The Research Of Full Waveform Inversion With Total Variation Regularization Method

Full waveform inversion is a kind of method to obtain the properties of underground medium in seismic exploration.Based on the propagation theory of seismic wave equation,it makes full use of the complete kinematic and dynamic information contained in the ground observation data,to obtain underground medium parameters,such as velocity,bulk modulus,density and so on.So,the full waveform inversion method can reveal the complex background of geological structure and characterize lithologic detail,and provides a new method to prospect oil.Therefore,it is of great significance to study the full waveform inversion.Full waveform inversion is a ill posed problem in the mathematics,so it needs some regularization methods to obtain stable,unique solutions.But based on the L2 norm,regularization methods,such as Tikhonov regularization,make the inversion results too smooth,and is not in line with some specific geological conditions,when changes of model parameters are relatively large,velocity interface is very discontinuous.In order to make the inversion results more consistent with the geological law mentioned above,the full waveform inversion method based on L1 norm is studied in this paper.The method use total variation regularization to constrain the traditional objective function,which can also be understood to constrain inverted parameters gradients in all directions.Therefore it constructs a new minimum value problem to preserve the edge of the model.In this paper,the objective function gradients are divided into two parts,which are summed by the gradient of the traditional objective function and the gradient of the total variation regularization term.In order to avoid the large computational amount and the ill posed problem brought by Hessian matrix’s inversion,we use L-BFGS optimization algorithm to generate pseudo Hessian matrix and make it as a pre-conditioner.Then,we use the preconditioned conjugate gradient method to form the search direction and iterative models.In the implementation of full waveform inversion with the total variation,we adopt the continuous inversion strategy.Current source inversion result model is used as the initial model for the next source inversion.In each inversion process,we timely adjust the regularization parameter by the previous results and preliminary regularization parameter value,to obtain the target inverted model.In the end,we apply the simultaneous multisource technique to the full waveform inversion with total variation method.In the method,we use simultaneous multisource technique to reduce computational cost of the full waveform inversion effectively,and use the total variation method to suppress the crosstalk interference caused by simultaneous multisource.At the same time it can also preserve the edge of the model and improve the solution.The one-dimensional,two-dimensional model and complex model example tests demonstrate that the method can render the result model well blocky in both the horizontal direction and the vertical direction,and the edges are preserved obviously,and the inverted models are very close to the real models.