  We present the result of calculations to optimize the search for molecular
oxygen (O2) in Earth analogs transiting around nearby, low-mass stars using
ground-based, high-resolution, Doppler shift techniques. We investigate a
series of parameters, namely spectral resolution, wavelength coverage of the
observations, and sky coordinates and systemic velocity of the exoplanetary
systems, to find the values that optimize detectability of O2. We find that
increasing the spectral resolution of observations to R = 300,000 - 400,000
from the typical R ~ 100,000, more than doubles the average depth of O2 lines
in planets with atmospheres similar to Earth's. Resolutions higher than about
500,000 do not produce significant gains in the depths of the O2 lines. We
confirm that observations in the O2 A-band are the most efficient except for
M9V host stars, for which observations in the O2 NIR-band are more efficient.
Combining observations in the O2 A, B, and NIR -bands can reduce the number of
transits needed to produce a detection of O2 by about 1/3 in the case of white
noise limited observations. However, that advantage disappears in the presence
of typical levels of red noise. Therefore, combining observations in more than
one band produces no significant gains versus observing only in the A-band,
unless red-noise can be significantly reduced. Blending between the exoplanet's
O2 lines and telluric O2 lines is a known problem. We find that problem can be
alleviated by increasing the resolution of the observations, and by giving
preference to targets near the ecliptic.
