The applicability of dip moveout/azimuth moveout in the presence of caustics

Abstract

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using whatever data are available. We develop a general theory of data continuation in the presence of caustics and illustrate it with three examples: dip moveout (DMO), azimuth moveout (AMO), and offset continuation. This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator, a modeling operator, and a restriction operator. This results in a single operator that maps directly from the input data to the desired output data. We use the calculus of Fourier integral operators to develop this theory in the presence of caustics. For both DMO and AMO, we compute impulse responses in a constant-velocity model and in a more complicated model in which caustics arise. This analysis reveals errors that can be introduced by assuming, for example, a model with a constant vertical velocity gradient when the true model is laterally heterogeneous. Data continuation uses as input a subset (common offset, common angle) of the available data, which may introduce artifacts in the continued data. One could suppress these artifacts by stacking over a neighborhood of input data (using a small range of offsets or angles, for example). We test data continuation on synthetic data from a model known to generate imaging artifacts. We show that stacking over input scattering angles suppresses artifacts in the continued data.

Appraisal problem in the 3D least squares Fourier seismic data reconstruction

“…Examples are the offset continuation operator (Bagaini and Spagnolini ) and the shot continuation operator (Fomel ). Moreover, a variety of continuation to zero‐offset implementations (better known as dip moveout operators) have been used to reconstruct seismic data as described by Canning and Gardner (), whereas Chemingui and Biondi () and Malcolm, De Hoop, and Le Rousseau () use a similar operator called azimuth moveout operator. Continuation operators are best applied to interpolate or extrapolate missing traces in an otherwise regularly sampled data set, but they can be also used for regularization (Mazzucchelli and Rocca ).…”

Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction

“…One category contains meth- * E-mail: gaojianjun2006@yahoo.com.cn ods based on signal processing principles. The other category is based on wave equation principles (Ronen 1987;Stolt 2002;Chemingui and Biondi 2002;Fomel 2003;Malcolm et al 2005). Another group relies on prediction error filtering techniques (Spitz 1991;Porsani 1999;Gulunay 2003;Naghizadeh andSacchi 2007, 2009).…”

“…Therefore, a rank reduction method can be used to attenuate noise and recover missing traces. The other category is based on wave equation principles (Ronen 1987;Stolt 2002;Chemingui and Biondi 2002;Fomel 2003;Malcolm et al 2005). These methods allow using the subsurface velocity information into the reconstruction of the seismic volume.…”

Interferometric imaging of multiples in an RTM approach

“…this equation is derived in a one-way framework in Malcolm et al (2005); another discussion of a related scattering series can be found in Weglein et al (2003). We have written an internal multiple in this form to demonstrate the ability of interferometry to simplify the wavefield and thus allow for the application of a multiple-targetted imaging procedure.…”

“…In the RTM case, including multiply-scattered waves in the imaging procedure requires the specific inclusion of a reflector in the velocity model; data requirements for this approach to avoid artifacts is discussed specifically in Mittet (2002Mittet ( , 2006. By contrast, in the one-way framework proposed in Malcolm et al (2009), an estimate of the image of the subsurface is used to include a single reflection in the back-propagation, when the imaging is done within the context of a scattering series such as those discussed in de Hoop (1996); Malcolm et al (2005) or Weglein et al (2003). This latter formulation has the advantage of being able to image with multiply scattered waves without explicitly defining a single reflector, but the formulation has so far been restricted to one-way imaging.…”