MSSA

Multichannel Singular Spectrum Analysis (MSSA) is a powerful noise attenuation technology that exploits the spatial redundancy of data. Incoherent noise is attenuated by thresholding the singular values of data embedded in structured matrices. MSSA can be applied in a variety of domains (including common source gathers, common receiver gathers, post stack volumes, common offset vectors, and cross-spreads), using up to five dimensions. Our implementation of MSSA can optionally use a statistical analysis of the singular values at all times, positions, and frequencies in a survey to optimally discriminate between signal and noise. MSSA is well suited for strong noise environments and regularly achieves a high level of signal preservation. With MSSA we are able to target a variety of noise types including random noise, high amplitude spikes, harmonics, as well as high amplitude, high frequency scattered energy.

The preservation of weak diffracted energy is often problematic during noise attenuation. MSSA is able to better preserve these events while attenuating noise. Figure 1a shows a stacked dataset containing high frequency noise overlaying weak diffractions. The results of applying MSSA are shown in figure 1b (with difference shown in figure 1c). Time slice displays (shown in figures 2a-2c) show the power of MSSA to reveal weak underlying diffractions.

fig. 1a - Input stack with high frequency noise overlaying weak diffractions fig. 1b - Results of applying MSSA fig. 1c - Difference
Figure 1. Post-stack MSSA is able to preserve diffractions while attenuating noise.

fig. 2a - Time slice before MSSA fig. 2b - Results of applying MSSA fig. 2c - Difference
Figure 2. Time slice of data from Figure 1.

Figure 3a shows a structured data set containing high frequency noise overlaying many diffractions. The results of applying MSSA are shown in figure 3b (with difference shown in figure 3c). Time slice displays (shown in figures 4a-4c) shows the ability of MSSA to remove high frequency noise while increasing coherency across events and maintaining diffraction energy.

fig. 3a - Input stack with high frequency noise overlaying many diffractions fig. 3b - Results of applying MSSA fig. 3c - Difference
Figure 3. Applying post-stack MSSA to a structured dataset.

fig. 4a - Time slice before MSSA fig. 4b - Results of applying MSSA fig. 4c - Difference
Figure 4. Time slice of data shown in Figure 3.

In this example pre-stack MSSA was applied in the cross-spread domain. The level of denoising was automatically determined by the distribution of singular values extracted from the data. Figure 5a shows the stacked input data, while figure 5b shows the data after MSSA and stacking. The algorithm has preserved coherent high frequency energy in the shallow portion of the stack, while targeting deeper incoherent noise. The difference panel (shown in figure 5c) indicates a high level of signal preservation. A CMP gather before MSSA, after MSSA, and a difference panel are shown in figure 6.

fig. 5a - Stacked input data fig. 5b - After MSSA and stacking  fig. 5c - Difference
Figure 5. Pre-stack MSSA applied in the cross-spread domain.

fig. 6a - Before MSSA fig. 6b - After MSSA fig. 6c - Difference
Figure 6. A CMP gather from the data show in Figure 5.