Extraction of the normal component of the particle velocity from marine pressure data

Abstract

We present a general wave theoretical method for extracting the normal component of the particle velocity from marine pressure data. A possible use of the normal component of the particle velocity and the pressure is the separation of upgoing and downgoing waves at the receivers. For one special acquisition geometry, the source wavelet can also be estimated. The method in principle is exact. No information about the properties of the elastic earth is required. When the pressure data are recorded on a single surface, it is necessary to know the source signatures if the source array location is above the receiver surface. If the sources are located below, the signatures need not be known. The locations of the individual receivers must be specified, and the reflecting properties of the sea surface must be known. When the receiver surface is plane and horizontal, the extraction process can be performed in the frequency‐horizontal wavenumber domain. The normal component of the particle velocity can furthermore be extracted from pressure data recorded at two surfaces at different depths. In this case the reflectivity of the sea surface does not come into play; it is only the medium properties between the two receiver surfaces that enter the problem. The actual depths of the receivers need not be known, only their relative distances. If the sources are located above the uppermost receiver surface, the source signatures can also be estimated. A simple synthetic data example demonstrates the extraction of the normal component of the pressure from the pressure field recorded along a dipping receiver line below a free surface.

Wavefield-separation methods for dual-sensor towed-streamer data

“…For cases in which the streamer is not horizontal, Riyanti et al (2008) present a method for deghosting pressure data acquired for an arbitrary recording surface, which is derived from application of the reciprocity theorem that Fokkema and van den Berg (1993) describe and is a generalization of the deghosting expressions in equation 7. Amundsen et al (1995) derive a similar approach using Green's theorem.…”

“…This procedure has been described by several authors (e.g., Amundsen, 1993;Fokkema and van den Berg, 1993;Amundsen et al, 1995) and can be derived by evaluating the wavefield-separation equations 4 at the sea surface (z o ¼ 0). If the sea surface can be assumed to behave as a free surface, the total pressure (i.e., the sum of P up and P down ) at this surface is zero by definition.…”

“…If the sea surface can be assumed to behave as a free surface, the total pressure (i.e., the sum of P up and P down ) at this surface is zero by definition. Imposing this boundary condition, and assuming a flat streamer, yields the following expression for the vertical component of particle velocity as a function of pressure (e.g., Amundsen et al, 1995):…”

“…proper handling of the direct incident wavefield, may be derived from the measured pressure wavefield using the knowledge of the source signatures (Amundsen et al, 1995). The denominator in equation 6 represents the ideal pressure ghost function, whereas the numerator is the ideal particle motion ghost.…”

Joint up/down decomposition and reconstruction using three‐component streamers with or without ghost model: the sampling theory

“…There exist two approaches to combine the complementary information from multi‐component sensors for deghosting. The approach in Amundsen, Serest, and Arntsen () is based on an assumption of a perfectly flat and perfectly reflecting sea surface (i.e., characterised with a reflection coefficient ), which will be referred to in this paper as a method “ with ghost model” because it bears a similar expression to the traditional ghost‐model‐based method in, e.g., Özbek et al . () and Özdemir et al .…”