Detecting weak seismic events from noisy sensors is a difficult perceptual task. We formulate this task as Bayesian inference and propose a generative model of seismic events and signals across a network of spatially distributed stations. Our system, SIGVISA, is the first to directly model seismic waveforms, allowing it to incorporate a rich representation of the physics underlying the signal generation process. We use Gaussian processes over wavelet parameters to predict detailed waveform fluctuations based on historical events, while degrading smoothly to simple parametric envelopes in regions with no historical seismicity. Evaluating on data from the western US, we recover three times as many events as previous work, and reduce mean location errors by a factor of four while greatly increasing sensitivity to low-magnitude events.