Measuring gravity curvature for mapping subterranean formations

1. A method comprising:

positioning a matter wave interferometer relative to a subterranean formation; and

measuring a derivative of gravity for multiple locations in the subterranean formation with the matter wave interferometer;

wherein measuring the derivative of gravity involves:

producing a superposition of atoms with a Raman laser beam, generated from a location using a laser;

combining the superposition of atoms with the Raman laser beam; and

maintaining a position of atoms with a plurality of trapping laser lights, produced from other locations using other lasers, before producing the superposition of atoms.

2. The method of claim 1 further comprising:

injecting water into the subterranean formation; and

producing a map of the water in the subterranean formation based on the derivative of gravity.

3. The method of claim 1 , wherein positioning the matter wave interferometer relative to the subterranean formation involves: conveying the matter wave interferometer along a wellbore penetrating the subterranean formation.

4. The method of claim 1 , wherein h wave interferometer is coupled to a land-based vehicle.

5. The method of claim 1 , wherein the matter wave interferometer is coupled to an air-based vehicle.

6. The method of claim 1 , wherein the matter wave interferometer is coupled to a water-based vehicle.

7. The method of claim 1 further comprising:

maintaining a position of the matter wave interferometer; and

measuring the derivative of gravity for the multiple locations in the subterranean formation at several times.

8. The method of claim 7 further comprising:

monitoring subsidence of a portion of the subterranean formation over time.

9. The method of claim 7 further comprising:

injecting water into the subterranean formation; and

monitoring movement of the water through the subterranean formation over time.

10. The method of claim 1 , wherein the derivative of gravity is the second derivative of gravity, and wherein measuring the second derivative of gravity involves:

producing three clouds of atoms;

producing a superposition of atoms in two different, spatially separated superimposed clouds from each of the three clouds of atoms;

allowing the two different, spatially separated superimposed clouds to propagate along the matter wave interferometer and interact with a gravitational field of the subterranean formation;

combining the two different, spatially separated superimposed clouds for each of the three clouds of atoms with the Raman laser beam;

measuring an interference produced by producing and combining the two different, spatially separated superimposed clouds for each of the three clouds; and

calculating the second derivative of gravity based on the interference, wherein the second derivative of gravity is a gravity curvature.

11. The method of claim 10 , wherein positioning the matter wave interferometer relative to the subterranean formation involves: conveying the matter wave interferometer along a wellbore penetrating the subterranean formation; and wherein the Raman laser beam is conveyed to the matter wave interferometer from a surface location at a well site via a slickline.

12. The method of claim 10 further comprising:

producing the trapping laser light with a laser; and

conveying the trapping laser light to the matter wave interferometer with fiber optics.

13. The method of claim 10 further comprising:

producing a 3-dimensional map of the subterranean formation based on the derivative of gravity.

14. A method comprising:

positioning a matter wave interferometer relative to a subterranean formation;

producing at least one cloud of atoms in the matter wave interferometer;

producing a superposition of atoms in two different, spatially separated superimposed clouds from each of the at least one cloud of atoms, wherein the superposition is produced with a Raman laser beam, generated from a location using a laser;

propagating the two different, spatially separated superimposed clouds along the matter wave interferometer as the two different, spatially separated superimposed clouds interact with a gravitational field of the subterranean formation;

combining the two different, spatially separated superimposed clouds for each of the at least one cloud of atoms with a Raman laser beam;

measuring an interference produced by producing and combining the two different, spatially separated superimposed clouds for each of the at least one cloud of atoms;

calculating gravity for the gravitational field of the subterranean formation based on the interference; and

maintaining a position of atoms with a plurality of trapping laser lights, produced from other locations using other lasers, before producing the superposition of atoms.

15. The method of claim 14 , wherein the at least one cloud of atoms is two clouds of atoms, and the method further comprises:

calculating a first derivative of gravity for the gravitational field of the subterranean formation based on the interference.

16. A wellbore tool comprising:

a housing coupled to a conveyance and containing at least a portion of a matter wave interferometer capable of producing, splitting, and recombining two or more clouds of atoms in a magnetic shield;

wherein the matter wave interferometer is further capable of measuring the derivative of gravity, wherein measuring the derivative of gravity involves:

producing a superposition of atoms with a Raman laser beam, generated from a location using a laser;

combining the superposition of atoms with a laser light; and

maintaining a position of atoms with a plurality of trapping laser lights, produced from other locations using other lasers, before producing the superposition of atoms.

17. The wellbore tool of claim 16 , wherein the conveyance is a slickline that comprises electrical transmission lines and fiber optic cables.

18. A system comprising:

the wellbore tool of claim 17 positioned within a wellbore penetrating a subterranean formation; and

a laser coupled to the fiber optic cables, wherein the laser is not positioned within the wellbore.

19. A system comprising:

a vehicle positioned relative to a subterranean formation, the vehicle coupled to a matter wave interferometer capable of producing two or more clouds of atoms in a magnetic shield;

wherein the matter wave interferometer is further capable of measuring the derivative of gravity, wherein measuring the derivative of gravity involves:

producing a superposition of atoms with a Raman laser beam, generated from a surface location;

combining the superposition of atoms with a laser light; and

maintaining a position of atoms with a plurality of trapping laser lights, produced from other locations using other lasers, before producing the superposition of atoms.

20. The system of claim 19 , wherein the vehicle is a drone.

21. The system of claim 19 , wherein the vehicle is a submarine.