State Key Laboratory of Petroleum Resources & Prospecting, China University of Petroleum (Beijing), Beijing, 102249, China.
Centre for Reservoir Geophysics, Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK.
Sci Rep. 2017 Aug 17;7(1):8494. doi: 10.1038/s41598-017-09294-y.
In seismic waveform tomography, or full-waveform inversion (FWI), one effective strategy used to reduce the computational cost is shot-encoding, which encodes all shots randomly and sums them into one super shot to significantly reduce the number of wavefield simulations in the inversion. However, this process will induce instability in the iterative inversion regardless of whether it uses a robust limited-memory BFGS (L-BFGS) algorithm. The restarted L-BFGS algorithm proposed here is both stable and efficient. This breakthrough ensures, for the first time, the applicability of advanced FWI methods to three-dimensional seismic field data. In a standard L-BFGS algorithm, if the shot-encoding remains unchanged, it will generate a crosstalk effect between different shots. This crosstalk effect can only be suppressed by employing sufficient randomness in the shot-encoding. Therefore, the implementation of the L-BFGS algorithm is restarted at every segment. Each segment consists of a number of iterations; the first few iterations use an invariant encoding, while the remainder use random re-coding. This restarted L-BFGS algorithm balances the computational efficiency of shot-encoding, the convergence stability of the L-BFGS algorithm, and the inversion quality characteristic of random encoding in FWI.
在地震波层析成像或全波形反演（FWI）中，一种有效降低计算成本的策略是射束编码，它将所有射束随机编码并求和为一个超级射束，从而显著减少反演中的波场模拟次数。然而，无论是否使用稳健的有限内存 BFGS（L-BFGS）算法，这一过程都会导致迭代反演不稳定。这里提出的重新启动的 L-BFGS 算法既稳定又高效。这一突破确保了先进的 FWI 方法首次适用于三维地震野外数据。在标准的 L-BFGS 算法中，如果射束编码保持不变，它会在不同的射束之间产生串扰效应。这种串扰效应只能通过在射束编码中采用足够的随机性来抑制。因此，L-BFGS 算法在每一段都会重新启动。每一段都包含一定数量的迭代；前几个迭代使用不变的编码，其余迭代则使用随机重新编码。这种重新启动的 L-BFGS 算法平衡了射束编码的计算效率、L-BFGS 算法的收敛稳定性以及 FWI 中随机编码的反演质量特性。
