Equivalent strike‐slip earthquake cycles in half‐space and lithosphere‐asthenosphere earth models

By virtue of the images used in the dislocation solution, the deformation at the free surface produced throughout the earthquake cycle by slippage on a long strike‐slip fault in an Earth model consisting of an elastic plate (lithosphere) overlying a viscoelastic half‐space (asthenosphere) can be duplicated by prescribed slip on a vertical fault embedded in an elastic half‐space. For the case in which each earthquake ruptures the entire lithosphere (thickness H), the half‐space equivalent slip rate is as follows: Depth interval 0‐H, slip identical to that in lithosphere‐asthenosphere model (i.e., abrupt coseismic slip and no subsequent slip); depth interval (2n−1)H to (2n+1)H (n = 1,2,…), slip rate uniform in space and dependent upon time as Fn(t) exp (−t/τa) where Fn is a (n ‐ 1) degree polynomial in t, τa is twice the asthenosphere relaxation time (η/μ), and t is measured from the instant after the preceding earthquake. The slip rate averaged over the seismic cycle in each depth interval equals the secular rate of relative plate motion. For reasonable values of τa, slip rates below 5H do not vary much from that mean value and can be treated as constant. Thus the surface deformation due to the earthquake cycle in the lithosphere‐asthenosphere model can be calculated very simply from the half‐space model with time‐dependent slip in the two depth intervals H−3H and 3H−5H, and uniform slip at a rate equal to the secular relative plate velocity below depth 5H. Inversion of 1973–1988 geodetic measurements of deformation across the segment of the San Andreas fault in the Transverse Ranges north of Los Angeles for the half‐space equivalent slip distribution suggests no significant slip on the fault above 30 km and a uniform slip rate of 36 mm/yr below 30 km. One equivalent lithosphere‐asthenosphere model would have a 30‐km thick lithosphere and an asthenosphere relaxation time greater than 33 years, but other models are possible.