In this paper, the detection of a correlated Gaussian field using a large multi-hop sensor network is investigated. A cooperative routing strategy is proposed by introducing a new link metric that characterizes the detection error exponent. Derived from the Chernoff information and Schweppe's likelihood recursion, this link metric captures the contribution of a given link to the decay rate of error probability and has the form of the capacity of a Gaussian channel with the sender transmitting the innovation of its measurement. For one-dimensional Gauss-Markov fields, the link metric can be represented explicitly as a function of the link length. Cooperative routing is achieved using the Kalman data aggregation and shortest path routing. Numerical simulations show that cooperative routing can be significantly more energy efficient than noncooperative routing for the same detection performance.