Jan Pajchel

Time-lapse tomography

In time-lapse analysis, we have to distinguish the seismic response changes due to oil and gas production at a reservoir over the years from several other causes, such as the recording signature and random noise. In this paper, we focus our attention on the velocity macromodel provided by seismic tomography, which is a basic tool for the data regularization, its depth or time migration, and a possible final subtraction among different vintages. We show first that we cannot use just a single velocity model for all data sets, because of seasonal variations of the overburden velocity (which is mainly due to seawater temperature in marine cases and to the water table depth in land cases). However, we can exploit the basic assumption of time-lapse analysis for constraining reflection/refraction tomography, i.e., by imposing the constraint that the layer structure and the local velocities do not change outside the reservoir (and in the shallowest part) over time. We thus get coupled models that are physically consistent, with a better spatial coverage and higher information redundancy. The new method is illustrated by a marine case history from the North Sea.

Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting

In Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting (SEG Geophysical Monograph Series No. 14), the theoretical framework of the edge and tip wave theory of diffractions has been elaborated from fundamental wave mechanics. Seismic diffractions are inevitable parts of the recorded wavefield scattered from complex structural settings and thus carry back to the surface information that can be exploited to enhance the resolution of details in the underground. The edge and tip wave theory of diffractions provides a physically sound and mathematically consistent method of computing diffraction phenomena in realistic geologic models. In this book, theoretical derivations are followed by their numerical implementation and application to real exploration problems. The book was written initially as lecture notes for an internal course in diffraction modeling at Norsk Hydro Research Center, Bergen, Norway, and later was used for a graduate course at Novosibirsk State University in Russia. The material is drawn from several previous publications and from unpublished technical reports. Edge and Tip Diffractions will be of interest to geoscientists, engineers, and students at graduate and Ph.D. levels.

3D diffraction modeling of singly scattered acoustic wavefields based on the combination of surface integral propagators and transmission operators

We present an improved method for modeling 3D acoustic wavefields scattered at smooth curved interfaces. The approach is based on a high-frequency approximation of surface integral propagators and a correct description of their boundary values in terms of transmission operators. The main improvement is a uniform local approximation of these operators in the form of effective reflection and transmission coefficients. We show that the effective coefficients represent a generalization of the plane-wave coefficients widely used in conventional seismic modeling, even for the case of curved reflectors, nonplanar wavefronts, and finite frequencies. The proposed method is capable of producing complex wave phenomenas, such as caustics, edge diffractions, and head waves. Seismograms modeled for even simple models reveal significant errors implicit in the plane-wave approximation. Comparison of modeling based on effective coefficients with the analytic solution reveals errors less than 4% in peak amplitude at seismic frequencies.

Target-oriented time-lapse analysis by AVO and tomographic inversion

Summary Time-lapse analysis is a powerful tool for optimising the oil and gas production. Often, a global approach is adopted for such analysis: one tries to compensate all differences in the seismic records not due to production, and then the data of different years are subtracted in the time or depth domain. Here we test a target-oriented approach, because we feel that the compensation of all other factors is often incomplete. By AVO and tomographic inversion, we highlight important variations of the seismic properties in a producing reservoir at the North Sea. A few problems Several successful case histories worldwide proved that time-lapse analysis allows optimising the oil and gas production. By detecting the variations of the seismic response ov er a field due to production,ne can reconstruct the preferential paths for the fluids’ flux, and the depleted or unswept parts of the reservoir. Ideally, one should use permanent sources and receivers, with constant properties over several years: in practice, this is almost impossible. Therefore, most of the ongoing research and development for time

A study of sub-basalt depth imaging using the local radon attributes on the Erlend Tertiary volcanic complex : north of Shetland, UK

I Acquiring conventional 3 km towed streamer data along a 2D profile in the North of Shetland (UK) enables us to use the local Radon-attributes within the context of depth processing methodology for accurate delineation of volcanic units and imaging beneath high-velocity layers. The objective is to map the radially-dipping structure of the Erlend pluton and to investigate the potential existence of relatively soft Cretaceous sediments underneath volcanic units. Success in the Erlend Volcano study requires strict attention to the separation between different groups of events. The crucial point is the generalized discrete Radon transform formulated in terms of local wavefront (dip and curvature) characteristics. This transform is utilized during pre-CMP processing and migration to minimize event-coupling artefacts. These artefacts represent cross-talk energy between various wave modes and include the unwanted part of the wavefield. We show how to produce detailed subsurface images within the region of interest (exploration prospect only) by applying the closely tied processes of prestack event enhancement and separation, well-driven time processing for velocity model building, and final event-based prestack depth imaging. Results show enhanced structural detail and good continuity of principal volcanic units and deeper reflections, suggesting a faulted 0.6 0.9 km thick layer of Cretaceous sediments in the proximity of well 209/09-1. Our interpretation complements existing low-resolution geophysical models inferred from gravity and wide-angle seismic data alone.

Multi-mode wavepath depth imaging for the SEG/EAGE salt model

Elastic depth imaging of both P-wave and S-wave prestack seismic reflection data is formulated as a degraded form of Kirchhoff migration known as Wavepath Migration (WM). Applications to the SEG/EAGE salt model show that the method is sufficiently versatile anti relaitively inexpensive. It handles S-wave data with at least the same accuracy as Pwave data when local mode conversions are removed. WM also provides an understanding of multi-mode illumination.

Diffraction modeling in time domain

The asymptotic theory of edge and vertex diffraction in time domain, developed in (Hanyga, 1994; Hanyga, 1995), allows a relatively simple numerical implementation based on ray tracing of reflected and diffracted rays to the receivers. Seismic traces are evaluated by the convolution of a known seismic signature with a kernel expressed in terms of elementary functions. We present here an outline of the theory and its application to the computation of reflected/diffracted fields from curved and discontinuous surfaces. The idea of modelling fields which exhibit focusing by superpositions of diffracted fields generated by a plane-triangulated surface goes back to (Aizenberg and KlemMusatov, 1984). Significant numerical simplifications result from applying the time-domain theory of edge and vertex diffraction.

Linear Inversion as a First Step in Entropy of Image Contrast Optimization

Inversion of seismic data usually exhibits a strong nonuniqueness. Constraints are necessary to reduce the large number of images (solutions of inversion) that all satisfy the requirements of minimal data misfit.

Modelling geological structures using splines

Abstract Our aim is to build a three dimensional geological model from interpreted seismic data using a spline representation of the geometry and other geological properties. The seismic interpretation is usually done in the time domain, and after a model is build in this domain, we perform a so called depth conversion, which transforms the model to depth domain. The input seismic interpretation yields no unique three dimensional geological model, which implies that we need a close interaction with the user of the system.