Claudia Vanelle

Traveltime-Based True-Amplitude Migration

True-amplitude Kirchhoff migration (TAKM) is an important tool in seismic-reflection imaging. In addition to a structural image, it leads to reflectivity maps of the subsurface. TAKM is carried out in terms of a weighted diffraction stack where the weight functions are computed with dynamic ray tracing (DRT) in addition to the diffraction traveltimes. DRT, however, is time-consuming and imposes restrictions on the velocity models, which are not always acceptable. An alternative approach to TAKM is proposed in which the weight functions are directly determined from the diffraction traveltimes. Because other methods exist for the generation of traveltimes, this approach is not limited by the requirements for DRT. Applications to a complex synthetic model and real data demonstrate that the image quality and accuracy of the reconstructed amplitudes are equivalent to those obtained from TAKM with DRT-generated weight functions.

Localization of Seismic Events By Diffraction Stacking

The localization of seismic events is of great importance for hydro frac and reservoir monitoring. For deposits with weak 4-D signatures the passive seismic method may provide an alternative option for reservoir characterization. We introduce a new localization technique which does not require any picking of events in the individual seismograms of the recording network. The localization is performed by a modified diffraction stack of the squared amplitudes of the input seismograms resulting in the image section. The method is target oriented and is best suited for large networks of surface and/or downhole receivers. The source location is obtained from the maximum of the image section for the time window under consideration. Since the focusing analysis is performed only in this section, no optimized search procedures are required. The source time is determined in a second processing step after the source location. Initial tests with 2-D homogeneous media indicate the high potential of the method. Since the maximum of the image section is distinct even very weak events can be detected.

Amplitude Preserving Kirchhoff Migration: A Traveltime Based Strategy

Amplitude versus offset information is a key feature to seismic reservoir characterization. Therefore amplitude preserving migration was developed to obtain this information from seismic reflection data. For complex 3-D media, however, this process is computationally expensive. In this paper we present an efficient traveltime based strategy for amplitude preserving migration of the Kirchhoff type. Its foundations are the generation of traveltime tables using a wavefront-oriented ray-tracing technique, and a generalized moveout relation for 3-D heterogeneous media. All required quantities for the amplitude preserving migration are computed from coarsely gridded traveltime tables. The migration includes the interpolation from the coarsely gridded input traveltimes onto the fine migration grid, the computation of amplitude preserving weight functions, and, optionally, the evaluation of an optimized migration aperture. Since ray tracing is employed for the traveltime computation the input velocity model needs to be smooth, i.e. velocity variations of spatial dimensions below the wavelength of the considered reflection signals are removed. Numerical examples on simple generic models validate the technique and an application to the Marmousi model demonstrates its potential to complex media. The major advantage of the traveltime based strategy consists of its computational efficiency by maintaining sufficient accuracy. Considerable savings in storage space (105 and more for 3-D data with respect to no interpolation at all) can be achieved. The computational time for the stack can be substantially reduced (up to 90% in 3-D) with the optimized migration aperture since only those traces are stacked which really contribute to the image point under consideration.

Influence of models on seismic-event localization

Source localization is a fundamental problem in seismology. Current localization techniques often rely on homogeneous isotropic models, even if a survey region is known to be geologically complex or anisotropic. We investigated a model’s influence on localization, using data from a hydraulic injection experiment at the Continental Deep Drilling (Kontinentale Tiefbohrung, or KTB) site in Germany. We performed the localization with a grid-search algorithm and two additional methods for verification. From previous work, a homogeneous isotropic model based on a borehole check shot and a heterogeneous 3D isotropic model were available. Vertical seismic profiling (VSP) and borehole data as well as laboratory data from rock samples provided homogeneous anisotropic models. Although localization with the isotropic and anisotropic models led to the same magnitude of residuals and therefore to a comparable quality of fit, the distribution of the event cloud differed significantly for isotropic and anisotropic media....

A new stacking operator for curved subsurface structures

Multiparameter stacking has become a standard tool for seismic reflection data processing. Different traveltime operators exist, whose accuracy depends on the offset and reflector curvature. We introduce a new, implicit stacking operator derived from evaluating Snell’s law at a locally spherical interface. Comparison of the resulting traveltime surface with those obtained from the common reflection surface and multifocusing expressions confirm high accuracy and only minor dependence on the reflector curvature. The examples show that the new method performs well for the whole range of reflector curvatures from nearly planar reflectors to the diffraction limit. INTRODUCTION Over the past years, a number of multiparameter stacking operators have been introduced as an extension of the CMP stacking technique. Examples of such operators are the common reflection surface stack (CRS, Mueller, 1999), Multifocusing (MF, Gelchinksy et al., 1999), and the shifted hyperbola (de Bazelaire, 1988). These operators describe the traveltime surface for a reflected event in the short offset limit. The accuracy of the individual methods differs and depends not only on the considered offset but also on the reflector curvature. In this work, we suggest a new stacking operator. It is derived from Snell’s law for a spherical interface and leads to an implicit expression for the traveltime surface. Although the operator can be applied in an iterative fashion, we show in our examples that already a single iteration leads to higher accuracy than the CRS and MF expressions. After a brief summary of the CRS and MF methods, we introduce a new implicit stacking operator (ISO) and examine its performance in comparison to CRS and MF. COMMON REFLECTION SURFACE The CRS stacking technique was introduced by Mueller (1999) to obtain a simulated zero offset section. The CRS stack can be considered as an extension of the classic CMP method, where stacking is carried out over offsets, while in the CRS technique the stack is applied over offsets and midpoints. This leads to a much larger number of contributing traces, and, thus, to a higher level of the signal to noise ratio. Whereas the CMP operator is a hyperbola, the corresponding CRS operator is a traveltime surface of second order that includes the CMP operator as subset. Written in midpoint (xm = x0 +∆xm) and halfoffset (h) coordinates, the CRS operator for monotypic reflections in the two-dimensional zero-offset case 248 Annual WIT report 2010

Application of Snell's law in weakly anisotropic media

Snell’s law describes the relationship between phase angles and velocities during the reflection or transmission of waves. It states that horizontal slowness with respect to an interface is preserved during reflection or transmission. Evaluation of this relationship at an interface between two isotropic media is straightforward. For anisotropic media, it is a complicated problem because phase velocity depends on the angle; in the anisotropic reflection/transmission problem, neither is known. Solving Snell’s law in the anisotropic case requires a numerical solution for a sixth-order polynomial. In addition to finding the roots, they must be assigned to the correct reflected or transmitted wave type. We show that if the anisotropy is weak, an approximate solution based on first-order perturbation theory can be obtained. This approach permits the computation of the full slowness vector and, thereby, the phase velocity and angle. In addition to replacing the need for solving the sixth-order polynomial, the re...

Application of sectorially best‐fitting isotropic background media

In this paper, we suggest an iterative approach to determine the missing third slowness component based on the rst-order perturbation method for anisotropic media (Jech and P sen c k, 1989). We suggest to apply the perturbation method in combination with the expressions for sectorially best-tting isotropic background media given in Vanelle and Gajewski (2004). We will briey review the basic equations of the perturbation method and weak anisotropy approximation underlying our technique, followed by the description of our procedure, including the updating of the velocity model. We will then illustrate the technique with two examples for qP- and qS-waves, and, nally , conclude our results.

3D CRS-based Prestack Diffraction Separation and Imaging

Imaging of seismic diffractions is a challenge since it is inherently a 3D problem. Diffractions carry useful information about the subsurface and allow to identify the presence of small-scale heterogeneities and structures e.g. fractures, pinch-outs, thin lenses etc. Thus, diffraction separation and imaging can lead to higher resolution, which is of particular interest for reservoir characterisation and exploration. In this work, we suggest a 3D workflow based on common-reflection-surface (CRS) method for prestack diffraction separation and imaging in time domain. The workflow combines the ideas developed for diffraction separation with the partial CRS stack technique. It comprises not only the diffraction separation facility but also includes a prestack data enhancement, i.e., an improved SNR in diffraction-only data. Application to a 3D synthetic model confirms its effectiveness in prestack diffraction separation. It also demonstrates potential for time migration velocity analysis using diffraction-only data.

Determination of Sectorially Best-fitting Isotropic Background Media

Summary Computations in anisotropic media are commonly simplied by applying perturbation methods. These require suitable background media, that are often chosen to be isotropic. In this paper we present expressions for sectorially best-tting isotropic P- and S-velocities. The equations follow from a generalisation of Fedorov’s (1968) technique. Examples for media with polar (VTI) and triclinic symmetry conrm the superiority of the results over the commonly used globally best-tting isotropic velocities by Fedorov (1968). This makes the method particularly suited for any application associated with perturbation techniques for anisotropic wave propagation.

Determining Geometrical Spreading from Traveltimes in Anisotropic Media

Summary Amplitude preserving migration based on a weighted diraction stack is a task of high computational eort. A major contribution to the costs is the determination of proper weight functions which countermand the eects of geometrical spreading. Whereas the demands in CPU time and computer storage are high already in isotropic media, they become even higher as soon as anisotropy is considered, since already the traveltime computation in anisotropic media requires a magnitude more in computational time. Although fast algorithms are available for the computation of the traveltimes required for the stacking surface, not all of them are capable of generating geometrical spreading, which is needed for the weight functions. In this paper we propose a technique to determine the geometrical spreading directly from coarsely gridded traveltimes. The method is based on a hyperbolic traveltime expression and also provides the possibility of an accurate and ecien t traveltime interpolation. This makes the technique well suited for application to amplitude preserving migration in anisotropic media.