We report systematic seismic velocity variations in response to tidal deformation. Measurements are made on correlation functions of the ambient seismic wavefield at 2-8 Hz recorded by a dense array at the site of the Piñon Flat Observatory, Southern California. The key observation is the dependence of the response on the component of wave motion and coda lapse time τ. Measurements on the vertical correlation component indicate reduced wave speeds during periods of volumetric compression, whereas data from horizontal components show the opposite behavior, compatible with previous observations. These effects are amplified by the directional sensitivities of the different surface wave types constituting the early coda of vertical and horizontal correlation components to the anisotropic behavior of the compliant layer. The decrease of the velocity (volumetric) strain sensitivity S_θ with τ indicates that this response is constrained to shallow depths. The observed velocity dependence on strain implies nonlinear behavior, but conclusions regarding elasticity are more ambiguous. The anisotropic response is possibly associated with inelastic dilatancy of the unconsolidated, low-velocity material above the granitic basement. However, equal polarity of vertical component velocity changes and deformation in the vertical direction indicate that a nonlinear Poisson effect is similarly compatible with the observed response pattern. Peak relative velocity changes at small τ are 0.03%, which translates into an absolute velocity strain sensitivity of S_θ≈5 × 10³ and a stress sensitivity of 0.5 MPa^-1. The potentially evolving velocity strain sensitivity of crustal and fault zone materials can be studied with the method introduced here.