of seismic inversion and imaging;starting from actual geology and physical reality,extracts more information to improve the resolution of physical models;from basic mathematical physics,research the essential geophysical medium,the forward propagation process of the wavefield and the mathematical inversion theory to optimize the theoretical framework of seismic exploration and achieve the goal of adapting to the exploration and development of oil and gas reservoirs under more complex geological conditions.Starting from the Bayesian inference theory,deriving the inversion problem,discussing the problem of different error distribution assumptions,combining the FWI research status and practical problems,and proposing the use of appropriate probability The distribution measurement method constructs a new objective function for solving,and provides an inversion method based on error update to improve the inversion accuracy;related work on weakening the PDE constraint conditions mainly focuses on weakening the nonlinearity by adding additional variables or To expand the optimization space,this type of method generally requires multiple adjustments to additional variables,and there is uncertainty.In this paper,the WRI method is extended to the time domain,and an optimization algorithm is proposed for its penalty factor;The method including the theoretical variance matrix is discussed,and finally,the application of WRI in some special cases is given;it is best to deeply analyze the strong nonlinearity under the PDE constraint,and propose to reduce the nonlinearity of the inversion by transforming the constraint expression To establish a more convex inversion problem and solve it;plan to modify the nonlinearity of the PDE constraint itself to obtain a more convex inversion problem;mainly include replacing the wave field with the instantaneous phase after unwinding And replace the time-space domain wave equation with the phase-space domain wave equationThe research results show that with the complication of exploration conditions and the improvement of exploration requirements,the traditional full-wave field wave equation has strong constraints on inversion problems no longer applicable.On the contrary,by appropriately relaxing this constraint,the accuracy of the inversion result can be improved to a certain extent.For inversion problems with strong constraints,the nonlinearity can be reduced to a certain extent by transforming the variables and space,but its application needs to be discussed separately.