Randall Marrett

Kinematic analysis of fault-slip data

Abstract An array of graphical and numerical techniques facilitate qualitative and quantitative kinematic analysis of fault-slip data. Graphical contouring and Bingham statistics of the shortening and extension axes for kinematically scale-invariant faults characterize the distributions and orientations of the principal axes of average incremental strain. Numerical analysis by means of moment tensor summation yields the orientations and magnitudes of the principal strain axes as well as rotational information. Field data can be weighted for moment tensor summation using measurements of fault gouge thickness and/or fault plane width, from which average displacement and fault area can be estimated. The greatest uncertainties of kinematic analysis derive from assumptions about the weighting of the data, the effects of post-faulting rotation on the data, the degree to which sampling is representative of the entire fault population, and the spatial homogeneity of strain. These assumptions can be evaluated for a specific data set. Geometric criteria can distinguish the kinematic heterogeneities produced by triaxial deformation, anisotropy reactivation, strain compatibility constraints and/or multiple deformations. Strain compatibility, material anisotropy and heterogeneity may be characterized by integrating the results of kinematic and dynamic fault-slip analyses.

Characteristics and origins of coal cleat: A review

Abstract Cleats are natural opening-mode fractures in coal beds. They account for most of the permeability and much of the porosity of coalbed gas reservoirs and can have a significant effect on the success of engineering procedures such as cavity stimulations. Because permeability and stimulation success are commonly limiting factors in gas well performance, knowledge of cleat characteristics and origins is essential for successful exploration and production. Although the coal–cleat literature spans at least 160 years, mining issues have been the principal focus, and quantitative data are almost exclusively limited to orientation and spacing information. Few data are available on apertures, heights, lengths, connectivity, and the relation of cleat formation to diagenesis, characteristics that are critical to permeability. Moreover, recent studies of cleat orientation patterns and fracture style suggest that new investigations of even these well-studied parameters can yield insight into coal permeability. More effective predictions of cleat patterns will come from advances in understanding cleat origins. Although cleat formation has been speculatively attributed to diagenetic and/or tectonic processes, a viable mechanical process for creating cleats has yet to be demonstrated. Progress in this area may come from recent developments in fracture mechanics and in coal geochemistry.

Estimates of strain due to brittle faulting: sampling of fault populations

Abstract The geometry of sampling domains is a first-order consideration in the characterization of brittle fault populations. In most cases, descriptions of fault size distributions based on map, cross-section, traverse or borehole data systematically underestimate the number of small faults present in a volume. The geometry of sampling domains may be accounted for using an empirical proportionality between fault displacement and trace length. Estimates of strain in which the sampling geometry is considered suggest that small faults accommodate a significant portion of the total strain due to the brittle faulting process.

Late Cenozoic tectonic evolution of the Puna Plateau and adjacent foreland, northwestern Argentine Andes

Abstract Kinematic analysis of ∼ 1500 fault-slip measurements from the Puna plateau and adjacent foreland of northwestern Argentina suggests that two regional kinematic regimes characterize late Cenozoic deformation: a thrust phase with ∼WNW-ESE shortening and subvertical extension followed by a strike-slip phase with ∼ENE-WSW shortening and ∼NNW-SSE extension. Radiometric dating combined with field relationships demonstrate that thrust faulting started by 13 Ma and lasted, at least locally, until 1 Ma, and that strike-slip faulting started by 2 Ma and is still active. The shortening direction of the thrust phase, which accounts for most of the Andean shortening, differs from the coeval plate tectonic convergence direction and probably cannot be explained by later oroclinal bending. Paleostructural control of deformation kinematics and/or strike-slip faulting along the thermally weakened volcanic arc might explain the Mio-Pliocene shortening direction. The subhorizontal extension direction of the strike-slip phase is evident at all elevations studied, suggesting that local body forces do not drive it. A decrease in South America-Nazca plate convergence rate and/or complex three-dimensional effects, possibly including kinematic variation with depth in the crust, might provide a satisfactory explanation.

A scale-independent approach to fracture intensity and average spacing measurement

Fracture intensity, the number of fractures per unit length along a sample line, is an important attribute of fracture systems that can be problematic to establish in the subsurface. Lack of adequate constraints on fracture intensity may limit the economic exploitation of fractured reservoirs because intensity describes the abundance of fractures potentially available for fluid flow and the probability of encountering fractures in a borehole. Traditional methods of fracture-intensity measurement are inadequate because they ignore the wide spectrum of fracture sizes found in many fracture systems and the consequent scale dependence of fracture intensity. An alternative approach makes use of fracture-size distributions, which allow more meaningful comparisons between different locations and allow microfractures in subsurface samples to be used for fracture-intensity measurement. Comparisons are more meaningful because sampling artifacts can be recognized and avoided, and because common thresholds of fracture size can be enforced for counting in different locations. Additionally, quantification of the fracture-size distribution provides a mechanism for evaluation of uncertainties. Estimates of fracture intensity using this approach for two carbonate beds in the Sierra Madre Oriental, Mexico, illustrate how size-cognizant measurements cast new light on widely accepted interpretation of geologic controls of fracture intensity.

Are fault growth and linkage models consistent with power-law distributions of fault lengths?

Abstract It has recently been recognized that fault lengths ( L ) in natural populations follow power-law scaling. Such power-law scaling is observed in a wide range of tectonic settings in regions that have experienced differing amounts of total strain, and exhibit faults over a very large range of dimensions. In this paper we explore possible constraints on fault growth and linkage required to maintain power-law length scaling during progressive deformation. We first consider a fault growth model in which individual faults in a population grow by an amount Δ L ∝ L F during slip increments (earthquakes), which have a recurrence interval τ ∝ L E . If an initial power-law length distribution is assumed for the population, it is found that the growth model exponents must be related by F − E = 1 in order to continually maintain the same scaling. If the requirement of constant moment release rate through time is also imposed, this implies that for large faults E = 2, which leads to a loss of power-law scaling with increasing strain, unless F = 3. Current mechanical models for growth of single faults by tip propagation propose E ≥ 1 and F = 1. Thus single-fault models are not consistent with observed power-law scaling. In a second model, fault lengths increase by growth specified by the first model, unless a nearby fault is encountered, in which case the two faults link. With this model, it is possible to produce a power-law distribution from a fault or flaw population that initially does not have a power-law distribution. Once a power-law distribution is developed, fault linkage causes the power-law exponent ( C ) to decrease as fault strain increases.

Response of intracontinental deformation in the central Andes to late Cenozoic reorganization of South American Plate motions

New stratigraphic, chronologic, and fault kinematic data from the Quebrada del Toro in northwestern Argentina provide a detailed view of late Cenozoic kinematic reorganization in the southern central Andes. The Quebrada del Toro is a thrust-bounded basin filled with 2 km of synorogenic clastic deposits, ranging in age from early Miocene to Holocene. As observed elsewhere in northwestern Argentina, faults in the Quebrada del Toro record an early phase of horizontal NW-SE contraction (beginning between early and late Miocene and ending after 0.98 Ma) and a later phase of horizontal NE-SW contraction (beginning between late Miocene and 4.17 Ma and still active). These results require both kinematic regimes to have been active between 4.17 and 0.98 Ma, compatible with timing and kinematic data from the adjacent central Andes and best explained by a temporal pattern of serial recurrence of the kinematic regimes. A hypothesis that intraplate deformation in the central Andes is driven by the absolute motion of the South American Plate with respect to the hotspot reference frame is tested by comparing Quebrada del Toro kinematics to plate reconstructions and space-based geodetic results. Nazca-South America relative motion and absolute Nazca Plate motion show consistent azimuths throughout the past 20.5 Myr. In contrast, absolute South American Plate motion azimuths mimic the changing contraction directions determined from intraplate Andean faults. Although the timing of the South American Plate motion change is poorly resolved by current data, it is compatible with the Quebrada del Toro data. Absolute upper plate motion might control intraplate kinematics along many of the Earths convergent margins.

Aggregate properties of fracture populations

Empirical studies indicate that the individual attributes of both faults and extension fractures follow power-law scaling. Aggregate properties of fracture populations are important in a variety of problems and can be specified in terms of the scaling parameters of individual fracture attributes. Development of an expression for an aggregate property requires consideration of a number of independent factors, including the topologic dimension of the aggregate property, the topologic dimension of sampling and the possibility of scaling changes for fractures that span some mechanically significant layer. The Riemann zeta function provides an alternative to integration for the analytical and numerical solution of aggregate problems. Previous work regarding aggregate properties of fracture populations has focused on the strain due to faulting. New expressions are developed here for other aggregate properties of interest: fracture surface area, fracture porosity, fracture permeability and shear-wave anisotropy. A general characteristic of these aggregate properties is that, for most values of scaling exponents, the aggregate properties are dependent on the size of the sampling domain. This implies that the aggregate properties are scale-dependent. Additionally, it appears that fracture surface area is concentrated in the smallest fractures of many populations. Fracture porosity is concentrated in the largest fractures of most populations but not as strongly as fracture permeability, which probably derives almost entirely from the largest fractures in populations.

Extent of power-law scaling for natural fractures in rock

New data sets from natural faults and extension fractures exhibit simple power-law scaling across 3.4‐4.9 orders of magnitude, regardless of rock type or movement mode. The data show no evidence of natural gaps or scaling changes. Each data set consists of independent measurements made at different observational scales; a power-law regression to the subset of smaller fractures in each case provides an extrapolation that accurately predicts associated larger fractures. Consequently, data representing a limited range of fracture sizes may be used to characterize a much broader spectrum of fracture sizes.

Strain and stress

Structural analyses of specific features in naturally deformed rock consist of geometric observations (e.g. shape), kinematic measurements (e.g. strain), and dynamic models (e.g. stress). Although analytical definitions clearly distinguish strain and stress, common usage of the terms tends to blur the conceptual diAerence. Strain and stress do not have a simple cause-and-eAect relationship. The fundamental diAerence between strain and stress is that strain terms reflect descriptive interpretations of what movements produced a structure, while stress terms reflect genetic interpretations of why the structure formed. This descriptive vs genetic distinction has several implications. First, kinematic analysis is less speculative and more directly related to observations than dynamic analysis. Second, kinematic analysis is less computationally and analytically intensive than dynamic analysis. Third, kinematic analysis is amenable to more intuitive, but shallower, understanding than dynamic analysis. The most useful terminology communicates this conceptual framework through clear and accurate use of terms for strain, stress, and related concepts. A variety of examples illustrate the descriptive and genetic usage of strain and stress terminology. # 1999 Elsevier Science Ltd. All rights reserved.