Dynamic Encoding vs Static Encoding

Following Krebs et al. (2009) and Boonyasiriwat and Schuster (2010), a different time-shift encoding of the shot gathers at each iteration can be used for MLSM; I call this dynamic encoding compared to static encoding where a shot gather has the same time shift for any iteration. To compare the effectiveness of the dynamic encoding method relative to static encoding, the MLSM of one 320-shot gather is computed with dynamic encoding. Figure e-f shows the migration images after 10, 30, and 60 iterations. Compared to Figure a-c, the MLSM result is improved, which indicates that dynamic encoding is more effective than static encoding in reducing crosstalk.

To quantitatively show the image quality improvement due to dynamic encoding, the SNR is calculated for the MLSM images and compared to the SNR of the statically encoded images in Figure . For each iteration, the corresponding conventional sources least-squares migration image is used as the reference signal. Here, I assume that the convergence rate is the same for conventional sources and multisource least-squares migration. Results clearly show that the dynamic encoding helps suppress the crosstalk and produce images with higher SNR compared to static encoding. With dynamic encoding, the assumption that the crosstalk noise at every iteration is uncorrelated with the crosstalk at previous iterations is closer to the ideal case compared to static encoding. The drawback is that now $I$ supergathers with different encoding functions are required at input, so that the I/O cost will increase and approach that of conventional migration for a large number of iterations ($I$ ).

However, the numerical results show that MLSM algorithm is less efficient in reducing crosstalk than the iterative stacking method as shown in Figure . The SNR of the 60-iteration MLSM image with dynamic encoding (Figure f) is comparable to the SNR of the 20-fold stacked image (Figure d: Note that the migration artifacts in this image are considered as signal in the SNR calculation). One possible explanation is that during the iterations of MLSM the gradients or conjugate directions are computed from different residual data and scaled by different step lengths to make different contributions to the MLSM image and cause the SNR enhancement of MLSM to be suboptimal. Therefore, in real applications, many supergathers ($N$ ) should be used. According to equation , more supergathers will greatly improve the SNR of final images, which is evident in examining the change from (f) to (a) in Figure .

When the processing technique for blending sources is used in full waveform inversion, the SNR of the inverted result is expected to behave in a manner similar to that of MLSM, but analysis is difficult because full waveform inversion is a highly non-linear process.

Figure 2.10: The solid line with squares shows the measured SNR for images of one 320-shot supergather with static encoding; the solid line with stars shows the results with dynamic encoding. Here the measured SNR is normalized by the first iteration result. The dashed line indicates the prediction from equation 2.11.