Near-bottom, high-resolution magnetic field data gathered at the southern East Pacific Rise near 17¿28'S, 18¿14'S, and 18¿37'S, using the autonomous underwater vehicle Autonomous Benthic Explorer (ABE) echo various geologic structures, including void space within lobate caverns, recent pillow mounds, and hydrothermal vent activity. This study is focused on a magnetic field low extending several kilometers along axis, coincident with a trough created by the draining of a lava lake during a highly effusive fissure eruption at 17¿28'S. Similar lows are observed at three other drained lava lake troughs, including one which is at least 1800 years old, residing 400 m away from the present-day axis. We attribute these lows to the presence of shallow dike swarms. The degree to which other geologic features may contribute to the lows is constrained using geologic, geophysical, and geochemical observations and forward modeling. Compositional analyses of Alvin samples at 17¿28'S do not support Fe or Ti variations as a primary source. Hypotheses requiring hydrothermal alteration and porosity variations are both inconsistent with geologic observations and near-bottom gravity data analysis from similar areas. Previous mappings between paleointensity variations and the observed magnetic field over distances of several kilometers from the axis suggest that such variations do not create the field low. The dominant source of the magnetization low is most likely the presence of a 100--200 m wide region of shallow dikes which are poorly magnetized relative to extrusives, or a region heated above magnetic blocking or Curie temperatures by intrusions during the most recent eruption (though the latter interpretation cannot explain the low at the fossil trough). In the first case, this extrusive thinning implies a change in eruptive behavior over the last 750--1500 years given the local spreading rate. For the latter case, thermal models suggest the anomaly had to have been created by a dike swarms totaling at least 45 m width during the most recent eruption(s), corresponding to ~300 years of plate spreading. Models indicate that the source of the low is centered slightly east of the axial trough. This offset suggests that the axis has been progressively migrating westward over the past millennium, consistent with other studies covering greater length and timescales. Westward migration provides an explanation for the preferential emplacement of recent lavas flows west of the axis, evident in ABE bathymetry and submersible observations.