Migration of primaries and multiples using an imaging condition for amplitude-normalized separated wavefields

Abstract

Migration of primary and multiple reflections leads to enhanced subsurface illumination and to increased image resolution. A joint migration approach using the complete wavefield requires properly imaged primaries and multiples of all orders. In recent works, primaries and multiples have therefore been imaged separately, using the upgoing and downgoing pressure wavefields obtained by decomposing dual-sensor streamer data. The matches between the corresponding depth images are still not found to be sufficiently accurate, so new and more appropriate imaging conditions need to be found. We reviewed the classical imaging approach used in one-way wave-equation migration, with the aim of extending it for simultaneous migration of primaries and all orders of multiples. Based on Rayleigh’s reciprocity theorem and well-known theoretical developments, we derived a new imaging condition described in terms of the upgoing pressure wavefield and a filtered version of the downgoing vertical-velocity wavefield. To evaluate the efficiency of this new imaging approach, primaries and multiples were separately migrated using synthetic and real data examples. These results were compared to those obtained using a conventional imaging condition. We found that the use of the new imaging condition led to a better match between the depth images and spectra of the migrated primaries and migrated multiples.

Imaging the total wavefields by reflectivity inversion using amplitude-normalized wavefield decomposition: Field data example

“…These decomposed wavefields are referred to as amplitude-normalized separated wavefields. Following Rayleigh's reciprocity theorem, the total upgoing pressure and the downgoing vertical velocity can be related with the following Fredholm integral equation (e.g., Amundsen, 2001;Ordoñez et al, 2014):…”

“…This offers the perspective to redefine the imaging framework based on up-and downgoing wavefields using primaries and multiples. For example, by adequately combining the up-and downgoing components of the pressure and vertical velocity measurements, we can retrieve the impulse response of the subsurface (e.g., Ordoñez et al, 2014 and2016). For complex inhomogeneous media, this impulse response (or reflectivity) can be computed by solving an integral equation in the frequency-space domain (e.g., Amundsen, 2001).…”

Reflectivity computation from separated wavefields: application on the Sigsbee2B example

“…It is well known from the literature that the reflectivity can be recovered from a Fredholm integral equation of the first kind defined in the frequency-space domain (see e.g. Amundsen, 2001;Ordoñez et al, 2014a). Assuming that sufficient data are available, an inversion of the matrix form of the integral gives an estimate of the reflectivity matrix .…”

“…The reflectivity can be recovered from a Fredholm integral equation of the first kind defined in the frequency-space domain, in terms of upgoing and downgoing separated wavefields (see e.g. Amundsen, 2001;Ordoñez et al, 2014a and2014b). An inversion of the matrix form of this integral problem at every image level gives the reflectivity, where cross-talk caused by the physical overburden should be eliminated.…”

“…An inversion of the matrix form of this integral problem at every image level gives the reflectivity, where cross-talk caused by the physical overburden should be eliminated. Here, we first review previous related work using upgoing and downgoing separated wavefields (Claerbout, 1971;Whitmore et al, 2010;Lu et al, 2011;Ordoñez et al, 2014a and2014b). Then, we compute the reflectivity matrix by integral inversion for a sediment section of the Sigsbee2B model (Paffenholz et al, 2002).…”