  Paleomagnetically useful information is expected to be recorded by samples
with moments up to three orders of magnitude below the detection limit of
standard superconducting rock magnetometers. Such samples are now detectable
using recently developed magnetic microscopes, which map the magnetic fields
above room-temperature samples with unprecedented spatial resolutions and field
sensitivities. However, realizing this potential requires the development of
techniques for retrieving sample moments from magnetic microscopy data. With
this goal, we developed a technique for uniquely obtaining the net magnetic
moment of geological samples from magnetic microscopy maps of unresolved or
nearly unresolved magnetization. This technique is particularly powerful for
analyzing small, weakly magnetized samples such as meteoritic chondrules and
terrestrial silicate crystals like zircons. We validated this technique by
applying it to field maps generated from synthetic sources and also to field
maps measured using a superconducting quantum interference device (SQUID)
microscope above geological samples with moments down to 10^-15 Am2. For the
most magnetic rock samples, the net moments estimated from the SQUID microscope
data are within error of independent moment measurements acquired using lower
sensitivity standard rock magnetometers. In addition to its superior moment
sensitivity, SQUID microscope net moment magnetometry also enables the
identification and isolation of magnetic contamination and background sources,
which is critical for improving accuracy in paleomagnetic studies of weakly
magnetic rocks.
