Moment tensor reconstruction
View Patent ↗A seismic monitoring system includes a plurality of seismic monitors and a processing device operatively coupled to the plurality of seismic monitors. The processing device receives recordings of waveforms of motion detected at the plurality of seismic detectors in a geographic area. The processing device applies the respective recordings to corresponding positions of the seismic detectors in a three-dimensional geological model that describes its elastic attributes and tests a plurality of moment tensors at a plurality of locations. Based on the testing, the processing device determines a globally convergent source location and moment tensor in the three-dimensional model based on the testing.
1. A seismic monitoring system comprising:
a plurality of seismic detectors; and
a processing device operatively coupled to the plurality of seismic detectors, wherein the processing device is to:
receive, from the plurality of seismic detectors, recordings of respective waveforms of motion detected at the plurality of seismic detectors in a geological area;
receive a three-dimensional seismic attribute model of a geological medium at the geological area;
apply the respective recordings to corresponding positions of the seismic detectors in the three-dimensional model;
test a plurality of moment tensors at a plurality of locations in the three-dimensional model to determine whether a location within the plurality of locations in the three-dimensional model satisfies Q({right arrow over (x)})=1,
wherein
Q
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l
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wherein N d is a total number of components of the respective recordings of the plurality of moment tensors, and
wherein q 1 ({right arrow over (x)}) is a vector based on respective velocity derivatives for each of the locations of the plurality of locations in the three-dimensional model; and
determine a globally convergent source location and moment tensor in the three-dimensional model based on the testing.
2. The system of claim 1 , wherein to apply the respective recordings, the processing device is further to:
transform the respective recordings to a frequency domain to generate transformation data; and
provide the transformation data as virtual sources at the corresponding positions of the seismic detectors in the three-dimensional model.
3. The system of claim 1 , wherein to apply the respective recordings, the processing device is further to back propagate the recordings of the respective waveforms to generate a wave-field in the three-dimensional model.
4. The system of claim 1 , wherein the three-dimensional model of the geological medium at the location defines elastic properties of the geological medium.
5. The system of claim 1 , wherein to test the plurality of moment tensors at the plurality of locations, the processing device is further to estimate point source earthquake mechanisms at each point in the geological medium.
6. The system of claim 1 , wherein the recordings of the respective waveforms comprise displacements, velocity, or acceleration data of a sensor of the seismic detectors.
7. The system of claim 1 , wherein the seismic detectors are deployed around the geological area to measure an effect of fracturing mechanisms in the geological area.
8. He system of claim 1 , wherein the determined location is globally unique based on the waveforms received from the plurality of seismic detectors.
9. A method comprising:
receiving waveforms of motion detected at a plurality of seismic detectors in a geological area;
receive a three-dimensional seismic attribute model of a geological medium at the geological area;
transforming the received waveforms to a frequency domain;
applying frequency domain representations of the waveforms at corresponding positions of the seismic detectors in three-dimensional model of the geological area;
testing a plurality of moment tensors at a plurality of locations in the three-dimensional model to determine whether a location within the plurality of locations in the three-dimensional model satisfies Q({right arrow over (x)})=1,
wherein
Q
(
x
→
)
=
❘
"\[LeftBracketingBar]"
∑
l
=
1
N
d
q
l
(
x
→
)
❘
"\[RightBracketingBar]"
wherein N d is a total number of components of the received waveforms of the plurality of moment tensors, and
wherein q 1 ({right arrow over (x)}) is a vector based on respective velocity derivatives for each of the locations of the plurality of locations in the three-dimensional model; and
determining a globally convergent source location and moment tensor in the three-dimensional model based on the testing.
10. The method of claim 9 , wherein testing the plurality of moment tensors at the plurality of locations comprises estimating point source earthquake mechanisms at each point in the geological medium.
11. The method of claim 9 , wherein applying the frequency domain representations of the waveforms comprises back propagating the received waveforms to generate a wave-field in the three-dimensional model.
12. The method of claim 9 , wherein the three-dimensional model of the geological medium at the location defines elastic properties of the geological medium.
13. The method of claim 9 , wherein the received waveforms comprise displacements, velocity, or acceleration data of a sensor of the seismic detectors.
14. A seismic monitor comprising:
a memory device; and
a processing device operatively coupled to the memory device, the processing device to:
receive, from a plurality of seismic detectors, recordings of respective waveforms of motion detected at the plurality of seismic detectors in a geological area of interest;
receive a three-dimensional model of a geological medium at the geological area;
apply the respective recordings to corresponding positions of the seismic detectors in the three-dimensional model;
test a plurality of moment tensors at a plurality of locations in the three-dimensional model to determine whether a location within the plurality of locations in the three-dimensional model satisfies Q({right arrow over (x)})=1,
wherein
Q
(
x
→
)
=
❘
"\[LeftBracketingBar]"
∑
l
=
1
N
d
q
l
(
x
→
)
❘
"\[RightBracketingBar]"
wherein N d is a total number of components of the respective recordings of the plurality of moment tensors, and
wherein q 1 ({right arrow over (x)}) is a vector based on respective velocity derivatives for each of the locations of the plurality of locations in the three-dimensional model; and
determine a globally convergent source location and moment tensor in the three-dimensional model based on the testing.
15. The seismic monitor of claim 14 , wherein to apply the respective recordings, the processing device is further to:
transform the respective recordings to a frequency domain to generate transformation data; and
provide the transformation data as virtual sources at the corresponding positions of the seismic detectors in the three-dimensional model.
16. The seismic monitor of claim 14 , wherein to apply the respective recordings, the processing device is further to back propagate the recordings of the respective waveforms to generate a wave-field in the three-dimensional model.
17. The seismic monitor of claim 14 , wherein the three-dimensional model of the geological medium at the location defines elastic properties of the geological medium.
18. The seismic monitor of claim 14 , wherein to test the plurality of moment tensors at the plurality of locations, the processing device is further to estimate point source earthquake mechanisms at each point in the geological medium.
19. The seismic monitor of claim 14 , wherein the recordings of the respective waveforms comprise displacements, velocity, or acceleration data of a sensor of the seismic detectors.