CRS as a tool for true amplitude imaging

2007

One-way wave equation migration is a powerful imaging tool for locating accurately reflectors in complex geologic structures; however, the classical formulation of one-way wave equations does not provide accurate amplitudes for the reflectors. When dynamic information is required after migration, such as studies for amplitude variation with angle or when the correct amplitudes of the reflectors in the zero-offset images are needed, some modifications to the one-way wave equations are required. The new equations, which are called "true-amplitude one-way wave equations," provide amplitudes that are equivalent to those provided by the leading order of the ray-theoretical approximation through the modification of the transverse Laplacian operator with dependence of lateral velocity variations, the introduction of a new term associated with the amplitudes, and the modification of the source representation. In a smoothly varying vertical medium, the extrapolation of the wavefields with the true-amplitude oneway wave equations simplifies to the product of two separable and commutative factors: one associated with the phase and equal to the phase-shift migration conventional and the other associated with the amplitude. To take advantage of this true-amplitude phase-shift migration, we developed the extension of conventional migration algorithms in a mixed domain, such as phase shift plus interpolation, split step, and Fourier finite difference. Two-dimensional numerical experiments that used a single-shot data set showed that the proposed mixed-domain trueamplitude algorithms combined with a deconvolution-type imaging condition recover the amplitudes of the reflectors better than conventional mixed-domain algorithms. Numerical experiments with multiple-shot Marmousi data showed improvement in the amplitudes of the deepest structures and preservation of higher frequency content in the migrated images.

2013

Kirchhoff migration has traditionally been the leading implementation for application of depth migration to seismic data. There are many reasons for this, such as efficiency, ability to image steep and even overhanging dips, and flexibility. However, the limitations of Kirchhoff migration are well known and its inability to image more than a single arrival is a major constraint. Downward continuation algorithms, on the other hand, handle all arrivals but their inability to image steep dips is a severe limitation. Instead, artifacts caused by the “swinging action” of the migration often obscure the real targets and it is very difficult to distinguish artifacts from geology.

2020

The true-amplitude (TA) imaging condition for reverse-time migration (RTM) is based on a combination of temporal and spatial derivatives of the upand downgoing wavefields. By means of partial integrations (or redistribution of the frequency factors in the frequency domain, we derive several alternative expressions for this imaging condition. Interestingly, the temporal derivatives can be completely replaced by spatial derivatives and temporal integrations. In this way, one version of the TA imaging condition makes use of the Laplacian operator, in this way relating to a common way of removing backscattering artifacts in RTM. We demonstrate by means of numerical examples using the Marmousi and Sigsbee2A data that the quality of the migrated image strongly depends on the version chosen for implementation. The best quality is achieved with a version that combines second derivatives of the source wavefield with the Laplacian operator. INTRODUCTION Reverse-time migration (RTM) is a seism...

2020

Using wave-equation migration and demigration in the extended subsurface domain, we introduce a practical leastsquares migration for the inversion of angle-domain common-image gathers. Through synthetic and field data examples, we demonstrate that least-squares migration provides high-resolution angle-domain common-image gathers with extended angle range, enhanced illumination, and balanced amplitudes. Similarly, the stacked images show better structural fidelity, improved resolution, balanced illumination, and reduced artifacts.

2019

By considering arbitrary source-receiver configurations the compressional primary reflections can be imaged into time or depth-migrated reflections so that the migrated wavefield amplitudes are a measured of angle-dependent reflection coeffients. In order to do this various migration algorithms were proposed in the recent past years based on Born or Kirchhoff approach. Both of them treats of a weighted diffraction stack integral operator that is applied to the input seismic data. As result we have a migrated seismic section where at each reflector point there is the source wavelet with the amplitude proportinal to the reflection coefficient at that point. Based on Kirchhoff approach, in this paper we derive the weight function and the diffraction stack integral operator for the two and one half (2.5-D) seimic model and apply it to a set of synthetic seismic data in noise enviroment. The result shows the accuracy and stability of the 2.5-D migration method as a tool for obtaining imp...

2005

Geophysical Journal International, 2010

The Common-Reflection-Surface (CRS) stack method is a powerful tool to produce high-quality stacked images of multicoverage seismic data. As a result of the CRS stack, not only a stacked section, but also a number of attributes defined at each point of that section, are produced. In this way, one can think of the CRS stack method as a transformation from data space to attribute space. Being a purely kinematic method, the CRS stack lacks amplitude information that can be useful for many purposes. Here we propose to fill this gap by means of a combined use of a zero-offset section (that could be a short-offset or amplitude-corrected stacked section) and common midpoint gather. We present an algorithm for an inverse CRS transformation, namely one that (approximately) transforms the CRS attributes back to data space. First synthetic tests provide satisfying results for the two simple cases of single dipping-plane and single circular reflectors with a homogeneous overburden, and provide estimates of the range of applicability, in both midpoint and offset directions. We further present an application for interpolating missing traces in a near-surface, high-resolution seismic experiment, conducted in the alluvial plain of the river Gave de Pau, near Assat, southern France, showing its ability to build coherent signals, where recording was not available. A somewhat unexpected good feature of the algorithm, is that it seems capable to reconstruct signals even in muted parts of the section.

Seg Technical Program Expanded Abstracts, 2004

In recent years, many case studies have demonstrated that the Common-Reflection-Surface (CRS) stack produces reliable stack sections with an excellent signal-to-noise ratio. In addition, an entire set of physically interpretable stacking parameters, so-called kinematic wavefield or CRS attributes, is determined. These attributes can be applied in further processing in such a way that a complete and consistent seismic reflection imaging workflow can be established which leads from the preprocessed multicoverage data in the time domain to migrated sections in the depth domain. The basic steps of this CRS-stack-based seismic reflection imaging workflow are the CRS stack itself, the determination of a smooth macrovelocity model by means of CRS attributes, and limited-aperture pre-and poststack Kirchhoff-type depth migration where the aperture is possibly optimized by means of the determined attributes. Our workflow approach has been applied to a recently acquired seismic dataset and revealed superior results compared to standard processing based on NMO/DMO/stack with a subsequent time migration and depth conversion.

2001

We analyze the amplitude variation as a function of reflection angle (AVA) for angle-domain common image gathers (ADCIG) produced via wave-equation migration. Straightforward implementations of the two main ADCIG methods lead to contradictory, thus inaccurate, amplitude responses. The amplitude inaccuracy is related to the fact that downward-continuation migration is the adjoint of upward-continuation modeling, but it is only a poor approximation of its inverse. We derive the frequency-wavenumber domain diagonal weighting operators that make migration a good approximation to the inverse of modeling. With these weights, both ADCIG methods produce consistent results. The main applications that follow from this paper are true-amplitude migration and pseudounitary modeling/migration, usable for iterative inversion. The two most important factors that degrade the accuracy of wave-equation ADCIGs are the limited sampling and offset range, combined with the band-limited nature of seismic data.

2002

Kirchhoff depth migration is an imaging process that transforms reflection seismic data into the depth domain in order to obtain a structural image of the subsurface. Mathematically, it can be formulated as a weighted diffraction stack which is related to the Kirchhoff integral representation of the scalar acoustic wave equation and, hence, usually only formulated for imaging of compressional or, more generally, monotypical waves. In this paper, the scalar approach to Kirchhoff imaging based on zero-order ray theory is extended to handle the full elastic wavefield recorded with multicomponent receivers by considering the polarization of respective wave modes scattered at an interface. The weight functions that remove the effect of geometrical spreading from the recorded amplitude change for each scattering mode and have thus to be extended for the case of an elastic multicomponent migration. The extended weight functions presented here are also valid for converted waves. It is shown, that the method allows to retrieve the full elastic scattering matrix of target reflectors.