Marine seismic wavefield measurement to remove sea‐surface multiples

Abstract

We propose a new method for removing sea‐surface multiples from marine seismic reflection data in which, in essence, the reflection response of the earth, referred to a plane just above the sea‐floor, is computed as the ratio of the plane‐wave components of the upgoing wave and the downgoing wave. Using source measurements of the wavefield made during data acquisition, three problems associated with earlier work are solved: (i) the method accommodates source arrays, rather than point sources; (ii) the incident field is removed without simultaneously removing part of the scattered field; and (iii) the minimum‐energy criterion to find a wavelet is eliminated. Pressure measurements are made in a horizontal plane in the water. The source can be a conventional array of airguns, but must have both in‐line and cross‐line symmetry, and its wavefield must be measured and be repeatable from shot to shot. The problem is formulated for multiple shots in a two‐dimensional configuration for each receiver, and for multiple receivers in a two‐dimensional configuration for each shot. The scattered field is obtained from the measurements by subtracting the incident field, known from measurements at the source. The scattered field response to a single incident plane wave at a single receiver is obtained by transforming the common‐receiver gather to the frequency–wavenumber domain, and a single component of this response is obtained by Fourier transforming over all receiver coordinates. Each scattered field component is separated into an upgoing wave and a downgoing wave using the zero‐pressure condition at the water‐surface. The upgoing wave may then be expressed as a reflection coefficient multiplied by the incident downgoing wave plus a sum of scattered downgoing plane waves, each multiplied by the corresponding reflection coefficient. Keeping the upgoing scattered wave fixed, and using all possible incident plane waves for a given frequency, yields a set of linear simultaneous equations for the reflection coefficients which are solved for each plane wave and for each frequency. To create the shot records that would have been measured if the sea‐surface had been absent, each reflection coefficient is multiplied by complex amplitude and phase factors, for source and receiver terms, before the five‐dimensional Fourier transformation back to the space–time domain.

Scattering diagrams in seismic imaging: More insights into the construction of virtual events and internal multiples

“…Other studies, especially those related to multiple attenuation and up/down wavefield separation, have used the convolution-type representation theorem as the starting point of the development of their solutions. They include Kennett (1979), van den Berg (1990, 1993), Ziolkowski et al (1999), Amundsen (2001), Amundsen et al (2001), andIkelle et al (2003). We have included van den Berg (1990, 1993) in the list, although their starting point is actually the convolution-type reciprocity theorems from which the convolution-type representation theorem can be deduced.…”

Accounting for free-surface multiples in Marchenko imaging

“…To remove surface multiples from the reflection response, there are model-based methods (Wiggins, 1988;Lokshtanov, 1999), inverse-scattering-based methods (Weglein et al, 1997), data-driven methods (Verschuur et al, 1992;Berkhout and Verschuur, 1997;Ziolkowski et al, 1999;Amundsen, 2001), and recently, inversion methods (van Groenestijn and Verschuur, 2009;Ypma and Verschuur, 2013). The data-driven technique proposed by Verschuur et al (1992), surface-related multiple elimination (SRME), is a popular method for attenuating multiples because it has been proven to be effective on many real data examples.…”

Elastic internal multiple analysis and attenuation using Marchenko and interferometric methods

“…Although a variety of different methods exist to predict and attenuate free-surface multiples in seismic reflection data (Verschuur, 1992;van Borselen, 1996;Weglein et al, 1997;Ziolkowski et al, 1999;Amundsen, 2001), considerably less attention has been directed toward internal multiple removal. In fact, internal multiple suppression is a relatively recent development in exploration seismology, with the first studies dating from the 1990s.…”