Single frequency 2D acoustic full waveform inversion |

The choice of the source 15 is dictated by the considerations of our CUDA implementation. We will now show how the time-domain kernel working with sources 15 can be adapted to solve the waveform inversion problem in the frequency domain for an arbitrary waveform source . First, Fourier-transforming 2, we can see that recovering the velocity from a solution to 2 with the source 15 is equivalent to recovering the velocity from a solution to

By choosing we get

in the right-hand side of 16. Now assuming that the velocity is an even function of the frequency, and that we attempt to reconstruct the velocity from 2 with , we can see from equation 16 that we can equivalently run 2D waveform inversion 2 for frequencies with in 15. For an odd waveform (but still even velocity) for each we use . An arbitrary waveform can be represented as the sum of an even and odd components, and equation 2 will have a linear combination of two source terms 15 in the right-hand side.

Single frequency 2D acoustic full waveform inversion |

2012-05-10