在频域中用有限元法解决地震勘探中的正反演问题

在时间域应用有限元法求解波动方程边值问题，存在不稳定的缺点。在频率域中应用有限元法求解波动方程边值问题，则可以避免上述缺点，而且由于采用了FFT，能使运算速度加快。频率域有限元解法的要点是先对时间进行一维傅氏变换，把波动方程化为Helmholtz方程，然后在频率中用有限元法对该方程进行求解，最后把求解结果经过反傅氏变换回到时间域。此法既可用于解决地震勘探中的正问题也可用于解决反问题。

The application of finite element method to forward and inverse seismic problems in freauency domain

Unstable result is obtained when the boundary problem of wave equation is solved using finite element method in time domain. However, when the boundary problem of wave equation is solved by finite element method in frequency domain, not only the unstability can be avoided but also camputation is speeded up because of using FFT. The procedure for solving the boundary problem using finite element method in frequency domain is as follows: 1.the wave equation is transformed into Helmholtz equation by making one-dimensional Fourier transform with respect to times 2. Helmholtz equation is solved using finite element method in freqaeney domain 3. the obtained result is returned to time domain by making inverse Fourier transform. Both forward and inverse seismic problems can be solved try this methods.