  We introduce methods to quantify the X-ray morphologies of supernova remnants
observed with the Chandra X-ray Telescope. These include a power-ratio
technique to measure morphological asymmetries, correlation-length analysis to
probe chemical segregation and distribution, and wavelet-transform analysis to
quantify X-ray substructure. We demonstrate the utility and accuracy of these
techniques on relevant synthetic data. Additionally, we show the methods'
capabilities by applying them to the 55-ks Chandra ACIS observation of the
galactic supernova remnant W49B. We analyze the images of prominent emission
lines in W49B and use the results to discern physical properties. We find that
the iron morphology is very distinct from the other elements: it is
statistically more asymmetric, more segregated, and has 25% larger emitting
substructures than the lighter ions. Comparatively, the silicon, sulfur, argon,
and calcium are well-mixed, more isotropic, and have smaller, equally-sized
emitting substructures. Based on fits of XMM-Newton spectra in regions
identified as iron rich and iron poor, we determine that the iron in W49B must
have been anisotropically ejected. We measure the abundance ratios in many
regions, and we find that large, local variations are persistent throughout the
remnant. We compare the mean, global abundance ratios to those predicted by
spherical and bipolar core-collapse explosions; the results are consistent with
a bipolar origin from a 25 solar mass progenitor. We calculate the filling
factor of iron from the volume of its emitting substructures, enabling more
precise mass estimates than previous studies. Overall, this work is a first
step toward rigorously describing the physical properties of supernova remnants
for comparison within and between sources.
