Seismic reflection profiles cross many continental margins have imaged bottom simulating reflectors (BSRs), which have been interpreted as being formed at the base of a methane hydrate stability field. Such reflectors might arise either from an impedance contrast between high-velocity, partially hydrated sediments and water-saturated sediments or from a contrast with partially gas-saturated sediments. These alternatives may be hard to distinguish by conventional amplitude-versus-offset or waveform modeling approaches. Here we investigate the origin of a high amplitude BSR in the accretionary wedge offshore of western Colombia by seismic waveform inversion. The inversion procedure consists of three steps: firstly, determination of root-mean-square velocities and hence estimates of the interval velocities between major reflectors by a global grid search for maximum normalized energy along elliptical trajectories in the intercept time-slowness domain; secondly, determination of accurate interval velocities between these reflectors by a Monte Carlo search for maximum energy; and thirdly, a waveform fit in the frequency-slowness domain, using differential reflectivity seismograms and a conjugate-gradient optimization algorithm to minimize the sample-by-sample waveform misfit between data and synthetic. At two locations, near a structural high, we find a ~30-m thick low-velocity zone beneath the BSR, with the properties of a partially gas-saturated zone, while at a third location, where BSR amplitude is lower, we find no evidence for anomalously low velocities. The preferential development of the BSR in structures that would tend to intercept fluid flow or migrating gas and the presence of free gas beneath the BSR indicate a mechanism of BSR formation in which free methane gas migrates upward into the hydrate stability field or is carried there in advecting pore water.