A compact mathematical formulation is presented for the estimation of crustal strain and fault displacement parameters from repeated geodetic observations. On the basis of the theory of Hilbert space optimization, complex linear forms are used to model spatially and temporally piecewise continuous relative horizontal displacement fields. A mathematical model for the simultaneous network adjustment and strain approximation is elaborated. In an application of the method to the Hollister network reobserved several times during the 1970s, several approximation models are evaluated. The final model, which incorporates a third degree complex algebraic polynomial with four block translation terms in space and a fifth degree algebraic polynomial with three episodic terms in time, is presented in detail. This approximation estimates coseismic fault slip and strain release associated with three moderate earthquakes which occurred in the Hollister area within the time interval spanned by the observations. ¿ American Geophysical Union 1991