Study On Regularized Joint Inversion Of Magnetotelluric And Gravity Based On Gramian Constraints

It is a trend to implement a joint inversion in the field of geophysical inversion,which can promote different geophysical methods to constrain each other and reduce the non uniqueness of solutions.Petrophysical constraints play an importrant role in the realization of joint inverions.Due to the complexity of actual statistical characteristics of rock physical properties,there are some shortages in the present study on geophysical joint inversion using petrophysical constraints:(1)The relationship of rock physical properties is not easy to identify;(2)The applicability of statistical or empirical petrophysical relationship is limited.Therefore,Gramian constraints,which are based on the linear correlation of vectors,have become a research hotspot of geophysical joint inversion.The constraints do not need to know specific petrophysical relationships,and have low dependence on prior information.However,in view of the petrophysical relationships change with space and lithology,the constraints lack differentiation implement strategy for different regions.The selection of regularization factors affects inversion results directly,and adaptive regularization algorithm is the hotspot and difficulty in the field of regularized inversion.In the previous study on adaptive regularization algorithm,the common consideration is the efficiency of data fitting.Literature analysis shows that considering the selection of regularization factor from the perspective of improving the stability of inversion is a new way.In addition,most of the previous regularization studies are based on linear optimization algorithms,and the randomness of nonlinear optimization algorithms is not considered enough.Based on this,aiming to improve the coupling of resistivity and density using the linear correlation of vectors,we introduce the Gramian constraints into the joint inversion of MT and gravity.In addition,we implement the Gramian constraints in areas to solve the problem that the constraints lack differentiation implement strategy.Moreover,we propose a new adaptive regularization algorithm,which is called as “Staged Adaptive Algorithm”,in which the regularization factor adjusted according to the "stage" adaptively.Model tests show that:(1)The joint inversion based on Gramian constraints can promote the coupling of rock physical parameters,besides,the region-divided Gramian constraints strategy,which is suitable for areas with complex petrophysical relationships,can improve the flexibility of the application of the constraints;(2)The staged adaptive algorithm can promote stabilizing functional to exert better function and reduce the instability of inversion,besides,the algorithm has the potential to apply on linear and nonlinear optimization algorithms.Finally,in order to test the practicability of the new methods proposed in this thesis,the joint inversion of MT and gravity in the lower Yangtze region is carried out.The density model is established based on MT inversion result and prior petrophysical information,then,MT and gravity staged adaptive regularized joint inversion based on region-divided Gramian constraints is carried out.Compared with the prior seismic profile,the joint inversion results are basically consistent with the seismic information above the Tg interface,in addition,Under the Tg interface,the results of density joint inversion show the distribution law of "low high low",which is consistent with the prior information...