Regularizing seismic inverse problems by model re-parameterization using plane-wave construction

Multiple suppression

Separation of primary and multiple reflections is one of the most important tasks in seismic data processing. A distinguishable characteristic of surface-related multiple events is different slopes because of different apparent velocities. The advantage of using slope-based prediction is that, for estimating dominant slopes of multiple events, we can utilize models of the multiples that may have incorrect amplitudes and wavelets as long as they correctly predict event geometry (Guitton, 2005). An example is shown in Figure 5, which contains a multiple-infested CMP gather from the Mobil AVO dataset (Keys and Foster, 1998), its prediction with the SRME (surface-related multiple elimination) method (Verschuur et al., 1992) and two dominant slopes estimated from the data and corresponding to primary and multiple reflections. Even though SRME does not provide correct amplitudes and wavelets in prediction of the multiple events, it can guide the slope estimation method toward extracting the dominant slopes of multiple events.

cmp
Figure 5. a: CMP gather from the Mobil AVO dataset, b: multiple model from SRME prediction, c: estimated dominant slope of the primary reflection events, d: estimated dominant slope of the multiple reflection events.

The model of the data is now (Nemeth et al., 2000; Guitton, 2002)

$$\mathbf{d} = \mathbf{C}_p \mathbf{p}+\mathbf{C}_n \mathbf... ...begin{array}{c} \mathbf{p} \mathbf{n} \end{array}\right]\;,$$ (9)

where $\mathbf{C}_p$ is plane-wave construction along primary slopes and $\mathbf{C}_n$ is plane-wave construction along multiple slopes. In accordance with equation (7), the least-squares estimates of the multiples is

$$\widehat{\mathbf{m}} = \mathbf{C}_n \widehat{\mathbf{n}} =... ...f{C}_n^T + \epsilon^2 \mathbf{I}_N\right)^{-1} \mathbf{d}\;.$$ (10)

Figure 6 shows the estimated primary and multiple events and comparison of velocity semblance scans before and after multiple suppression. A large portion of the multiple energy is successfully removed from the data.

super
Figure 6. a: estimated primary reflections (data with multiples removed), b: estimated multiple reflections, c: velocity scan of the original gather, d: velocity scan of the gather after multiple suppression.

Regularizing seismic inverse problems by model re-parameterization using plane-wave construction