The Research On The Method Of Finite Difference Contrast Source Inversion Based On Acoustic Equation

At present,the main method for complex geological structure imaging is pre-stack depth migration,and the pre-stack depth migration requires more accurate velocity.The full waveform inversion technology can obtain fine velocity,but the conventional full waveform inversion is large computation cost and low efficiency.Some scholars have studied the full waveform inversion from the scattering theory,and proposed the finite difference contrast source inversion method,which can greatly reduce the computation cost.The finite difference contrast source inversion method is a frequency-domain wave equation waveform inversion algorithm,which is an inversion method to solve the wave equation inverse scattering problem.This method constructs objective function by introducing contrast function(model disturbance)and contrast source(scattering source).In the inversion process,the forward operator is constructed by using the frequency-spatial domain 9-point difference and PML absorbing boundary condition.Because the finite difference operator is constructed by background model and the background model does not change,so the difference operator needs to LU decomposition only once,which reduce the computation cost.The objective gradient is obtained by Fréchet derivative,and the nonlinear conjugate gradient method is applied to continuously optimize the objective function and iteratively update the contrast source and contrast function.There are two-term updates,so we first update contrast source,then update contrast function according to the relation between contrast source and contrast function,complete an iteration.The final contrast and background model are combined to obtain the velocity model of inversion.The validity of the finite difference contrast source inversion method is verified by numerical simulation.Based on the finite difference contrast source inversion of the conventional conjugate gradient method,this paper improves the super-memory gradient method and proposed the super-memory hybrid conjugate gradient method,which is applied to the finite difference contrast source inversion.The method uses the gradient information of the previous iterations to reconstruct the new gradient direction.In the process of inversion,the computer memory consumption is not significantly increased,and the convergence speed is accelerated.The numerical simulation results show that the method is efficient in the finite difference contrast source inversion method.