Steen A. Petersen

Simulating migrated and inverted seismic data by filtering a geologic model

The simulation of migrated and inverted data is hampered by the high computational cost of generating 3D synthetic data, followed by processes of migration and inversion. For example, simulating the migrated seismic signature of subtle stratigraphic traps demands the expensive exercise of 3D forward modeling, followed by 3D migration of the synthetic seismograms. This computational cost can be overcome using a strategy for simulating migrated and inverted data by filtering a geologic model with 3D spatial-resolution and angle filters, respectively. A key property of the approach is this: The geologic model that describes a target zone is decoupled from the macrovelocity model used to compute the filters. The process enables a target-orientedapproach, by which a geologically detailed earth model describing a reservoir is adjusted without having to recalculate the filters. Because a spatial-resolution filter combines the results of the modeling and migration operators, the simulated images can be compared directly to a real migration image. We decompose the spatial-resolution filter into two parts and show that applying one of those parts produces output directly comparable to 1D inverted real data. Two-dimensional synthetic examples that include seismic uncertainties demonstrate the usefulness of the approach. Results from a real data example show that horizontal smearing, which is not simulated by the 1D convolution model result, is essential to understand the seismic expression of the deformation related to sulfate dissolution and karst collapse.

Constraining uncertainty in interpretation of seismically imaged clinoforms in deltaic reservoirs, Troll field, Norwegian North Sea: Insights from forward seismic models of outcrop analogs

Forward seismic modeling of outcrop analogs has been used to characterize the seismic expression of clinoforms in different deltaic depositional environments, and thus constrain uncertainty in interpretation of intra-reservoir clinoforms imaged in seismic data from the Troll field, Norwegian North Sea. Three outcrop analogs from the Cretaceous Western Interior seaway, United States, were studied to quantify the geometry, distribution, and lithologic character of clinoforms in fluvial-dominated and mixed-influence deltaic deposits. Outcrop-derived geometric data were calibrated to sedimentological and petrophysical data from the Krossfjord and Fensfjord Formations in the Troll field, and then used to create a suite of forward seismic models for comparison with real seismic reflection data from the Troll field. Clinoforms were imaged in the forward seismic models in which they were (1) spaced wider than the tuning thickness (>10 m [>33 ft]); (2) marked by pronounced interfingering of facies associations with different acoustic properties; and/or (3) lined by relatively thick (>50 cm [>20 in.]) carbonate-cemented layers. However, where clinothems are thinner than the vertical resolution limit of seismic data, destructive interference occurred creating misleading geometrical relationships. Furthermore, our ability to image clinoforms is dependent on (1) the frequency of the seismic wavelet; (2) the overburden velocity; and/or (3) the acoustic impedance contrast at the boundary between the overburden and the clinoform-bearing target. The established methodology has allowed characterization of deltaic clinoformal architectures in reservoir seismic data from the Troll field, and has facilitated a more robust interpretation by bridging the critical gap in resolution between well and seismic data.

Geological modelling and finite difference forward realization of a regional section from the Zagros fold-and-thrust belt

This paper provides detailed geological modelling and finite difference realization results of a 2D regional section from the Zagros fold-and-thrust belt, Iran. Different scale geological detail has been included in the model. The modelling approach is based on a hierarchical procedure and the model is made up of cells representing the geometry and properties (such as seismic P-wave velocity) of parts of the model. By using a hierarchical procedure for building the model, the time and space consistency of the geological model is preserved. The constructed model is 81 × 17 km and crosses several drilled and undrilled structures. The model geometry is controlled by surface, subsurface and seismic interpretation results along the model. The model building blocks were chosen based on the deformation history of the area and the modelling was carried out in two stages. First, a regional model was constructed including the major structural elements. At the second stage (fine tuning of the regional model), structural and stratigraphic details, such as onlap, truncations, pinch-outs and thickening/thinning of salt beds, were added to the regional model. The velocity and density models were extracted from well logs, check shots and seismic processing-derived velocity data. A few shots were generated using an acoustic finite difference method to see the effect of the inclusion of detailed internal geometry in the model and the seismic wave complexity around three main anticlines of the model. The seismic response shows that the detailed modelling of stratigraphy and structure gives results that simulate the real data better. It shows the existence of complex diffracted and non-hyperbolic events, suggesting the poor image quality of real data is not related entirely to acquisition problems caused by irregular topography. Advanced depth-imaging methods (e.g. reflection tomography and wave-equation-based extrapolation or migration algorithms) are required to get better images. The sharp lateral velocity changes associated with major thrust faults cause the generation of diffractions that can compromise reliable velocity analysis, especially at conventional offsets. This effect could be considered as one of the causes of the poor seismic response observed on real data. The use of larger offsets, therefore, can distinguish between diffractions and primary reflections during velocity analysis in time and depth.

A Numerical Framework for Modeling Folds in Structural Geology

A numerical framework for modeling folds in structural geology is presented. This framework is based on a novel and recently published Hamilton–Jacobi formulation by which a continuum of layer boundaries of a fold is modeled as a propagating front. All the fold classes from the classical literature (parallel folds, similar folds, and other fold types with convergent and divergent dip isogons) are modeled in two and three dimensions as continua defined on a finite difference grid. The propagating front describing the fold geometry is governed by a static Hamilton–Jacobi equation, which is discretized by upwind finite differences and a dynamic stencil construction. This forms the basis of numerical solution by finite difference solvers such as fast marching and fast sweeping methods. A new robust and accurate scheme for initialization of finite difference solvers for the static Hamilton–Jacobi equation is also derived. The framework has been integrated in simulation software, and a numerical example is presented based on seismic data collected from the Karama Block in the North Makassar Strait outside Sulawesi.

2D Walk-Away Transmission Stereotomography

We present a 2D slope borehole tomography method handling walk-away transmitted data. The specific parameterization of stereotomographic model, including both velocity field and ray parameters, leads us to propose an original way to process direct arrivals at well : pairs of direct arrivals are created and processed as surface reflected data would be. Such an approach allows to keep a common inversion formalism and to perform final model QC. Moreover, specific information brought by direct arrivals, such as one way travel times, are introduced in the inversion process as a priori information. This approach was tested on synthetic picks and applied to a real data set.

Improved geological modeling and interpretation by simulated migrated seismics

Using a combined Forward and Inverse operator (resolution function), a fast method is presented to construct a simulated migrated seismic section from a geological depth model. Unlike the 1D convolution model, the resolution function expresses both vertical and horizontal resolution. This gives an interpreter a powerful tool to create simulated migrated seismics, which includes migration effects. Further due to its low computational costs, different geological models can rapidly be evaluated.

Simulating migrated seismic data by filtering an earth model: A MATLAB® implementation

An earth model is used in a collaborative environment in which some members provide information for its construction and others utilize the result. Validating an earth model by simulating a migration image is an important step. However, the high computational cost of generating 3D synthetic data, followed by the process of migration, limits the number of scenarios that can be validated. To overcome this computational cost, a novel strategy is used where a migration image is simulated by filtering a model with a spatial resolution filter. One of the key properties of this approach is that the model that describes a target-zone is decoupled from the macro-velocity model that is used to compute the spatial resolution filters. Consequently, different models can be filtered with the same resolution filter. For a horizontally layered medium, the Gazdag phase-shift operators are used to construct a common-offset spatial resolution filter to simulate the phase of 2D primary reflection data. To approximate a spatial resolution filter in a laterally variant medium, ray trace information is used as an illumination constraint. Additionally, the influence of seismic uncertainties on the shape of a spatial resolution filter and the resulting migration image are simulated. These filters enhance an iterative earth modeling approach.

Simulating high resolution inversion: Decomposing the resolution function

In order to correctly compare an impedance section obtained from industry practice inversion algorithms to the impedance of a synthetic geological model (velocity times density), the synthetic impedance values have to be filtered by an Angle filter. This is concluded after decomposing the resolution function into an Angle and Band limiting filter. The low computational costs of the method make it possible that an interpreter can iteratively use the method to minimize the mismatch between a real and a synthetic impedance section.

Horizontal resolution of 3‐D VSP data

In this paper we study the horizontal resolution of 3-D VSP data and compare it to the resolution of surface seismic data for various acquisition configurations. The Kirchhoff migration formula is calculated analytically for a point diffractor, and several measures of horizontal resolution are estimated from the migration images. We have performed full 3-D finite-difference modeling for two acquisition configurations, 1) 3-D VSP in a horizontal well, and 2) 3-D surface seismics. A simplified model with well defined reflectors was used, and the data were migrated using a Krichhoff migration scheme. The results shows that the horizontal resolution of both 3-D VSP and 3-D surface seismic data is in agreement with Beylkin’s classical formula.

An Approximate 3D Computational Method for Real-time Computation of Induction Logging Responses

Induction logging is used in hydrocarbon drilling operations to probe the local subsurface around a drilling bit. The scattered electromagnetic field at the tool receivers depends directly on the conductivity of its surroundings. These differences in conductivity can serve as a proxy to discriminate between oil- and water baring layers. The computation of the tool response requires to solve the electromagnetic equations in the borehole domain. Due to the computational burden such computations are often not feasible if the results are required in real-time. We present an approximation for the electric field based on the integral equation, that requires a only point-wise multiplication. Based on the diffusive nature of low frequency electromagnetic waves we also devise a boundary for our computational domain. We find that our approximation has a better tracking of the signal generated by the electric field integral equation as a tool progresses through a (synthetic) medium than the Born approximation, especially in the vicinity of boundaries between large conductivity variations. We show that our simplified model can give a more accurate reproduction of the tool response, which makes the use of induction logging for real-time modelling during operations viable possibility.