Frantz Maerten

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.

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.

Modeling mixed-mode fracture propagation in isotropic elastic three dimensional solid

A planar fracture when subjected to sufficient tensile and shear stresses will propagate off-plane, in what is known as mixed-mode propagation. Predicting the fracture path relies on an accurate calculation of the near-tip stress and an appropriate propagation criterion. The new criterion we present scales the propagation magnitude and direction with the near-tip tensile stress in the form of vectors that originate from the fracture tip-line. Boundary element method (BEM) models enable us to calculate the near-tip stress field of an arbitrary fracture. We use analytical Eshelby’s solution that evaluates near-tip stress of an ellipsoidal fracture to validate the BEM results. We feed the near-tip stress to the propagation criterion to determine the propagation vectors, and grow the BEM mesh by adding new tip-elements whose size and orientation are given by the propagation vectors. Then, we feed the new mesh back to the BEM to calculate the new near-tip stress. By running the BEM and the propagation criterion in a loop, we are able to model 3D fracture propagation.

On a method for reducing interpretation uncertainty of poorly imaged seismic horizons and faults using geomechanically based restoration technique

To reduce exploration risk and optimize production in structurally complex areas, the geologic interpretation must be based on sound geomechanical principles. Despite advances in 3D seismic acquisition and processing techniques as well as in the availability of computationally robust interpretation software, the challenge associated with interpreting complex structures from seismic reflection data is that highly deformed areas surrounding faults, folds, and salt surfaces are often poorly imaged and therefore their interpretation is highly uncertain. We have developed a methodology that should help geophysicists quickly check the strengths and weaknesses of their interpretation and to automatically reduce the uncertainty in a faulted horizon geometry. Our workflow consisted of restoring interpreted seismic horizons and relating the concentrations of computed deformation attributes to areas of interpretation uncertainty. We used the technique based on an iterative finite-element formulation that allowed unfolding and unfaulting of 3D horizons using physical elastic behavior. A fast algorithm has been developed to automatically correct the interpreted structures in zones that exhibited anomalous deformation concentrations after restoration. This approach is able to mechanically check and reduce uncertainty in a faulted seismic horizon interpretation. Its application to synthetic and reservoir data has a high degree of reliability in the characterization of structurally complex reservoirs. This technique is also applicable to 2D models (geologic cross sections) and 3D models (volume).