An acceleration time history can be decomposed into a series of operations that transfers energy from each point on the fault to the recording station
where S is the source time function, R represents rupture over a finite fault, E is the elastic propagation through the earth, and Q is the path attenuation, assumed to be linear. If these operators were exactly known, a deterministic approach to predicting strong ground motions would be straightforward. For the current study, E was computed from a velocity model that incorporates a stiff sedimentary layer over a southern California crust. A range of realistic rupture velocities have been obtained by other investigators and is incorporated into the simulation. Assumptions of the path averaged attenuation, Q, can be tested by comparing with observational data, as a function of distance, the parameters peak acceleration, and computed ML. This provides a check on both the high frequency (∼ 5 Hz) and long-period (∼ 1 sec) behavior of E* Q. An average curstal shear wave Qβ of 300 is found to be compatible with observational data (ML = 4.5 to 5.0). Assumptions of S can be avoided by using real sources derived from accelerograms recorded at small epicentral distances (epicentral distance/source depth < 1). Using these operators, accelerograms have been simulated for strike-slip faulting for four magnitudes: 4.5; 5.5; 6.5; and 7.0. The shapes of the derived average peak ground acceleration (PGA) versus distance curves are well described by the simple equation PGA α [R + C(M)]−1.75, where R is the closest distance to the fault surface and C(4.5) = 6, C(5.5) = 12, C(6.5) = 22, and C(7.0) = 36 km.