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We present a new application of superconductive magnetic gradiometry to a geophysical problem. Changing stresses in the earth's crust produce magnetic variations through the piezomagnetic effect. Seismic wave stress fluctuations cause magnetic variations measurable by a superconductive gradiometer. Their magnitude depends both on the wave stress and on the ambient stress. Measurements repeated over time can monitor changes in the ambient stress of magnetic strata near earthquake faults. Estimates of the signal size expected from the sources used in seismic surveying show that they comfortably exceed the sensitivity limits of present-day superconductive magnetic gradiometers. A first field trial of the method, conducted in the Whipple Mountains near Parker, AZ, in November 1985, shows magnetic gradient fluctuations several pT/m in amplitude coincident with the passage of seismic waves. However, ground motion can excite mechanical resonances in the gradiometer that contaminate the signal. The field trial points the way to refinements that lead to suppression of interference from ground motion.