全波形反演

全波形反演，一纬，二维

Frequency-domain full-waveform tomography for visco-acoustic media.

! #

! # Program FWT2D is a massively parallel code for distributed memory platform ! # which performs frequency-domain full-waveform inversion of seismic data [10,11,12,13].

! # The program is more specifically designed for wide-angle or global offset data !!!!!!!!!更特别设计

! # (that is, for any acquisition system involving dense wide-aperture acquisitions ! # and for which sources share a significant range of receivers spanning over large ! # offsets). The inversion looks for the P-wave velocity only. However, heterogeneous

! # density and attenuation can be provided for the forward modeling.

! # The inversion relies on a classic iterative steepest descent algorithm [1,2]. Iterations !!!!!!反演依赖于经典的迭代最速下降法

! # are performed in a non linear way which means that the final model at a given ! # iteration is used as the starting model for the next iteration.

! # Single or group of frequencies are inverted successively. The classic procedure ! # is to proceed from the low frequencies to the higher ones [3]. Note however that

! # all the frequencies can be inverted simultaneously by defining a single group ! # of nw frequencies (nw is the total number of frequencies to be inverted).

! # The cost function is based on the least-squares norm. The cost function is weighted !!!!!!!!!!!!!!!成本函数是基于最小二乘范

! # with an operator which applies a gain with offset to the residuals.

! # The gradient of the cost function is properly scaled by the diagonal terms of the ! # approximate hessian J^t J where J is the sensitivity matrix [4].

! # The source can be approximated in the program solving a linear inverse problem

! # (see [2], [10], [13]).

! # The step length is computed by parabolic fitting.抛物线拟合

! # The forward problem, that is, wave propagation modeling, is performed with a ! # finite-difference frequency-domain method [6,7,14] and relies on a direct solver to

! # solve the associate sparse system of linear equations whose right-hand sides

(RHS) are

! # the sources. We use the massively parallel direct solver MUMPS for distributed memory

! # platform to solve this system [15,16].

! # Note however that the code can also be run in sequential (see MUMPS documentation).

! # Absorbing boundary condition in the FDFD code are combination of PML [9,14] and 4