Inversion of up and down going signal for ocean bottom data

Introduction

Traditionally, multiples in seismic surveying are considered as noise to be removed because most migration algorithims do not account for multiples. Recently, there have been efforts to use multiples as signals. For example, Berkhout and Verschuur (2003) and Guitton (2002) image the multiples with shot-profile migration while Shan (2003) transforms multiples into pseudo-primaries by cross-correlation in the souce-receiver domain.

One motivation to image with multiples is that multiples can provide subsurface information not found in primaries. The angular and spatial ranges covered by multiples are different than that of primaries (Figure 1). Ronen et al. (2005); Guimaraes et al. (1998) propose a mirror imaging technique that takes advantage of this property for ocean bottom and vertical cable acquisition geometry, respectively. By using receiver ghosts as signals, mirror imaging provides a much wider aperture in the image space, given the same set of data. While mirror imaging correctly images multiples by using down-going receiver ghost at the ocean bottom, the primary signal is imaged separately. On the other hand, Brown and Guitton (2005); Brown (2004) proposed joint imaging between primaries and multiples by using least-square inversion. One advantage of joint inversion is that both the primary and multiple signals are used.

Fig1
Figure 1. The angular and spatial ranges covered by multiples is different than that of primary. Near the edge of the receiver array, A can only be illuminated by multiple as primary can only illuminate up to a spatial extend of B.[NR]

For the case of ocean bottom data, signals can be separated into up- and down-going parts. Traditioanlly, up- and down-going signals are used for de-ghosting (Canales and Bell, 1996). Muijs et al. (2007) use this property to formulate prestack depth migration of primary and surface-related multiple using downward continuation. In this study, we carry on the work of Brown (2004) and discuss the theory of joint imaging of multiples and primaries using up- and down-going signals of ocean bottom data.

We will first discuss the geometry of ocean bottom data acquisition. Next, we will consider the techniques available to separate data into up-going and down-going wavefields. We will discuss the theory of joint imaging of multiples and primaries using up- and down-going ocean bottom data. Such an inversion scheme requires a good modeling operator for up- and down-going signals. To a first order accuracy and flat water bottom, we use mirror imaging to define the two modeling operators. A more accurate modeling scheme requires an over-under modeling and an up-down decomposition operator. This scheme effectively images all primaries, water reveberations, and multiples. It also reduces crosstalk leakage between up- and down-going signals and hence reduces incorrectly placed reflectors. The testing of this thoery would be the focus of my research for the next quarter.

Inversion of up and down going signal for ocean bottom data