The equation of motion dM/dt Γ
gM 1 B is solved numerically tion then induces a signal in the coil, with signal amplitude in order to study the dynamic behavior of the magnetization during proportional to M sin u f , the component of M perpendicular the cutoff of the polarizing field in the earth's-field NMR techto B 0 . For maximum signal, the polarizing field must be nique. It is assumed that the polarizing field is perpendicular to reduced to zero quickly in order to achieve the desired sudthe earth's field and is reduced to zero linearly in a time short den passage condition u f Γ a 0 Γ 90Π.
compared to all spin relaxation times. The numerical solution for
Originally, this technique was used in earth's-field magnearbitrary cutoff rates is obtained using the fourth-order Rungetometry (3) and has since found application in well logging Kutta algorithm and is found to be consistent with a power series (4), in research on spin relaxation in liquids and solutions solution. It is shown that the magnetization remains within a single
(5-7), and even in magnetic-resonance imaging ( 8). An octant, and that, for moderate to rapid cutoff, the cutoff rate is attractive feature of the technique is that the earth provides related to the cone angle of the subsequent free precession by a stable uniform magnetic field in which to detect the free precession. Free induction decays having time constants (T 2 )
as long as 13 s have been observed ( 7). Also, with some modification of the apparatus (2), longitudinal relaxation times T 1 can be measured as a function of field in the range Here u c is the complement of the cone angle in radians, g is the B 0 Γ΅ B Γ΅ B p . However, because of the low precession proton gyromagnetic ratio, and B 0 is the magnitude of the static frequency, only relatively long relaxation times ( T 1 Υ 50 field (normally, the earth's field) used to detect the free precession. ms, T 2 Υ 20 ms) are measurable, and sample volumes on