Full Waveform Inversion Based On The Time-domain Elastic Wave Equations

Full waveform inversion can obtain the parameter of the subsurface medium by calculating the minimum of the objective function which is built by the residuals between the observed and simulated seismic data.Due to its high resolution,it has become a research hotspot in recent years.Because only P-wave velocity cannot satisfy the requirements of the seismic imaging as the increase of the exploration sophistication and refinement,we conduct a study on time domain elastic full waveform inversion in this paper.According to the Lagrange adjoint theory,we derive the adjoint wave equations and gradient expressions based on the 1st-order velocity-stress elastic wave equations.We adopt the convolutional perfectly matched layer(CPML)to absorb the reflections from the boundary caused by the manual intercept.With respect to the high dependency of FWI on the initial models,we apply the multi-scale inversion strategy based on the low-pass filter,reducing the dependency on the initial models and improving the inversion results.We use the 2D and 3D synthetic seismic data to perform the tests and the corresponding results show the feasibility of this algorithm.Considering that it is difficult to acquire accurate wavelet in practical seismic exploration and inaccurate wavelet may lead to the collapse of the inversion,we perform propose the source-independent elastic full waveform inversion based on the convolutional objective function,and add a time window on the reference trace to suppress the noise induced by the convolution and cross-correlation operation.In order to improve the robustness of our algorithm to the noises,we adopt the L1-,Huber-and hybrid-norm objective function.In addition,based on the filtering effect of convolution operation,we design a multi-scale inversion strategy based on this objective function.By gradually improving the dominant frequency of source wavelet,we can reduce the dependency on the initial models and improve the accuracy of inversion results.The inversion results of the synthetic seismic data show that although the wavelet is estimated inaccurately,we can still obtain the accurate inversion results.The inversion results of real seismic data further verify the reasonability and accuracy of this method.For the problems of high amount of computation and storage of seismic wavefields,we apply the source-encoding method based on the orthogonal basis of trigonometric functions to FWI,by which we can not only avoid the high storage amount,but also encode many individual excited sources into one super source,reducing the times of wavefield forward-and backward-propagation and improving the efficiency of FWI.More importantly,this method does not have cross-talk noises which is induced by the conventional source-encoding method.Inversion results of synthetic seismic data prove the feasibility and accuracy of this algorithm.