Ketil Hokstad

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data.Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but ...

Elastic reverse time migration of marine walkaway vertical seismic profiling data

Walkaway vertical seismic profiling (VSP) acquisition with three-component geophones allows for direct measurement of compressional as well as shear energy. This makes full elastic reverse time migration an attractive alternative for imaging data. We present results from elastic reverse time migration of a marine walkaway VSP acquired offshore Norway. The reverse time migration scheme is based on a high-order finite-difference solution to the two-way elastic wave equation. Depth images of the subsurface are constructed by correlation of forward- and back-propagated elastic wavefields. In the walkaway VSP configuration, the number of shots is much larger than the number of geophone levels. Using processing methods operating in the shot/receiver domain, it is advantageous to use the reciprocal relationship between the walkaway VSP and the reverse VSP configurations. We do this by imaging each component of each geophone level as a reverse VSP common shot gather. The final images are constructed by stacking partial images from each level. The depth images obtained from the vertical components reveal the major characteristics of the geological structure below geophone depth. A graben in the base Cretaceous unconformity and a faulted coal layer can be identified. The horizontal components are more difficult to image. Compared to the vertical components, the horizontal component images are more corrupted by migration artifacts. This is because the horizontal component images are more sensitive to aperture effects and to the shear-wave velocity macromodel. When converted to two-way time, the migration results tie well with the surface seismic section. Comparison of fully elastic and acoustic reverse time migration shows that the vertical component is dominantly PP-reflected events, whereas the horizontal components get important contributions from PS-converted energy. The horizontal components also provide higher resolution because of the shorter wavelength of the shear waves.

Integration of multiple electromagnetic imaging and inversion techniques for prospect evaluation

The use of controlled source electromagnetics (CSEM) in the marine environment has grown rapidly in the past few years from a simple anomaly fluid-hunting technique used in geologically simple environments to a modeling and inversion based technique applied in structurally and lithologically complex environments (Carazzone et al., 2005). The tool set most commonly available to interpreters includes one-, twoand three-dimensional forward and inverse modeling codes. All previous examples, reported in the literature, of inversion codes applied to marine CSEM data have been cell-based regularized techniques designed to produce the smoothest possible isotropic conductivity model (in twoor three-dimensions) which fits the observed data. We report on the development of a new technique, anisotropic sharp-boundary inversion in which the model is parameterized by two-dimensional interfaces. In this approach anisotropic conductivity can have sharp contrasts across interfaces. Regularization is applied to the smoothness of the interface and the lateral variations of conductivity between interfaces. We demonstrate a work flow that progresses from forward modeling through fast depth migration to smooth cell based inversion, concluding with sharp boundary inversion for the final interpreted conductivity image.

3D surface-related multiple elimination using parabolic sparse inversion

The basic theory of surface-related multiple elimination (SRME) can be formulated easily for 3D seismic data. However, because standard 3D seismic acquisition geometries violate the requirements of the method, the practical implementation for 3D seismic data is far from trivial. A major problem is to perform the crossline-summation step of 3D SRME, which becomes aliased because of the large separation between receiver cables and between source lines. A solution to this problem, based on hyperbolic sparse inversion, has been presented previously. This method is an alternative to extensive interpolation and extrapolation of data. The hyperbolic sparse inversion is formulated in the time domain and leads to few, but large, systems of equations. In this paper, we propose an alternative formulation using parabolic sparse inversion based on an efficient weighted minimum-norm solution that can be computed in the angular frequency domain. The main advantage of the new method is numerical efficiency because solving many small systems of equations often is faster than solving a few big ones. The method is demonstrated on 3D synthetic and real data with reflected and diffracted multiples. Numerical results show that the proposed method gives improved results compared to 2D SRME. For typical seismic acquisition geometries, the numerical cost running on 50 processors is 0.05 s per output trace. This makes production-scale processing of 3D seismic data feasible on current Linux clusters.

Transforming walk‐away VSP data into reverse VSP data

Marine walk-away vertical seismic profiling (VSP) data can be transformed into reverse VSP data using an elastic reciprocity transformation. A reciprocity transform is derived and tested using data generated with a 2-D high-order, finite-difference modeling scheme in a complex elastic model. First, 201 shots are generated with a walk-away VSP experimental configuration. Both the x-component and the z-component of the displacement are measured. These data are collected in two common receiver data sets. Then two shots are generated in a reverse VSP configuration. We demonstrate that subtraction of the reverse VSP data from the walk-away VSP data gives very small residuals. The transformation of walk-away data into reverse VSP data makes prestack shot-domain migration feasible for walk-away data. Synthetic data from a multishot walk-away experiment can be obtained from one or a few modeling operations with a RVSP experimental configuration. The required computer time is reduced by two orders of magnitude.

Improved salt imaging in a basin context by high resolution potential field data: Nordkapp Basin, Barents Sea

ABSTRACT The seismic imaging of salt diapirs in the Nordkapp Basin gave rise to considerable problems in defining their shape and volume. Independent information was added by integrating the interpretation with high resolution gravity and magnetic data. We developed a novel, iterative workflow, separated into sub‐categories: sediments, salt structures, basement and Moho. Distinctions between the sources of the anomalies from different depths was achieved by utilizing the different decay characteristics of gravity, gravity gradiometry and high resolution magnetic anomalies. The workflow was applied to the southern part of the Nordkapp Basin. It started with the sedimentary model derived from seismics, populated with measured densities and magnetic susceptibilities and a starting model for the base salt. The residual after the removal of this model was interpreted in terms of a crustal model, including flexural isostatic calculations for the Moho with the sedimentary load. The residual after the removal of crustal and early sedimentary model was used to tune the salt model. As these major and minor modelling steps depend on each other, an iterative process was applied to stepwise improve the density and magnetic susceptibility model. The first vertical gradient of gravity and the magnetic field were found to give most information about the cap rock of the diapirs. The improvement in salt imaging, integrated with results from controlled‐source electromagnetic and magneto‐telluric modelling is shown for the salt diapir Uranus, where a well, terminated in the salt, constrains the minimum of the depth to base salt.

TIV Contrast Source Inversion of mCSEM data

We present a 3D contrast source inversion scheme for electromagnetic data in conductive media. We consider only contrasts in electric conductivity but allow the medium to be transversely isotropic in the vertical direction. This has applications in, for instance, inversion of marine controlled-source electromagnetic data. The contrast source inversion (CSI) method is based on the integral equation formulation of electromagnetic field propagation and solves the inverse problem of determining the conductivity structure of the subsurface. The method minimizes a cost functional that enforces both data fidelity and that the solution satisfy the Lippmann-Schwinger equation. Further regularization is introduced linearly into the cost functional to incorporate prior model information. Although the problem is nonlinear, the chosen strategy splits the minimization problem into two linear problems, which are solved alternatingly. To this end, contrast sources are introduced, which may be interpreted as sources emitting the scattered field from a scattering object. Two synthetic and two real field examples are inverted, which demonstrates the method and how the transversely isotropic in the vertical direction (TIV) inversion performs compared with isotropic inversion. The CSI method is found to be applicable to real field examples, and the results show that a TIV inversion is preferred over isotropic to identify weak anomalies in these examples. The reason for this is that both the horizontal and vertical conductivity affects the signal propagation in the overburden.

Positioning drill-bit and look-ahead events using seismic traveltime data

We study seismic traveltime measurements acquired in the borehole, including vertical seismic profiling, seismic measurements while drilling, and drill-bit noise generated data. These traveltime data are used to assess informative parameters, including drill-bit position, distance to drilling target, and parameters of the velocity model. First, we analyze seismic traveltime data using a simple hyperbolic traveltime equation for rays between surface sampling locations and the drill bit. Second, we describe a model for estimating both the position of the drill bit and the relative distance to geologic interfaces ahead of the bit. Finally, we present a dynamic Bayesian strategy for real-time prediction of drill-bit positions, velocity parameters, and distances to geologic markers. Walk-away vertical seismic profiling data from the Norwegian Sea are used to demonstrate our methods. For this data set, we pick five key reflectors ahead of the drill bit. The deepest reflector is estimated to be 207±5 m ahead of ...

Fast repeated seismic modelling of local complex targets.

Summary A new modelling scheme is described, for very fast repeated calculation of the seismic response of a local complex target below a structurally simpler overburden. The method combines a petrophysical modelling system with a hybrid ray tracing/finite difference scheme. Both acoustic and elastic waves can be modelled. For the example shown, the new modelling scheme required about 2.5% of CPU resources and 1.7% of the grid size when compared to the global finite difference calculation.

Strategies for petroleum exploration based on Bayesian Networks: a case study

The paper presents a new approach for modeling important geological elements, such as reservoir, trap and source, in a unified statistical model. This joint modeling of these geological variables is useful for reliable prospect evaluation, and provides a framework for consistent decision making under uncertainty. A Bayesian Network, involving different kinds of dependency structures, is used to model the correlation within the various geological elements, and to couple the elements. Based on the constructed network, an optimal sequential exploration strategy is established via dynamic programming. This strategy is useful for selecting the first prospect to explore, and which decisions to make next, depending on the outcome of the first well. A risk neutral decision maker will continue exploring new wells as long as the expected profit is positive. The model and choice of exploration strategy is tailored to a case study represented by five prospects in a salt basin, but it will also be useful for other contexts. For the particular case study we show how the strategy clearly depends on the exploration and development cost, and the expected volumes and recovery factors. The most lucrative prospect tends to be selected first, but the sequential decisions depend on the outcome of the exploration well in this first prospect.