Laurent Maerten

Effects of local stress perturbation on secondary fault development

The complex patterns of normal faults in sedimentary basins are commonly attributed to a complex geological history with varying directions of tectonic extension. However, we show an example of normal faulting from a North Sea hydrocarbon reservoir where the variability in secondary fault orientations can be attributed to stress perturbations that developed around the larger faults during a single phase of extension. This is demonstrated by comparing attributes of the stress fields computed around largest faults from detailed three-dimensional (3D) geomechanical models, with fault data such as discretized fault orientation and density observed from a high quality 3D seismic reflection survey. The modeling results show the strong influence of the irregular geometry (bends and intersections) of larger faults on the development of smaller faults. Methods developed in this study can be applied to predict likely locations and orientations of subseismic faults.

Orthogonal cross joints: do they imply a regional stress rotation?

Abstract Orthogonal cross joints extend across intervals between systematic joints in brittle sedimentary strata and abut the systematic joints at about 90° angles. These joints typically form a ‘ladder-like’ pattern if viewed on a bedding surface. A common interpretation is that orthogonal cross joints define the orientation of the regional stress field during their formation: least compressive stress perpendicular to the joints. It follows that they indicate a rotation of regional principal stresses by 90° after the formation of the systematic joints. Using a three-dimensional boundary element code (Poly3D), we considered a simple geologic case of vertical systematic fractures developing in horizontal strata under a triaxial remote load with: the maximum principal tensile stress being horizontal and perpendicular to the strike of the fractures, the intermediate principal stress being horizontal and parallel to the strike of the fractures, and the least principal tensile stress (i.e. maximum compressive stress) being vertical. The results show that the local maximum principal stress is first perpendicular, and then parallel to, the strike of the systematic fractures as the ratio of fracture spacing to height changes from greater than to less than a critical value when the horizontal remote principal stress ratio, the ratio of the intermediate remote principal stress to the maximum remote principal stress under the sign convention of positive for tensile stresses, is greater than a threshold value (∼0.2). Thus, the fracturing process changes from infilling of systematic fractures to the formation of orthogonal cross fractures. This provides an alternative mechanism for the formation of orthogonal cross joints that does not require a systematic rotation of the regional stress field by 90°. The critical spacing to height ratio for the local principal stress switch is independent of the least remote principal stress (i.e. overburden). It increases nonlinearly with increasing ratio of the horizontal remote principal stresses, and decreases nonlinearly with increasing Poissons ratio of the material.

Inverting for Slip on Three-Dimensional Fault Surfaces Using Angular Dislocations

The increasing quality of geodetic data (synthetic aperture radar interferometry [insar] dense Global Positioning System [gps] arrays) now available to geophysicists and geologists are not fully exploited in slip-inversion procedures. Most common methods of inversion use rectangular dislocation segments to model fault ruptures and therefore oversimplify fault geometries. These geometric simplifications can lead to inconsistencies when inverting for slip on earthquake faults, and they preclude a more complete understanding of the role of fault geometry in the earthquake process. We have developed a new three-dimensional slip-inversion method based on the analytical solution for an angular dislocation in a linear-elastic, homogeneous, isotropic, half-space. The approach uses the boundary element code Poly3D that employs a set of planar triangular elements of constant displacement discontinuity to model fault surfaces. The use of triangulated surfaces as discontinuities permits one to construct fault models that better approximate curved three-dimensional surfaces bounded by curved tiplines: shapes that commonly are imaged by three-dimensional reflection seismic data and inferred from relocated aftershock data. We demonstrate the method’s ability to model three-dimensional rupture geometries by inverting for slip associated with the 1999 Hector Mine earthquake. The resulting model avoids displacement anomalies associated with the overlapping rectangular dislocations used in previous models, improving the fit to the geodetic data by 32%, and honors the observed surface ruptures, thereby allowing more direct comparisons between geologic and geodetic data on slip distributions. Online Material : Hector Mine input files and file format description.

Slip distributions on intersecting normal faults

Abstract Slip distributions on normal faults often are asymmetric and display multiple local maxima. Numerically computed slip distributions from elastic models indicate that such irregular slip distributions can be caused by mechanical interaction between intersecting faults that produce local perturbations of the stress field resolved on the faults. A three-dimensional boundary element model based on the displacement discontinuity method has been used to analyze the mechanical interaction of faults that form Y- or T-shaped intersections. Slip distributions are asymmetric with a steeper slip gradient toward the line of intersection. Multiple slip maxima occur, depending on the angle between the faults, but generally they are not located along the intersections, nor at the fault centers. Examples of intersecting normal faults taken from oil reservoir seismic surveys and sandbox experiments have been used to confirm the application of the theoretical results. Despite considerable simplifications in terms of geometry and boundary conditions, the computed slip distributions capture the characteristics of the observed slip distributions.

Chronologic modeling of faulted and fractured reservoirs using geomechanically based restoration: Technique and industry applications

We have developed a geomechanically based restoration method to model reservoir deformation. The approach, founded on the finite-element method, simulates the physical behavior of the rock mass and considers heterogeneous material properties, bedding slip, and the mechanical interaction of faults. To demonstrate the methods potential, we analyze the deformation and fault growth in the hanging wall of a synsedimentary listric normal fault from a sand-box model, which provides an analog for evaluating complex faulted reservoirs. The numerical model results are then analyzed to investigate the chronology of faulting. The numerical model corresponds well to the physical model and provides additional insights about reservoir evolution and deformation. The approach is also tested on a natural example of folding using outcrop data to study contractional deformation. These examples illustrate how undetected faults and fractures, reservoir compartmentalization, hydrocarbon-migration pathways, and hydrocarbon traps can be understood in the context of tectonic processes and how this understanding can be exploited in decision making and reducing risk. We conclude that the geomechanically based restoration of faulted and fractured reservoirs has significant potential for industry applications compared to common geometric restoration techniques, which lack a mechanical basis.

Digital mapping of three-dimensional structures of the Chimney Rock fault system, central Utah

Part of the Chimney Rock fault system, located on the northern San Rafael Swell, Utah, was mapped by integrating air photograph interpretation and differential global positioning system (GPS) location data. Fault slip, slip directions, and hanging wall subsidence/footwall uplift were digitally recorded in the field along and between the normal faults using Trimble PathFinder equipment and software. GPS was used to record (with sub-meter precision) the location of each measurement as well as the UTM coordinates and elevation of stratigraphic markers at the top of the Jurassic Navajo Sandstone and near the base of the overlying Carmel Formation. The fault system, as well as the associated deformation of the sedimentary layers within the fault blocks, have been precisely characterized using this technique. The geographic coordinates and local elevation were transferred to gOcad to produce a three-dimensional surface representation of a selected resistant limestone layer, by interpolating the elevation between the collected data points using imposed constraints such as the dips of the layers and the locations of the major faults. Separations of the selected horizon from the footwall to the hanging wall were used to calculate the dip-slip distribution along the faults. The digital field data were compared with the results of numerical modeling based on continuum mechanics to study the mechanical interaction among intersecting normal faults and the effects of this interaction on slip distribution and direction. This project illustrates the complete circle from digital mapping to data analysis to numerical modeling to quantitative comparison of theoretical models and field data. q 2001 Elsevier Science Ltd. All rights reserved.

Three-dimensional geomechanical modeling for constraint of subseismic fault simulation

Within any faulted reservoir, there are large numbers of faults that are below the resolution of seismic surveys. Some of these faults are encountered in wells, but most of them remain undetected. Such subseismic faults can significantly influence the flow of hydrocarbons during production. The size distribution of subseismic faults can be predicted by extrapolating the size distribution measured at the seismic scale down to the subseismic scale. However, the positions and orientations of the subseismic faults are more difficult to determine. A method based on mechanical modeling is described here to constrain the positions and orientations of subseismic faults. The large, seismically resolvable faults are brought into a three-dimensional (3-D) numerical mechanical model to determine the stress conditions near these faults at the time of faulting. The stress field is then combined with a Coulomb failure criterion to predict the orientations and densities of the smaller faults. This information is represented on a pair of grids (i.e., a density and strike grid). The grids are then used to condition two-dimensional or 3-D stochastic models of faulting, which use a power-law distribution and/or stochastic growth processes to simulate subseismic faults. Two contrasting stochastic methods are used: (1) a method in which the subseismic faults are placed in the volume as fully grown structures and (2) a method in which the faults are allowed to grow and interact. The Oseberg Sor reservoir, northern North Sea, is used as an example of the application of these methods. Methods for incorporating modeled subseismic faults into the reservoir-flow simulation are also discussed.

How to Constrain 3-D Fault Continuity and Linkage Using Reflection Seismic Data: A Geomechanical Approach

Spatial continuity and linkage of faults may substantially affect fluid flow either by compartmentalizing the reservoir or by increasing the tortuosity of flow pathways, whether the faults act as seals or conduits; therefore, understanding fault linkage geometry should improve reservoir flow simulation models and, in turn, significantly reduce the number of wells required to drain reserves.

iBem3D, a three-dimensional iterative boundary element method using angular dislocations for modeling geologic structures

Most analytical solutions to engineering or geological problems are limited to simple geometries. For example, analytical solutions have been found to solve for stresses around a circular hole in a plate. To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods. The finite element method (FEM) is a differential method that was developed in the 1950s and is one of the most commonly used numerical methods today. Since its development, other differential methods, including the boundary element method (BEM), have been developed to solve different types of problems. The purpose of this paper is to describe iBem3D, formally called Poly3D, a C++ and modular 3D boundary element computer program based on the theory of angular dislocations for modeling three-dimensional (3D) discontinuities in an elastic, heterogeneous, isotropic whole- or half-space. After 20 years and more than 150 scientific publications, we present in detail the formulation behind this method, its enhancements over the years as well as some important applications in several domains of the geosciences. The main advantage of using this formulation, for describing geological objects such as faults, resides in the possibility of modeling complex geometries without gaps and overlaps between adjacent triangular dislocation elements, which is a significant shortcoming for models using rectangular dislocation elements. Reliability, speed, simplicity, and accuracy are enhanced in the latest version of the computer code. Industrial applications include subseismic fault modeling, fractured reservoir modeling, interpretation and validation of fault connectivity and reservoir compartmentalization, depleted area and fault reactivation, and pressurized wellbore stability. Academic applications include earthquake and volcano monitoring, hazard mitigation, and slope stability modeling.

Integrated charge and seal assessment in the Monagas fold and thrust belt of Venezuela

Conventional basin and petroleum systems modeling uses the vertical backstripping approach to describe the structural evolution of a basin. In structurally complex regions, this is not sufficient. If lateral rock movement and faulting are inputs, the basin and petroleum systems modeling should be performed using structurally restored models. This requires a specific methodology to simulate rock stress, pore pressure, and compaction, followed by the modeling of the thermal history and the petroleum systems. We demonstrate the strength of this approach in a case study from the Monagas fold and thrust belt (Eastern Venezuela Basin). The different petroleum systems have been evaluated through geologic time within a pressure and temperature framework. Particular emphasis has been given to investigating structural dependencies of the petroleum systems such as the relationship between thrusting and hydrocarbon generation, dynamic structure-related migration pathways, and the general impact of deformation. We also focus on seal integrity through geologic time by using two independent methods: forward rock stress simulation and fault activity analysis. We describe the uncertainty that is introduced by replacing backstripped paleogeometry with structural restoration, and discuss decompaction adequacy. We have built two end-member scenarios using structural restoration, one assuming hydrostatic decompaction, and one neglecting it. We have quantified the impact through geologic time of both scenarios by analyzing important parameters such as rock matrix mass balance, source rock burial depth, temperature, and transformation ratio.