Piezomagnetic field variations can result from tectonic stress changes in the focal zone of an impending earthquake. Interpretation of such observed tectonomagnetic effects requires modeling of the stress response of magnetic properties of the lithosphere. Calculations have been made to estimate the here piezomagnetic effect as a function of depth, by considering the effect of stress on the magnetization of magnetite (Fe3O4) with increasing temperature and hydrostatic pressure. The responsiveness of magnetization to seismotectonic stress is gauged by an appropriate balancing of magnetocrystalline and magnetoelastic anisotropy energies. The calculations indicate that magnetite becomes progressively more responsive to stress at depth increases. The rate of change depends on the local geothermal gradient. The upper 15km of the lithosphere is likely to be the most important in yielding observable piezomagnetic field effects. Such shallow-focus earthquakes are expected to be best for monitoring tectonomagnetic anomalies for earthquake prediction.