The Salton Trough is one of the few regions on Earth where rifting is sub-aerial instead of sub-marine. We use the relative attenuation of teleseismic P phases recorded by the Salton Trough Seismic Imaging Project to investigate lithospheric and asthenospheric structures that form during extension. Map-view analysis reveals stronger attenuation within the Salton Trough than in the adjacent provinces. We then construct tomographic models for variations in seismic attenuation with depth to discriminate between crustal and mantle signals with a damped least-squares approach and a Bayesian approach. Synthetic tests show that models from damped least-squares significantly under-estimate the strength of attenuation and cannot separate crustal and mantle signals even when the tomographic models are allowed to be discontinuous at the lithosphere-asthenosphere boundary. We show that a Bayesian approach overcomes these problems when inverting the same synthetic datasets, and that shallow and deep signals are more clearly separated when imposing a discontinuity. With greater than 95% confidence, the results reveal first, that attenuation occurs primarily beneath the LAB; second, that the width of the attenuative region is narrower than the rift at 120 km depth; and third, that the strength of attenuation requires that the attenuative feature represents a melting-column similar to those beneath mid-ocean ridges. The narrow width of the melting-column below the volatile-free solidus is inconsistent with models for passive upwelling, where flow is driven only by rifting. Instead, we attribute the generation of incipient oceanic crust to mantle upwelling focused by buoyancy into a narrow diapir.