Randall M. Richardson

Ridge forces, absolute plate motions, and the intraplate stress field

Torque poles are calculated for a variety of possible forces acting on the plates, including ridge push, slab pull, and collisional resistance. These torque poles are then compared to the directions of absolute plate motions. There is a strong correlation between ridge torque poles and the azimuth of absolute plate motions for the North American, South American, Pacific, Cocos, and Eurasian plates. Simple slab pull torques correlate well with absolute motion azimuths for the Pacific, Nazca, and Cocos plates and moderately well with the absolute motion azimuth of the IndoAustralian plate. Collisional resistance torque poles correlate with the absolute motion azimuth of the Eurasian plate only. The correlations are presented as further evidence that the absolute reference frame for plate motion is determined by the surface plates themselves. Torque poles for various forces are also compared with several long-wavelength features of the global intraplate stress field that also tend to be aligned with absolute motion directions. In general, ridge torque directions agree well with the orientations of maximum horizontal stresses for stable North America, western Europe, and South America and provide an alternative explanation for the alignment in terms of ridge push forces rather than basal drag. Collisional resistance forces can also explain the alignment of stresses in western Europe. For the IndoAustralian plate, the torque pole for collisional resistance forces is consistent with the general pattern of stresses in at least the western half of the plate but is not a good predictor of the entire data set for the plate. Other processes, in addition to collisional resistance, must be important for the Indo-Australian plate. Ridge push forces may account for a significant portion of the long-wavelength features of the intraplate stress field, especially away from continental collisions. Such a conclusion is consistent with negative buoyancy of the slab being an important component of the driving mechanism. As previously suggested, slab forces may be largely balanced within the subducted slab itself and thus have limited effect on deformation of the surface plates.

Topography, boundary forces, and the Indo-Australian intraplate stress field

The relative contribution of topographic (e.g., ridge push, continental margins, and elevated continental crust) and plate boundary (e.g., subduction and collisional) forces to the intraplate stress field in the Indo-Australian plate (IAP) is evaluated through a finite element analysis. Two important aspects of the IAP intraplate stress field are highlighted in the present study: (1) if substantial focusing of the ridge push torque occurs along the collisional boundaries (i.e., Himalaya, New Guinea, and New Zealand), many of the first-order features of the observed stress field can be explained without appealing to either subduction or basal drag forces; and (2) it is possible to fit the observed SHmax, (maximum horizontal stress orientation) and stress regime information with a set of boundary conditions that results in low tectonic stress magnitudes (e.g., tens of megapascals, averaged over the thickness of the lithosphere) throughout the plate. This study therefore presents a plausible alternative to previous studies of the IAP intraplate stress field, which predicted very large tectonic stress magnitudes (hundreds of megapascals) in some parts of the plate. In addition, topographic forces due to continental margins and elevated continental material were found to play an important role in the predicted stress fields of continental India and Australia, and the inclusion of these forces in the modeling produced a significant improvement in the fit of the predicted intraplate stresses to the available observed stress information in these continental regions. A central focus of this study is the relative importance of the boundary conditions used to represent forces acting along the northern plate margin. We note that a wide range of boundary conditions can be configured to match the large portion of the observed intraplate stress field, and this nonuniqueness continues to make modeling the IAP stress field problematic. While our study is an important step forward in understanding the sources of the IAP intraplate stress field, a more complete understanding awaits a better understanding of the relative magnitude of the boundary forces acting along the northern plate margin.

The origins of the intraplate stress field in continental Australia

The ridge push force acting on the Indo-Australian plate exerts a significant torque (8.5 × 1025N m) about a pole at 30.3°N, 34.5°E. The angular difference between this torque pole and the observed pole of rotation for the plate (19.2°N, 35.6°E) is less than 12° and suggests that the ridge push force plays an important role in the dynamics of the Indo-Australian plate. We have used an elastic finite-element analysis to study the predicted intraplate stress field in continental Australia for four models which employ different boundary conditions to balance the ridge push torque acting on the plate. The modeling indicates that a number of important features of the observed stress field within the Australian continent can be explained in terms of balancing the ridge push torque with resistance imposed along the Himalaya, Papua New Guinea, and New Zealand collisional boundaries segments. These features include NS-to NE-SW-oriented compression in the northern Australia and E-W-oriented compression in southern Australia. Our analysis also shows that subduction processes along the northern and eastern boundaries provide only second-order controls on the intraplate stress field in continental Australia.

Analysis of the South American intraplate stress field

The first-order South American intraplate stress field was modeled through a finite element analysis to evaluate the relative contribution of plate boundary forces and intraplate stress sources. The finite element mesh consisted of 3100 nodes in a network of 5993 equal-area triangular elements which provided a spatial resolution of about 1° at the equator. An important aspect of our modeling is the inclusion of topographic forces due to the cooling oceanic lithosphere along the Mid-Atlantic Ridge (e.g., ridge push), the continental margins along the east coast of Brazil and Argentina, and the elevated continental crust (e.g., the Andean Cordillera). Predicted intraplate stresses for two representations of the western collisional boundary forces are evaluated: pinned collisional boundaries and applied collisional boundary forces. Constraint for the modeling was provided by information about the orientation of the maximum horizontal compressive stress, SHmax, provided by 217 stress indicators from the World Stress Map Project as well as by SHmax magnitude estimates and torque information from previous investigations. Our modeling results demonstrate that the first-order features of the observed stress field can be explained with simple tectonic models which balance the torque acting on the plate either with a fixed western margin or drag forces applied along the base of the plate. The predicted intraplate stress field is characterized by a nearly uniform E-W SHmax orientation throughout most regions of the plate, with stress magnitudes generally less than 20 MPa averaged over a 100-km-thick lithosphere. Significant perturbation of this regional stress field occurs in the western part of the plate in response to forces associated with the high topography of the Andes. Although the magnitude of the collisional boundary forces acting along the western margin remains poorly constrained, we estimate a plausible upper bound on the force per unit length acting along the Peru-Chile Trench to be about 2.5 × 1012 N m−1. While some of our models are consistent with a driving basal drag to balance the torques acting on the plate, the magnitude of the drag torque is small compared to the contribution from other sources of stress such as the ridge push force.

A RHEOLOGICALLY LAYERED THREE-DIMENSIONAL MODEL OF THE SAN ANDREAS FAULT IN CENTRAL AND SOUTHERN CALIFORNIA

Three-dimensional kinematic finite element models of the San Andreas fault in central and southern California have been used to estimate the effects of rheological parameters and fault slip distribution on the horizontal and vertical deformation in the vicinity of the fault. The models include the effects of vertically layered power law viscoelastic rheology, and isostatic forces are considered in calculations of vertical uplift. Several different rheological layering schemes are used, using laboratory results on rock rheology to define the properties of the various layers. The depth to which the fault remains locked between earthquakes (D) is held constant at 20 km for the entire locked portion of the fault between Cholame and the Salton Sea. Between Hollister and Cholame the entire fault is assumed to slip at a rate consistent with a relative plate velocity of 35 mm/yr along a direction striking N41°W. Steady aseismic slip corresponding to plate velocity is imposed below the fault locking depth to a depth H on the locked section of the fault. The depth to which aseismic slip occurs (H) is assigned a value of either 20 km or 40 km, resulting in two versions of each rheological model. Variations in the model parameters are found to produce distinctive deformation patterns, providing a means for differentiating between models. Specifically, lower effective viscosities near the surface result in increased strain rates and uplift rates at all times during the earthquake cycle. Lower effective viscosities also produce subsidence near the creeping portion of the fault. Models that do not include aseismic slip below the fault locking depth (H = 20 km) display greater time dependence in both horizontal and vertical deformation than those including aseismic slip below the locking depth (H = 40 km). These differences are due, in part, to the time-invariant nature of the imposed slip condition. The differences are more pronounced as the effective viscosity close to the surface is increased. The vertical uplift rate is particularly sensitive to the depth of aseismic slip (H) at the two bends in the fault, especially for models with high effective viscosities below the surface. For models in which the effective viscosity near the surface is relatively low, measurements of total uplift at the two bends in the fault could provide sufficient resolution to distinguish between models with and without aseismic slip over time periods of 10 to 20 years or more with current abilities to measure vertical uplift. Among our San Andreas fault models, the one most consistent with current strain rate data includes aseismic slip between 20 and 40 km (H = 40 km) and uses assumed rheological properties from the surface to 100 km depth consistent with laboratory results for wet rock samples. The rheological parameters for this model are based on laboratory results for the following rock types wet granite in the upper crust (0 to 20 km), wet diabase in the lower crust (20 to 40 km), wet dunite in the upper mantle (40 to 100 km), and dry olivine below 100 km. These modeling results are preliminary, however, and several additional factors should be considered prior to constructing a comprehensive model. Furthermore, it should be emphasized that the present models represent a small subset of possible rheological models, and numerous other models may provide similar or better fits to the data. The field of possible models will continue to narrow with further knowledge of the variations in Earth composition and temperature with depth, with more information on rock rheology, and with further observations of the earthquake cycle.

North American plate dynamics

Deformation within the North American plate in response to various tectonic processes is modeled using an elastic finite element analysis. A coarse grid contains 328 elements and 190 nodes, while a fine grid contains 718 elements and 396 nodes for a spatial resolution of 2°–3°. Abundant information about the present-day state of intraplate stress constrains the modeling. The dominant pattern that must be fit by all acceptable models is an ENE trend for the maximum compressive stress for most of the plate east of the Rocky Mountains. The tectonic processes considered in the modeling include ridge forces associated with the normal thermal evolution of oceanic lithosphere, shear and normal stresses transmitted across transforms, normal stresses transmitted across convergent boundaries, stresses due to horizontal density contrasts within the continent, and shear tractions applied along the base of the plate. Model stresses are calculated with respect to a lithostatic reference stress state. Distributed ridge forces of magnitude 2×1012 N/m predict deviatoric stresses of the order of 20–40 MPa that are capable of accounting for the dominant observed ENE stress trend. Driving drag models also fit the trend but are not preferred because of a predicted tenfold increase in compressive stress magnitudes from east to west across the plate. Assuming that ridge forces account for the dominant ENE stress trend, bounds may be placed on other possible forces. For example, shear stresses transmitted across transform boundaries along the San Andreas and Caribbean are small, of the order of 5–10 MPa. Also, compressive stresses of the order of 5–10 MPa transmitted across the major transforms improve the fit to the data. Compressive stresses across convergent margins along the Aleutians and the Middle America trench are important.

On the gravitational potential of the Earth's lithosphere

The mean potential energy of the lithosphere is useful for defining the tectonic reference state (TRS) of the Earth and can be used to constrain the ambient state of stress in the plates. In the absence of external forces applied at the base or along plate boundaries a lithospheric column with the potential energy of the TRS would remain undeformed. Thus the difference between the potential energy of a lithospheric column and the TRS determines whether the column is in an extensional, joeutral, or compressional state of stress. We evaluate and intraplate variations about this mean, using a simple, first-order lithospheric density model. This model assumed that the continental geotherm is linear, and density variations below a depth of 125 km have negligible influence on , and is consistent with observed geoid anomalies across continental margins. is estimated to be 2.379 × 1014 N m−1, which is equivalent to the potential energy of both near sea level continental lithosphere (−160 to +220 m for an assumed crustal density, ρc, in the range 2800–2700 kg m−3) and cooling oceanic lithosphere at a depth of 4.3 km. With the exception of Eurasia, which has anomalously high mean potential energy ( = 2.383 × 1014 N m−1), the mean potential energies of the continental plates are nearly identical to the global mean . The mean potential of the oceanic plates was found to be a strong function of the mean age of the oceanic lithosphere. Both the global and plate mean potential energies are relatively insensitive to a wide range in ρc. The potential of the mid-ocean ridges ( ), 2.391 × 1014 N m−1, is greater than the global mean, which is consistent with the divergent nature of the ridges. Elevated continental lithosphere with a height of about 70 m has an equivalent potential energy to , suggesting that in the absence of external forces, continental regions will be in a slightly extensional state of stress. The importance of our potential energy formulation is substantiated by the strong correlation between the torque poles associated with the potential energy distributions and the observed plate velocity poles for the South American, Nazca, Indo-Australian, and Pacific plates.

Stress perturbation associated with the Amazonas and other ancient continental rifts

The state of stress in the vicinity of old continental rifts is examined to investigate the possibility that crustal structure associated with ancient rifts (specifically a dense rift pillow in the lower crust) may modify substantially the regional stress field. Both shallow (2.0–2.6 km depth) breakout data and deep (20–45 km depth) crustal earthquake focal mechanisms indicate a N to NNE maximum horizontal compression in the vicinity of the Paleozoic Amazonas rift in central Brazil. This compressive stress direction is nearly perpendicular to the rift structure and represents a ∼75° rotation relative to a regional E-W compressive stress direction in the South American plate. Elastic two-dimensional finite element models of the density structure associated with the Amazonas rift (as inferred from independent gravity modeling) indicate that elastic support of this dense feature would generate horizontal rift-normal compressional stresses between 60 and 120 MPa, with values of 80–100 MPa probably most representative of the overall structure. The observed ∼75° stress rotation constrains the ratio of the regional horizontal stress difference to the rift-normal compressive stress to be between 0.25 and 1.0, suggesting that this rift-normal stress may be from 1 to 4 times larger than the regional horizontal stress difference. A general expression for the modification of the normalized local horizontal shear stress (relative to the regional horizontal shear stress) shows that the same ratio of the rift-normal compression relative to the regional horizontal stress difference, which controls the amount of stress rotation, also determines whether the superposed stress increases or decreases the local maximum horizontal shear stress. The potential for fault reactivation of ancient continental rifts in general is analyzed considering both the local stress rotation and modification of horizontal shear stress for both thrust and strike-slip stress regimes. In the Amazonas rift case, because the observed stress rotation only weakly constrains the ratio of the regional horizontal stress difference to the rift-normal compression to be between 0.25 and 1.0, our analysis is inconclusive because the resultant normalized horizontal shear stress may be reduced (for ratios >0.5) or enhanced (for ratios <0.5). Additional information is needed on all three stress magnitudes to predict how a change in horizontal shear stress directly influences the likelihood of faulting in the thrust-faulting stress regime in the vicinity of the Amazonas rift. A rift-normal stress associated with the seismically active New Madrid ancient rift may be sufficient to rotate the horizontal stress field consistent with strike-slip faults parallel to the axis of the rift, although this results in a 20–40% reduction in the local horizontal shear stress within the seismic zone. Sparse stress data in the vicinity of the seismically quiescent Midcontinent rift of the central United States suggest a stress state similar to that of New Madrid, with the local horizontal shear stress potentially reduced by as much as 60%. Thus the markedly different levels of seismic activity associated with these two subparallel ancient rifts is probably due to other factors than stress perturbations due to dense rift pillows. The modeling and analysis here demonstrate that rift-normal compressive stresses are a significant source of stress acting on the lithosphere and that in some cases may be a contributing factor to the association of intraplate seismicity with old zones of continental extension.

Tectonic stress within the New Madrid seismic zone

Refraction data indicate a significant high-density rift pillow beneath the New Madrid seismic zone. We present results of linear and nonlinear viscoelastic finite element modeling to determine whether support of the rift pillow may contribute significantly to the total present-day stress field, and we consider the implications for intraplate seismicity. These models were run for a loading time of 100 m.y. to account for relaxation and transfer of stress since the last reactivation of the rift in the mid-Mesozoic. Results indicate that the nonlinear viscoelastic model with rheological stratification based on composition and temperature agrees well with the observed deformation within the seismic zone and with estimates of regional stress magnitudes. The model predicts a maximum compression of 30–40 MPa above the rift pillow in the center of the rift axis. If the magnitude of local compression predicted by the nonlinear model produces the inferred clockwise rotation of the order of 10°–30° in the direction of SHmax (maximum horizontal compression) near the rift axis, the magnitude of regional compression is a factor of 1 to 2 times the magnitude of local compression and consistent with an origin due to ridge push forces. The addition of the local stress associated with the rift pillow, however, results in an approximately 30% reduction in the resolved maximum horizontal shear stress. Thus, while the stress associated with the rift pillow can rotate the stress field into an orientation favorable for failure, reduction in the resolved shear stress requires a separate mechanism for strength reduction. Results of the modeling indicate that stresses from the load of the rift pillow may still be present in the upper crust even after 100 m.y. and may still play a role in present-day deformation and seismicity of the New Madrid seismic zone. Local stress fields of significant tectonic magnitudes may also occur around other ancient rift pillows and help explain the observed correlation between intraplate seismicity and failed rift zones.

Statistical trends in the intraplate stress field

The World Stress Map (WSM) database contains thousands of intraplate stress indicators, with the potential to provide important constraint for arguments about the relationship between tectonic stresses and both the kinematics and dynamics of plate motion. Previous studies, which relied almost exclusively on visual inspection of the data, established the existence of broad regions of uniform maximum horizontal compressive stress orientation (SHmax) and stress regimes on a regional scale. In the present study, we present a statistical analysis of the WSM stress indicators with the aim of quantifying trends in both the SHmax orientations and stress regimes. The analysis was carried out within 5° × 5° bins which provide a resolution of several hundred kilometers. Only the 4537 high-quality WSM indicators with rating of A to C were used in the analysis. We present results for two types of analysis on the information contained within the bins. First, we evaluate the spatial distribution of the average stress regime (normal, strike-slip, or thrust). Second, we apply the Rayleigh test, a standard statistical method in the analysis of directional data, to the distribution of SHmax orientations to test the null hypothesis that the orientations are random. An important aspect of our study is the quantification of the conclusions drawn from visual inspection of the World Stress Map. Our results indicate that broad regions of uniform SHmax orientations exist in most continental regions at high confidence levels (90% and 95%) and are less robust in the slowest moving continental plates. We also quantify the predominance of strike-slip and compressional stress regimes in continental regions. Importantly, our analysis provides information about trends in the SHmax orientations in regions where large amounts of scatter in the directional data prevented conclusions being drawn from visual inspection of the data, for example, in western North America and continental Australia. Furthermore, we find a strong correlation between average SHmax orientations and both the ridge push torque and the absolute plate velocity azimuths. Our observation that a greater number of SHmax orientations correlate with the ridge push torque directions is further evidence that the intraplate stress field is strongly influenced by the ridge push force.