Modelo de suelo no Homogéneo

We use SHELLS (Kong and Bird, 1995; Bird, 1999), a global finite element code, for modeling. We opted for a global finite element code instead of a flat-Earth one in order to avoid unphysical boundary conditions at the edges of our area of interest. A global code has never been used before to model the behavior of a regional area in such detail, therefore our work is as much an investigation of fault strength as it is a feasibility test for this type of models.

In SHELLS, elastic strain is neglected and only permanent strain is considered, therefore the results of SHELLS calculations correspond to an average over several seismic cycles. The rheology of the model is thus elastic everywhere, and the active deformation mechanisms are either frictional sliding along faults or nonlinear dislocation creep. In dislocation creep, ˙ε (strain-rate) relates to stress (σ) and creep activation energy (Q) through the power-law equation

˙ ε∝A σnexp − Q R T , (3.1)

whereAis the shear stress coefficient, Rthe gas constant, andT is the temperature. In the model frictional sliding and dislocation creep compete at faults: friction dominates in the upper part, where the normal force is small, while dislocation creep dominates at depth, where the temperature is high enough to achieve substantial slip-rates. The depth of the transition between the two for each fault element (brittle–ductile transition depth) is calculated by assuming that the rheology resulting in the lowest shear stress will prevail.

Figure 3.1: Global grid showing temperature at 100 km depth as deviation from

the average calculated at that depth, and MCM velocity vectors (blue arrows) at 100 km depth. Faults and plate boundaries are in yellow. PA = Pacific, NA = North America, CO = Cocos, CA = Caribbean, NZ = Nazca, SA = South America.

The only boundary conditions that need to be specified are the global plate-driving forces, for which we tested both NUVEL-1A velocities, and velocities derived from global mantle circulation modeling (Bunge et al., 1998, 2002) applied at the bottom of the plates everywhere in our model. The actual depth at which velocities are applied does not significantly affect results, as long as the velocities are not applied within the crust itself. We adopt a high-resolution mantle circulation model (Fig. 3.1,Schuberth et al., 2009) that provides sufficient spatial resolution to resolve the vigorous convective regime of the mantle. In addition to representing the dynamic effects from a mechanically weak asthenosphere on mantle flow (Richards et al., 2001), the model incorporates internal heat generation from radioactivity together with a significant amount of heat flow from the core, for which there is growing evidence (Bunge, 2005; van der Hilst et al., 2007). Combined with constraints on the history of subduction (Engebretson et al., 1984; Richards and

Engebretson, 1992) this allows us to place first-order estimates on the internal mantle buoyancy forces that drive plates.

We assume we have a good knowledge of the 3-D fault geometry, and then solve for fault strength. In particular, we examine the effect of effective fault friction (µ∗) in the upper brittle part of the crust and of creep activation energy (Q) in the ductile lower crust. SHELLS calculates forces and velocities, which we use to compute parameters that can be directly compared with data (fault slip-rates, GPS velocities, earthquakes depth distribution, and stress directions) in order to score our model and determine fault strength. Input for the model is provided as information about fault geometry, topography and heat flow, stored in the finite element grid, and as parameters like friction coefficients and creep activation energies for crust and mantle (a complete list of parameters and values used is provided in table 3.1). Such models have already been shown to produce realistic results at global scale (e.g. Bird, 1999; Iaffaldano and Bunge, 2009) and therefore we chose our set of global parameters to match published models. In this paper we limit ourselves to describing the local modifications to strength-controlling parameters, with the understanding that global parameters remain unchanged throughout the entire set of simulations.

Figure 3.2: Variable-resolution grid, global view. The largest elements at global

level have sides of ≈2× 103_{km away from plate boundaries, and 1 × 10}3 _{km at}

plate boundaries. NA = North American plate, PA = Pacific plate, CO = Cocos plate, NZ = Nazca plate, CA = Caribbean plate. Plate boundaries from Bird (1999).

SHELLS uses a grid of spherical triangles for the continuum elements, and arcs of great circle for the fault elements (Kong and Bird, 1995). To drive the local model

as part of a global one, we constructed a variable-resolution grid (Fig. 3.2) that gradually transitions from a low-resolution global grid to a high-resolution local one covering California and western Nevada (Fig. 3.3). In order to position the fault elements as accurately as possible, we built the grid using Gocad (Mallet, 2002), which allows us to incorporate the faults directly into the local grid and to optimize the mesh for triangle equilaterality and smooth transition between local and global grid, while keeping the fault elements fixed in 3-D space. The distance between nodes in the local part of the grid varies between about 5 km and 50 km. This distance is based on the level of complexity of the fault geometry in a given area, rather than on the resolution of the topography and heat flow data: complex fault junctions and closely-spaced faults need a higher density of nodes, because they cannot otherwise be separated and represented in the grid. At every point the node spacing in our grid is at least the minimum required to separate the faults that we want to represent. Tests with a grid finer than that did not produce any significant changes in the results. Removing minor faults from the grid also did not alter significantly the slip-rates of remaining faults, it simply resulted in more distributed deformation of the continuum in between them.

In addition to defining grid geometry, we must also define the values of topography and heat flow at each grid node (to compute thickness of crust and lithospheric mantle), and the dip of each fault element. Topography is linearly interpolated onto our grid from the ETOPO2 data set (Fig. 3.3;National Geophysical Data Center, 2006). We generated a surface heat flow map for California and western Nevada by merging the heat flow data of the U.S. Geological SurveyU.S. Geological Survey (2007) and of the Southern Methodist University Southern Methodist University (2007) heat flow databases. The remainder of the grid is assigned heat flow values based on the Global Heat Flow Database of the International Heat Flow Commission International Heat Flow Commission (2005). Crustal thickness is then calculated from topography and heat flow assuming an isostatically compensated crust and using the Airy compensation (Bird, 1999). Where necessary, we locally correct heat flow values so that the calculated crustal thickness matches the crustal thickness map of Fuis and Mooney (1990).

Only active faults, here defined as faults that show signs of Quaternary activity, are included in the model. The assumption of well-known fault geometry for active faults is a reasonable one in most of California and at our current resolution. In the past 5 – 10 years, efforts towards building reliable fault models have resulted in two major 3-D fault geometry databases available for California: the SCEC Community Fault Model (Fig. 3.4) (SCEC CFM; Plesch et al., 2007) and the U.S. Geological Survey 3-D Bay Area Geologic Model (Graymer et al., 2005;Horsman et al., 2008; Jachens et al., 2009). The geometry of the faults at the margin of the

Figure 3.3: Local, high-resolution grid, with topography from ETOPO2 (National Geophysical Data Center, 2006) and fault elements (thick black lines). M = Mendo-

cino triple junction, WH = Wasatch-Hurricane fault system, SAF = San Andreas fault.

Figure 3.4: Perspective view of the SCEC Community Fault Model, simplified

version that represents fault segments as rectangular patches (Plesch et al., 2007).

SAF = San Andreas fault, SJFZ = San Jacinto fault zone.

area of interest (northeastern California and western Nevada) is less constrained. For most of these fault, we obtained the strike and dip information from the USGS Quaternary Fault and Fold database (U.S. Geological Survey, 2006). Most of the faults in northeastern California and western Nevada are not used in scoring the model due to the uncertainties in both geometry and slip-rates. We do not force connections between faults in the grid unless they are documented, because fault segmentation is usually real. Our purpose is to keep the model network geometry as close to reality as possible. Connectivity between faults is accomplished by including all known active faults in the model, without imposing any cutoff at a predetermined slip-rate. This allows us to preserve small connecting faults in the model that would otherwise be excluded due to their small slip-rates.