Angle‐dependent reflectivity by means of prestack migration

Abstract

Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent reflectivity in the imaging we must not only add all frequency contributions but we should extend the imaging principle by adding along lines of constant angle in the wavenumber‐frequency domain. This procedure is carried out for each grid point. The resulting amplitude information provides a rigorous approach to amplitude‐versus‐offset related methods. The new imaging technique has been tested on media with horizontal layers. However, with our shot‐record oriented algorithm it is possible to handle any subsurface geometry. The first tests show excellent results up to high angles, both in the acoustic and in the elastic case. With angle‐dependent reflectivity information it becomes feasible to derive detailed velocity and density information in a subsequent stratigraphic inversion step.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

“…By applying the methodology at each depth level in the subsurface and taking the response at zero time lag and zero space lag, an image with accurate amplitudes can be obtained without artefacts from internal multiple reflections Broggini et al 2014a;Behura et al 2014). By including non-zero lags, equivalent extended images can also be created (Vasconcelos & Rickett 2013), which can be useful input for migration velocity analysis (Sava & Vasconcelos 2011), reservoir characterization (De Bruin et al 1990;Thomson 2012) and novel schemes for nonlinear imaging (Fleury & Vasconcelos 2012;Ravasi & Curtis 2012) and waveform inversion (Vasconcelos et al 2014a). Alternatively, we can use the Marchenko equations to retrieve internal multiples at the acquisition level, which could then be adaptively subtracted from the recorded data .…”

Evolution-equation approach to seismic image, and data, continuation

“…For purpose of this example one can think of operator A we as a 'black box' for which we can calculate a canonical relation Λ Awe ; w g is closely related angle gathers; p is related to scattering angle in the beam-forming approach (cf. [47]) or subsurface offset in the differential semblance approach (cf. [34]).…”

“…(This type of transform was introduced in [47].) Equations (B.1)-(B.2) define the so-called angle transform [36,37], A we : u(s, r, t) → w g (x, z, p).…”

Target-enclosed seismic imaging

“…A conventional image can be computed by evaluating the extended image at zero time and zero subsurface offset. This methodology can be applied for various purposes, including structural reflection imaging (Claerbout, 1971;Berkhout, 1980), migration velocity analysis Mildner et al, 2017), and more quantitative subsurface characterization (de Bruin et al, 1990;Ordoñez et al, 2016;Thomson et al, 2016).…”