Computing a gradient based on differences of plural pairs of particle motion sensors
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.
1. A seismic sensor system comprising:
a seismic sensor device comprising:
an elongated housing for placement at an earth surface;
a plurality of particle motion sensors contained in the elongated housing to measure translational data in a first direction while the elongated housing is placed at the earth surface, 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; and
at least one processor 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, the respective differences of the measured translational data comprising a first difference of the measured translational data of a first pair of the plural pairs of particle motion sensors, and a second difference of the measured translational data of a second pair of the plural pairs of particle motion sensors.
2. The seismic sensor system of claim 1 , wherein a first spacing along the longitudinal axis between the particle motion sensors of the first pair is different from a second spacing along the longitudinal axis between the particle motion sensors of the second pair.
3. The seismic sensor system of claim 1 , wherein the first pair is spaced apart from the second pair along the first direction, wherein the particle motion sensors of the first pair are spaced apart along the longitudinal axis, and wherein the particle motion sensors of the second pair are spaced apart along the longitudinal axis.
4. The seismic sensor system of claim 3 , wherein the particle motion sensors of the first pair are spaced apart along the longitudinal axis by a first distance, and wherein the particle motion sensors of the second pair are spaced apart along the longitudinal axis by the first distance.
5. The seismic sensor system of claim 1 , wherein the at least one processor is configured to compute a first gradient from the measured translational data of the first pair of particle motion sensors, and a second gradient from the measured translational data of the second pair of particle motion sensors, and wherein the gradient is an aggregate of the first and second gradients.
6. The seismic sensor system of claim 1 , wherein the at least one processor is included in the seismic sensor device.
7. The seismic sensor system of claim 1 , wherein the at least one processor is part of a computer system remotely located from the seismic sensor device.
8. 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.
9. The system of claim 8 , wherein the distributed sensor comprises an optical fiber.
10. 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.
11. The method of claim 10 , wherein a first spacing along the longitudinal axis between the particle motion sensors of the first pair is different from a second spacing along the longitudinal axis between the particle motion sensors of the second pair.
12. The method of claim 10 , wherein the first pair is spaced apart from the second pair along the first direction, wherein the particle motion sensors of the first pair are spaced apart along the longitudinal axis, and wherein the particle motion sensors of the second pair are spaced apart along the longitudinal axis.
13. The method of claim 12 , wherein the particle motion sensors of the first pair are spaced apart along the longitudinal axis by a first distance, and wherein the particle motion sensors of the second pair are spaced apart along the longitudinal axis by the first distance.
14. The method of claim 10 , further comprising computing a first gradient from the translational data of the first pair of particle motion sensors, and a second gradient from the translational data of the second pair of particle motion sensors, and wherein the gradient is an aggregate of the first and second gradients.
15. The method of claim 10 , wherein the plural pairs includes at least four particle motion sensors, and wherein the least four pairs of the at least four particle motion sensors are useable to compute at least four respective estimated gradients, wherein the gradient of the translational data is an aggregate of the estimated gradients.
16. 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.
17. The article of claim 16 , wherein the first direction is a horizontal direction, and the second direction is a vertical direction.
18. The article of claim 16 , wherein the first pair is spaced apart from the second pair along the first direction, wherein the particle motion sensors of the first pair are spaced apart along the longitudinal axis by a first distance, and wherein the particle motion sensors of the second pair are spaced apart along the longitudinal axis by the first distance.
19. The article of claim 16 , wherein the computer system is part of the seismic sensor device.