[52] The detailed expressions for our block modeling method are provided by *Hammond and Thatcher* [2007]. We extend the method to additionally solve for a constant horizontal tensor strain rate in each block (when desired), and to regularize the solution by including a damping constraint on vertical axis rotation rates. We summarize the relationships here to place our new features into context.

[53] The long-term velocity averaged over many seismic cycles is equal to the sum of the interseismic and coseismic velocities

rearranging gives

which is the relationship between the GPS velocities, block motion and fault slip. This implements the back slip approach introduced by *Savage* [1983]. Coseismic velocity is defined as the rate of movement of a point near the fault associated with coseismic offsets averaged over many seismic cycles. We parameterize block motion with Euler rotations and slip with

where *ω*_{j} is an unknown block rotation vector of block *j*. The strike slip *a*_{k} and dip slip *b*_{k} rates are unknowns that scale the unit slip functions *G*_{SS} and *G*_{N} that represent the pattern of strike slip and normal slip, respectively, for each fault segment *k*. These functions are calculated for each fault segment using the functions of *Okada* [1985], since the dip, length, and width of the fault are predefined. Positive unit slip is sinistral for *a*_{k} and in the thrust sense for *b*_{k}. Since GPS sites can be affected by elastic strain accumulation on more than one fault segment, especially in complex zones with densely spaced faults, this term is summed over the nearest *L* fault segments.

[54] We add model parameters for horizontal tensor strain rate and take the dot product with the north *e*_{N} and east *e*_{E} unit vectors to obtain separate equations for each component

where ɛ_{ϕϕ}, ɛ_{θθ}, and ɛ_{θϕ} are the three strain rate free parameters, expressed in colatitude θ and longitude ϕ following *Savage et al.* [2001], *r*_{0} is the radius of the Earth, Δθ and Δϕ are the angles from the center of the block to the site.

[55] We regularize the inversion by applying three types of constraints which are additional equations that must be satisfied in the inversion. The first condition is the consistency between relative block motions and slip rates. This condition provides two additional equations for each fault segment because it is evaluated at the mid point of each fault segment for both components of slip [*Hammond and Thatcher*, 2007]. In all models this condition is assigned a very strong weight in the inversion, with a prior uncertainty *α* of 10^{−6} m/yr (Table 1), since it is fundamental to the estimation of slip rates from relative block motions.

[56] The second condition is that vertical axis rotations, i.e., spin rates, must be minimized. Equations (A4) and (A5) solve for Euler rotation vectors which amount to spin-free translation when the angle between *r*_{i} and *ω*_{i} is 90°. We set the condition that

for each block *j*. When the prior uncertainty of *β* is very small, the vertical axis rotation rates are forced to be zero, restricting to solution to one where blocks only translate but do not spin. When this condition is relaxed by using larger values of *β*, vertical axis rotations are minimized subject to the other constraints, e.g., that the data be fit.

[57] The third condition is that both components of the fault slip rates are minimized. This condition is applied by adding the additional equations *a*_{k} = 0 and *b*_{k} = 0 for each fault. A very small value for the prior uncertainty of these constraints *γ* results in a model with no relative motion of blocks since slip rates are connected to block motions through slip rate consistency.

[58] For the NWL we identify *β* and *γ* values that strike a balance between minimizing misfit to the data, and minimizing slip rates and spin rates. We iterate through trial values of these parameters, solving for the model, and evaluating misfit and parameter norms. For *γ* we iterate through values between 10^{−6} to 1 m/yr, and calculate the *χ*^{2} per degree of freedom misfit and the norm of the model slip rates vector (Figure 9b). For *β* we iterate through values between 10^{−12} to 10^{−18}/yr, and calculate *χ*^{2} and the norm of the model spin rates (Figure 9c). For our preferred model (Figures 10a and 10b) we chose values that provide both low misfit and low model norm (Table 1).