一种基于动态目标泛函的全波形反演多解性评估方法

Multi-solution analysis of full waveform inversion based on dynamic misfit function

全波形反演是一种精度较高的地下速度建模方法,但其存在计算量巨大、反演多解性、初始模型依赖性强、适用条件苛刻等困难,生产实用化仍然较为困难。将基于动态目标泛函的全波形反演方法应用于反演解的讨论中,利用已有的反演解作为先验信息,通过动态调整目标泛函,在保证地下介质模型能够准确解释地震数据的前提下得到尽可能不同的反演结果。进一步根据数据约束强弱差异选取不同的反演策略,新方法能够对数据覆盖较弱区域的反演结果进行有效评估。在实现算法和反演流程的基础上,通过典型海底模型进行试算。结果表明,新方法能够在保证解的准确性前提下对全波形反演的特征给出合理分析,相对于传统方法计算效率也有了明显提高。

Full wave-form inversion(FWI)is one of the most promising velocity model building tools for its high precision andresolution which theoretically can utilize all the information carried by seismic record.However,because of the multi-solutionproperty of the geophysical inversion problem and the limitation of the quality of seismic data,FWI can only generate one of thelocal optimize solutions which partly explain the seismic data.The analysis of the inversion result and the multi-solution proper-ty is one of the key problems in geophysical inversion.In order to mitigate the computational burden and strict application con-ditions in conventional result analysis methods,we introduce a dynamic function to analyze the multi-solution property of FWI.The technique designed for generating multiple solutions is based on the modification of objective function using the informationof the previous results.The searching for a new model is achieved by adding a feedback term which creates a local maximum ateach point in parameter space filled with previously computed models.For the model where the objective function defines a lo-cal maximum,the gradient is randomly perturbed to create a family of distinct solutions which helps evaluate the model wherepoorly illuminated by seismic data.The application on the sea model verifies that the method is efficient in terms of analyzing the inversion results of conventional FWI while keeping the accuracy.The merit of the proposed method is that it only needs toproduce a relatively small ensemble of solutions,since each model will substantially differ from all others to the extent permittedby the data and the computational burden compared with the traditional method is significantly reduced