Multiscale variations of the crustal stress field throughout North America

The Earth’s crustal stress field controls active deformation and reflects the processes driving plate tectonics. Here we present the first quantitative synthesis of relative principal stress magnitudes throughout North America together with hundreds of new horizontal stress orientations, revealing coherent stress fields at various scales. A continent-scale transition from compression (strike-slip and/or reverse faulting) in eastern North America to strike-slip faulting in the mid-continent to predominantly extension in western intraplate North America is likely due (at least in part) to drag at the base of the lithosphere. Published geodynamic models, incorporating gravitational potential energy and tractions from plate motions or relative mantle flow, successfully predict most large-wavelength stress rotations but not the shorter-wavelength (<~200 km) rotations observed in the western USA. The stresses resulting from glacial isostatic adjustment appear to be much smaller than the magnitude of ambient tectonic stresses in the crust at depth.

We applied quality ratings ranging from A (best) to D (lowest) to each SHmax orientation and to Aϕ measurements obtained from earthquake focal mechanism inversions. Only A-C-quality measurements are considered sufficiently reliable to be plotted on stress maps (Fig. 1).
Supplementary Table 1 provides the quality criteria used to apply these ratings, which are updated from previously published quality criteria 6,13,55 and newly include criteria for earthquake focal mechanism inversions. These quality criteria are very similar to those employed by the and S1 [59] . Some of these measurements were obtained from figures included in previously published papers, as referenced

Supplementary Note 3. Stress measurements from earthquake focal mechanism inversions
We conducted 50 formal stress inversions using the earthquake focal mechanism catalog uncertainty bounds for inversions to be considered reliable, we did not conduct inversions in some areas for which those authors previously obtained formal Aϕ estimates, and older inversions in those areas may be less reliable. Nevertheless, in such cases Aϕ was interpreted informally based on the available mechanisms, using the techniques described below. In addition, we did not invert for specifically Aϕ using TexNet mechanisms in Texas due to considerable variability in focal plane geometries in certain areas and other indications of elevated uncertainty. However, we did formally invert for only SHmax orientations using the TexNet mechanisms based on evidence mentioned above that SHmax is less sensitive to nodal plane uncertainties 91 .
Finally, because multiple plate-bounding fault zones cut North America, we note that estimates of faulting regime from earthquake focal mechanism stress inversions are unreliable if they include events that occurred on faults with anomalously low coefficients of friction. On such faults, the sense of slip (e.g., strike-slip) may differ from the faulting regime (e.g., reverse faulting), as is the case in some areas near the San Andreas fault zone 96 . Perhaps related to this effect, as well as the very high rate of seismicity in the area, Abolfathian et al. 97 have shown appreciable stress changes with depth near major faults associated with the plate boundary in Southern California. For these reasons, we do not include events that occurred within 10 km of plate bounding faults or major, potentially weak subsidiary structures near plate boundary zones.
We also exclude previously published Aϕ inversion results that include such earthquakes.

Supplementary Note 4. Interpretation of relative stress magnitudes from earthquake focal mechanisms and Quaternary fault offsets
Of Based on this framework, we interpreted Aϕ and its uncertainty using the information provided by earthquake focal mechanisms and Quaternary fault offsets, with interpretations informed by formal focal mechanism stress inversions. We assumed normal uncertainty distributions for each Aϕ measurement, for which we interpret the mean (µ, presented in Fig. 1), standard deviation (1s, illustrated in Supplementary Fig. 3), and minimum and maximum truncation bounds (tmin and tmax) for the distribution.  64 . Focal mechanisms were compiled as described above. In general, focal mechanisms were considered more reliable than Quaternary offsets due to the lower precision of the fault offset record (e.g., slip vectors are not typically recorded for Quaternary offsets, limiting the potential to recognize oblique slip) and a potential bias against sampling strike-slip faults due to greater challenges identifying offsets without significant vertical components.

Supplementary Note 5. Estimation of divergence angle α between SHmax orientations and absolute plate motion directions
SHmax orientations were gridded using EBK with the same parameters as in the interpolation of Aϕ (see above). To reduce noise, only higher (A and B) quality SHmax orientations were used for the interpolation. The resulting grid is presented in Supplementary Fig. 6a. The SHmax orientation raster was subtracted from a grid of orientations of NNR-MORVEL56 absolute plate motions 19 using the ArcGIS Raster Calculator. The resulting grid of divergence angles ( Supplementary Fig. 6b) was smoothed slightly using a 3 × 3 low-pass filter. Divergence angles were extracted from this grid along three 2º-wide swath profiles (Fig. 2) that were constructed approximately parallel to plate motion using TopoToolbox v.2.3 100 in MATLAB. Divergence angles were sampled every 0.1º along and across the swath profiles. The negative mean acrossprofile value for each point along the profile is shown in Fig. 2b.