A down hole vertical seismic array is a sequence of instruments installed at various depths in the earth to record the ground motion at multiple points during an earthquake. Numerous studies demonstrate the unique utility of vertical seismic arrays for studying in situ site response and soil behavior. Examples are given of analyses made at two sites to show the value of data from vertical seismic arrays. The sites examined are the Lotung, Taiwan SMART1 array and a new site installed at Jingliao, Taiwan. Details of the installation of the Jingliao array are given. ARX models are theoretically the correct process models for vertical wave propagation in the layered earth, and are used to linearly map deeper sensor input signals to shallower sensor output signals. An example of Event 16 at the Lotung array is given. This same data, when examined in detail with a Bayesian inference model, can also be explained by nonlinear filters yielding commonly accepted soil degradation curves. Results from applying an ARMAX model to data from the Jingliao vertical seismic array are presented. Estimates of inter-transducer soil increment resonant frequency, shear modulus, and damping ratio are presented. The shear modulus varied from 50 to 150 MPa, and damping ratio between 8% and 15%. A new hardware monitoring system - TerraScope - is an affordable 4-D down-hole seismic monitoring system based on independent, microprocessor-controlled sensor Pods. The Pods are nominally 50 mm in diameter, and about 120 mm long. An internal 16-bit micro-controller oversees all aspects of instrumentation, eight programmable gain amplifiers, and local signal storage.