Summary

In Chapter 2 I proposed frequency selection to remove multisource crosstalk, aiming to solve the problem of inconsistent sets of receivers in modeling compared to in marine streamer survey. This approach requires that any crosstalk-prone sources should only emit signals in non-overlapping frequency bands. This approach allows any receiver to selectively tune in to the valid sources: the ones that indeed have contributed to this receiver and to selectively disregard potentially confounding sources, which are not associated with this receiver in the survey. Numerical results with a 2D salt model by marine survey show that the crosstalk is completely removed and compared to the standard migration, the speedup is nearly 10$\times$ . In the 3D example with a fixed obs geometry, a speedup of 40$\times$ is achieved.

In Chapter 3 I extended this research avenue to handle multisource fwi for marine streamer data. I adopted fdtd instead of the split-step method employed in Chapter 2. Sine waves of different frequencies are injected at sources that belong to one supergather. Due to delays in arrival time, an injected sine wave shows up at receivers delayed with onsets, which is no longer a pure sine wave. To mitigate this problem of spectral leakage, the simulation time is doubled, keeping only the second half of the duration. Numerical tests on synthetic and gom data sets demonstrate speedups around 4$\times$ .

Of interest to fwi, formulae are derived for the resolution limits of migration-data kernels associated with diving waves, primary reflections, diffractions, and multiple reflections. The formulae suggests that inverting multiples can provide some low- and intermediate-wavenumber components of the velocity model not available in the primaries. Futhermore, diffractions can provide twice or better the resolution as specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is on the order of lambda at the diffractor location for the diffraction-transmission wavepath.