Beneath the southern East Pacific Rise resides a crustal magma chamber confined to the immediate vicinity of the rise axis, yet the mantle melt production region is broad and asymmetric. Short-period (4--17 s) Love waves propagating along the rise provide a means of probing the transition from the asymmetric melt production region to the rise-centered crustal magma chamber. Low velocities beneath the rise act as a waveguide for Love wave energy. We model this complex wave propagation with a Gaussian beam representation as part of our nonlinear inversion for velocity structure. Our results show that the asymmetry exists at the crust-mantle interface, or Moho, and increases downward; the lowest velocities are located beneath the rise at the Moho; beneath the rise there is an asymmetric gap in the high-velocity lid at the top of the mantle; and there are lower asthenospheric velocities beneath the Pacific plate than the Nazca plate. The transition from the broad upwelling region to the narrow crustal magmatic system occurs over a ~15-km-depth interval at the top of the mantle. Our observations indicate higher temperatures and greater melt production beneath the Pacific plate. East of the rise, melting appears to abruptly shut off at shallow levels, perhaps due to a component of downward mantle flow. We suggest that melt percolates upward, increasing in concentration, until reaching a permeability barrier beneath the lithosphere, it then moves up along the lithosphere to accumulate at the Moho beneath the rise. West of the rise, higher temperatures and upward percolation of melt delay growth of the lithosphere.