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Energy spectra of Martian leakage neutrons are calculated by a high-energy nucleon-meson transport code using a Monte Carlo technique and a one-dimensional diffusion accelerated neutral-particle transport code, which solves the Boltzmann equation. Four series of calculations were made to simulate (1) a uniform surface layer containing various amounts of H2O, (2) different burial depths of a 50% H2O layer underneath a 1% H2O layer, (3) changing atmospheric pressure, and (4) a thick CO2 ice sheet overlying a “dirty” water ice sheet. We found that all calculated spectra at energies less than about 1000 eV could be fitted by a superposition of thermal and epithermal functions having four free parameters. Two of these parameters, the thermal and epithermal amplitudes, were found to vary systematically over ranges exceeding 1 order of magnitude and to specify uniquely the configuration in each of the series. We conclude that measurements of leakage neutron spectra should allow determination of the hydrogen content of surface layers buried to depths up to about 100 g/cm2 and determination of the thickness of a polar dry ice cap up to thicknesses of about 250 g/cm2. Variations of these parameters were also shown to depend on the composition of the assumed surface layers through the average atomic mass and the macroscopic scattering and absorption cross sections.