1Rosalia Daví1Václav Vavryčuk2Elli-Maria Charalampidou2Grzegorz Kwiatek

1Institute of Geophysics, Academy of Sciences, Praha2GFZ German Research Centre for Geosciences

e-mail: rosi.davi@ig.cas.cz

Accurate moment tensor inversion of acoustic emissions

Moment tensor inversion is one of the basic tools for analyzing source mechanisms of tectonic and volcanic earthquakes observed in the Earth’s crust, but also of acoustic emissions (AEs) recorded in laboratory environments.

AEs and earthquakes are different in size, strength and radiated frequencies.

The physics of the source and the source mechanisms are basically similar.

The moment tensors can provide insights into fracture processes (geometry and orientation, stress field, shear-tensile type).

Motivations:

Accurate locations Accurate velocity model Focal sphere coverage High-quality data - high signal-to-noise ratio

- high-quality stations

High-quality stations:

Accurate moment tensor solutions require:

Unified transfer functionsCorrect amplificationsCorrect sensor orientationsCorrect polaritiesNo local site effects

Network calibrationusing a joint inversion for MTs of many events

The complete network calibration can adjust station amplifications by including the local site effects at all stations.

In order to increase the accuracy of the amplifications, the inversion is performed in iterations.

The sensor amplifications are calculated repeatedly with gradually increasing accuracy.

If the difference between the amplifications from the previous and the current iterations are less than a prescribed error, the iteration process is stopped.

COMPLETE NETWORK CALIBRATION

umG

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.....................NNNNNNN GGGGGG

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INVERSION FOR SINGLE EVENT

Moment tensor inversion for a single event

G - Green’s function amplitudes

u - amplitudes observed at N stations

m - moment tensor

)1()1()1( NNN uCmg

0)1()1()1(

umg

0GNNN Cu

One station with unknown amplification C (N+1)

Stations with known and unknown amplifications

JOINT INVERSION FOR MANY EVENTS

Triaxial compression experiment on a cylindrical Bentheim sandstone specimen (50 mm diameter and 105 mm in length).

Sixteen P-wave sensors (resonant frequency of 1 MHz) glued to the surface of the specimen, providing a good azimuthal coverage.

Half of the sensors (red) were applying consecutively a square pulse of 100 V amplitude every 30 s. Pulses were recorded on the remaining sensors (blue).

Vertical projections of the hypocentre locations (accuracy of 2 mm) of AE events recorded during three different time windows.

The AE hypocentre locations were calculated by minimizing the travel time residuals (time-dependent 1D anisotropic velocity model).

Amplitudes calibrated

for the coupling

effects.

The ultrasonic calibration estimates the coupling correction factors of all sensors and provides information on incidence angle correction.

AE sensors 8, 10, 13 display major coupling problems.

Raw amplitudes recorded as a function of incidence angle.

estimated calibration curve

3 selected temporal stages (1250, 5500 and 3750 events).

42 subsets.

250 events per subset

25 iterations.

Uncalibrated sensors Calibrated sensors

Raw data: the network calibration should yield identical amplifications as the ultrasonic calibration.

Calibrated data: the network calibration should yield amplifications equal to 1.

The amplifications show a very similar trend for the 3 time intervals (robustness of the network calibration and a high degree of time stability).

The amplifications retrieved using the network calibration show roughly similar trends as those retrieved using the ultrasonic calibration. (Sensor 8, 10 and 13 are badly coupled and require a significant correction high values of the amplification factors).

The amplification corrections produced by the network calibration are closer to 1 if the ultrasonically calibrated data are used especially for the sensors with bad coupling.

The network inversion yields reliable amplification values for all sensors (high level of stability).

The coupling effects between the sensors and specimen are similar in all three stages of the experiment.

We do not observe any significant evolution in time (no considerable develop of damage in the specimen).

The ultrasonic calibration of sensors improved the quality of the data (amplifications of calibrated sensors closer to 1).

The accuracy of the sensor amplifications is further improved by applying the network calibration.

Calibrated sensors: amplification less scattered (0.8 and 1.2) with the variation of amplifications for different subsets less pronounced.

Uncalibrated sensors: amplification with scattered values (between 0.6 and 2) but stable for different subsets of events.

Jack-knife to estimate the accuracy (run the iterative procedure 50 times for 100 randomly chosen events) .

Calculate the mean value and the standard deviation of the amplifications.

The standard deviations of sensor amplifications calculated for raw data are about three times higher.

Accuracy

Highest accuracy is achieved when the inversion for amplifications is applied to calibrated data.

The standard deviations span from 0.02 to 0.05 except for sensors 2 and 10 with the standard deviation about 0.07.

Average values of amplifications over all subsets for each of the three stages (due to high stability in time).

These values retrieved for uncalibrated (raw) and calibrated data are used to correct the amplitudes of the waveforms.

Accuracy

Uncalibrated (raw) amplitudes.

The amplitudes obtained using the ultrasonic calibration.

The corrected amplitudes using the network calibration of the raw data.

The corrected amplitudes using the network calibration of the ultrasonically calibrated data.

Moment Tensor inversions: inverted data set

P axes have nearly vertical directions while the T axes are rather horizontal.

The CLVD and ISO components are negative and indicate compressional mechanisms.

The non-DC components are more clustered for corrected moment tensors. The corrected moment tensors show significantly lower values of RMS (0.12 against 0.3)

Moment tensors calculated from the uncalibrated (raw) data

More clustered non-DC components and a lower value of the RMS (0.1 against 0.17).

Moment tensors calculated from calibrated data

Comparison of the RMS values before and after corrections

Significant reduction of the RMS values after applying the standard calibration of amplitudes.Applying the joint inversion the RMS is further reduced.Avoiding the standard calibration and applying the joint inversion to uncalibrated data, we can still achieve a higher accuracy of moment tensors

Corrected, calibrated data. Corrected, uncalibrated data.

Uncorrected, calibrated data. Uncorrected, uncalibrated data.

Accurate and undistorted recordings of AEs in laboratory experiments are a necessary condition for any advanced source studies and interpretations.

A careful calibration of sensors including both their frequency response and a measurement of the coupling effects between the sensor and the specimen is required for such studies.

By applying a joint inversion for sensor amplifications and moment tensors to a set of sufficiently large number of AEs (hundreds of events), we can determine the actual sensor amplifications including the coupling effects.

The calibration method applied to AEs recorded in a compaction band experiment performed on the Bentheim sandstone proved to produce more accurate sensor amplifications than the standard procedure.

The increase of the accuracy is indicated by lower RMS values and a more compact clustering of the Non-DC.

If the standard calibration of sensors is available, the proposed joint inversion can be applied to calibrated data and further to improve their accuracy.

CONCLUSIONS

Thank you for your attention!