- 1.
- This approach tries to find proxies for the missing traces.
- 2.
- To be qualified as a proxy, a trace must have the same offset and either a similar CMP location or a similar azimuth angle.
- 3.
- Those proxies for the missing traces are used to predict multiples with first-order accuracy in multi-streamer geometry.

In order to better understand the approach, let's assume that we have a
multi-streamer acquisition system, as shown in Figure
1, with one shotline and seven streamers.
Supposing that we want to predict the multiple from source *S _{0}* to
receiver

Figure 1

There is one well-known geophysical concept that can help us meet the challenge, the common-midpoint (CMP), which assumes that traces with the same CMP location and the same offset contain the same information about one location in the earth. Although the common-midpoint assumption is a first-order approximation when the structure is not strictly flat, I will demonstrate that it is useful in our search for the substitute traces.

For example, for the virtual trace ,the real trace shares the same CMP location and has the same offset as well. The only difference is the azimuth angle. Therefore, trace is a proxy for trace in the multiple prediction, with first-order accuracy. Similarly, we can find substitutes for other virtual traces.

The central streamer in Figure 1 is a special case, in which we can always find substitute traces for the virtual ones with the same CMP location and offset. When we try to predict other streamers' multiple reflections, though, as in Figure 2, we are not so lucky to find proxies with the same CMP location and offset. However, we can relax the definition of a substitute trace by giving up the requirement that the proxy share the same CMP location. Then we can find another group of proxies for the missing traces, as Figure 2 illustrates. Since the cross-line spreading aperture is usually smaller than the in-line aperture, this extension may be acceptable in many real applications.

Figure 2

There are some limitations to the method discussed in this paper. Before
addressing those limitations, I would first classify the surface multiple
reflections into two categories. Figure 3 depicts
two types of geometries for the surface multiples,
and
. The difference between these two
categories is that, source *S _{0}*, surface multiple reflection position

The definition of proxies in my proposal guarantees that the method in this paper is fully applicable to the multiples like without kinematic approximations. The approximation errors occur only when we deal with the multiples like . In other words, when there are strong cross-line dips or scattering reflectors, my approach will introduce the approximation errors inevitably.

multiple-type
Two types of surface multiples. , in which the source Figure 3 S, the multiple reflection point _{0}M, and the receiver _{2}R can be aligned, is more likely caused by cross-line dips or scattering reflectors. , in which _{2}S, _{0}M, and _{1}R are aligned together, occurs when the earth's structures are approximately 1-D or there are only in-line dip reflectors.
_{1} |

4/20/1999