Computing a gradient based on differences of plural pairs of particle motion sensors

A system comprising:

• a seismic sensor device comprising:
• an elongated housing for placement at least partially into an earth surface;
• a distributed sensor in the housing, the distributed sensor to provide continuous measurements of translational data along a length of the distributed sensor;
• and
• at least one processor configured to compute a gradient based on respective differences of corresponding plural pairs of the measurements, and compute one or more of rotation data and divergence data using the gradient, the respective differences of the corresponding plural pairs of the measurements comprising a first difference of the measurements at a first pair of points along the length of the distributed sensor, and a second difference of the measurements at a second pair of points along the length of the distributed sensor.

A method comprising:

• actuating a seismic source to transmit impulses into an earth subsurface;
• receiving, by a system from a seismic sensor device, translational data in a first direction measured by plural pairs of particle motion sensors contained in an elongated housing of the seismic sensor device placed at a ground surface, the particle motion sensors in each pair of the plural pairs spaced apart along a second, different direction along a longitudinal axis of the elongated housing;
• computing, by the system, a gradient based on respective differences of the translational data of the corresponding plural pairs of particle motion sensors, the respective differences of the translational data comprising a first difference of the translational data of a first pair of the plural pairs of particle motion sensors, and a second difference of the translational data of a second pair of the plural pairs of particle motion sensors;
• and
• computing, by the system, a rotation data using the gradient.

An article comprising at least one non-transitory computer-readable storage medium storing instructions that upon execution cause a computer system to:

• receive, from a seismic sensor system placed at least partially into an earth surface, translational data in a first direction measured by a plurality of particle motion sensors contained in an elongated housing of a seismic sensor device placed at the earth surface, the seismic sensor device being part of the seismic sensor system, the plurality of particle motion sensors comprising plural pairs of particle motion sensors, wherein the particle motion sensors of each pair of the plural pairs of particle motion sensors are spaced apart along a second, different direction along a longitudinal axis of the elongated housing;
• compute a gradient based on respective differences of the translational data measured by the corresponding plural pairs of particle motions sensors contained in the elongated housing of the seismic sensor device placed at the earth surface, the respective differences of the translational data comprising a first difference of the translational data of a first pair of the plural pairs of particle motion sensors, and a second difference of the translational data of a second pair of the plural pairs of particle motion sensors;
• and
• compute one or more of rotation data and divergence data using the gradient.