Translational data in a first direction is measured by particle motion sensors contained in an elongated housing of a sensor device provided at an earth surface. The particle motion sensors are spaced apart along a second, different direction along a longitudinal axis of the elongated housing. Rotation data around a third direction is computed based at least in part on computing a gradient of the translational data with respect to the second direction.

A geophone includes a magnet, an electrical coil assembly, and a tubular case. The electrical coil assembly is disposed about the magnet, and is movable in an axial direction with respect to the magnet. The electrical coil assembly includes a coil, a first spring disposed at a first end of the electrical coil assembly, and a second spring disposed at a second end of the electrical coil assembly. The first spring and the second spring are configured to produce a natural frequency of 9 Hertz to 12.5 Hertz in oscillation of the coil about the magnet. The magnet and the coil assembly are coaxially disposed within the tubular case. The tubular case is no more than 1.7 inches in length. The electrical coil assembly is configured to move in an axial direction with respect to the magnet in any orientation of the tubular case.

A seismic sensor device includes an elongated housing for placement at least partially into an earth surface. A plurality of particle motion sensors are contained in the elongated housing to measure translational data in a first direction, where plural pairs of the particle motion sensors are spaced apart along a second, different direction along a longitudinal axis of the elongated housing. A communication interface communicates the measured translational data to a computer system configured to compute a gradient based on respective differences of the measured translational data of the corresponding plural pairs of the particle motion sensors, and compute one or more of rotation data and divergence data using the gradient.

Translational data in a first direction is measured by particle motion sensors contained in an elongated housing of a sensor device provided at an earth surface. The particle motion sensors are spaced apart along a second, different direction along a longitudinal axis of the elongated housing. Rotation data around a third direction is computed based at least in part on computing a gradient of the translational data with respect to the second direction.

A device and method for improved geodetic and seismic measurements are disclosed. The device comprises a triaxial accelerometer assembly, mounted to a reference structure, having full scale ranges greater than +/1 G on three orthogonal axes and a mechanism for rotating the triaxial accelerometer assembly on the reference structure. The triaxial acceleration assembly is calibrated with an internal alignment matrix such that measurements of Earth's gravity vector are rotationally invariant with respect to the direction of Earth's 1 G static gravity vector irrespective of the orientation of the triaxial assembly on the reference structure. In-situ calibrations are performed by rotating the axes of the triaxial acceleration assembly in the direction of Earth's static gravity vector. Drift of the triaxial accelerometer assembly is compensated for by measuring changes in the values of the invariant static gravity vector for each axis and correcting for the drift with new calibration coefficients.

Translational data in a first direction is measured by particle motion sensors contained in an elongated housing of a sensor device provided at an earth surface. The particle motion sensors are spaced apart along a second, different direction along a longitudinal axis of the elongated housing. Rotation data around a third direction is computed based at least in part on computing a gradient of the translational data with respect to the second direction.