  We describe the theoretical modeling and analysis techniques associated with
a preliminary search for correlated neutrino emission from GRB980703a, which
triggered the Burst and Transient Source Experiment (BATSE GRB trigger 6891),
using archived data from the Antarctic Muon and Neutrino Detector Array
(AMANDA-B10). Under the assumption of associated hadronic acceleration, the
expected observed neutrino energy flux is directly derived, based upon
confronting the fireball phenomenology with the discrete set of observed
electromagnetic parameters of GRB980703a, gleaned from ground-based and
satellite observations, for four models, corrected for oscillations. Models 1
and 2, based upon spectral analysis featuring a prompt photon energy fit to the
Band function, utilize an observed spectroscopic redshift, for isotropic and
anisotropic emission geometry, respectively. Model 3 is based upon averaged
burst parameters, assuming isotropic emission. Model 4, based upon a Band fit,
features an estimated redshift from the lag-luminosity relation with isotropic
emission. Consistent with our AMANDA-II analysis of GRB030329, which resulted
in a flux upper limit of ~0.150 GeV/cm^2/s for model 1, we find differences in
excess of an order of magnitude in the response of AMANDA-B10, among the
various models for GRB980703a. Implications for future searches in the era of
Swift and IceCube are discussed.
