Sergius Dell

Image-ray Tomography

ABSTRACT Seismic tomography is a well‐established approach to invert smooth macro‐velocity models from kinematic parameters, such as traveltimes and their derivatives, which can be directly estimated from data. Tomographic methods differ more with respect to data domains than in the specifications of inverse‐problem solving schemes. Typical examples are stereotomography, which is applied to prestack data and Normal‐Incidence‐Point‐wave tomography, which is applied to common midpoint stacked data. One of the main challenges within the tomographic approach is the reliable estimation of the kinematic attributes from the data that are used in the inversion process. Estimations in the prestack domain (weak and noisy signals), as well as in the post‐stack domain (occurrence of triplications and diffractions leading to numerous conflicting dip situations) may lead to parameter inaccuracies that will adversely impact the resulting velocity models. To overcome the above limitations, a new tomographic procedure applied in the time‐migrated domain is proposed. We call this method Image‐Incident‐Point‐wave tomography. The new scheme can be seen as an alternative to Normal‐Incidence‐Point‐wave tomography. The latter method is based on traveltime attributes associated with normal rays, whereas the Image‐Incidence‐Point‐wave technique is based on the corresponding quantities for the image rays. Compared to Normal‐Incidence‐Point‐wave tomography the proposed method eases the selection of the tomography attributes, which is shown by synthetic and field data examples. Moreover, the method provides a direct way to convert time‐migration velocities into depth‐migration velocities without the need of any Dix‐style inversion.

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

Diffraction Imaging Based On Common-Reflection-Surface Attributes

Imaging of diffractions is a challenge in seismic processing. Standard seismic processing is tuned to enhance reflections. Separation of diffracted from reflected events is frequently used to achieve an optimized image of diffractions. We present a method to effectively separate and image diffracted events in the time domain. The method is based on the CommonReflection-Surface-based diffraction stacking and the application of a diffraction-filter. The diffraction-filter uses kinematic wavefield attributes determined by the Common-ReflectionSurface approach. The procedure is incorporated into the conventional CommonReflection-Surface workflow. The application of the method to the complex model shows promising results.

Image Ray Tomography

Tomographic methods for the determination of velocity models using kinematic wavefield attributes strongly depend on the accuracy of the attributes. The Common-Reflection-Surface method applied to prestack data provides the attributes already with high quality. However, one difficulty of the CRS method is the treatment of diffractions and triplications, especially when located close to reflections. In such areas the quality of the attributes is not sufficient and, therefore, velocity model building with Normal Incident Point wave tomography does not provide an optimum result. Thus, it is reasonable to extract the kinematic wavefield attributes in the time-migrated domain. The Common-Reflection-Surface method applied to the time-migrated data approximates the zero-offset traveltime as a second-order Taylor expansion in the vicinity of the image ray. The data vector for the inversion contains the wavefront curvatures of the image rays. The model vector is calculated by dynamic ray-tracing along central image rays. The inversion problem is solved iteratively by computing the least-squares solution to the locally linearized problem during each iteration step. The required Frechet derivatives for the tomographic matrix are calculated with ray perturbation theory.