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Alexey Sukhovich - MERMAID (Mobile Earthquake Recording in Marine Areas)

Introduction

What is MERMAID?

MERMAID stands for Mobile Earthquake Recording in Marine Areas by Independent Divers. The principal goal of the project is to create a recording network which will provide new data for the purposes of the seismic tomography. Seismic tomography attempts imaging of the interior of the Earth by using teleseismic P-waves (i.e. the P-waves generated by distant earthquakes of appreciable magnitude and which propagated great distances inside the globe).

Why MERMAID?

The arrivals of seismic waves, used in seismic tomography, are recorded by seismic stations. The accuracy of the imaging critically depends on the number of recorded arrivals. While the land is covered by a dense network of seismic stations, the coverage of the oceans remains poor, principally due to high cost of the installation and recovery of the conventionally used instruments, such as ocean bottom seismometers (OBS) and moored hydrophones. The project aims to eliminate the gap in the data by developing new low-cost instruments called MERMAID. At the beginning, we plan to deploy MERMAIDs in the Indian ocean. This interest is dictated by the recent discovery by Montelli et al. (Geophys.J.Int.,167,1204-1210,2006) of the presence of a hot plume under the bottom of the Indian ocean. To detect this plume, they used the method of the finite-frequency tomography (which so far remains the only method which was able to detect this object). The data, collected by the MERMAIDs in this part of the globe will help to further understand the structure of the plume.

How does the MERMAID work?

MERMAID is an autonomous freely-drifting underwater robot, which, by changing its buoyancy, is able to dive to and remain at a programmed depth. A seismic wave arriving at the ocean bottom refracts into the water and generates an acoustic wave, which propagates almost vertically due to large acoustic impedance mismatch between the water and the Earth crust. To record these acoustic signals, the MERMAID is equipped with a hydrophone and will continuously monitor the pressure variation by calculating the ratio of Short-Term to Long-Term moving averages (STA/LTA algorithm). Once an acoustic signal generated by a teleseismic P-wave is detected, the MERMAID will surface as quickly as possible to transmit via satellite connection the recorded signal and other important information (e.g. time of the signal arrival, robot's depth at the moment of detection and its position at the surface). The cycle will then repeat. The principal advantage of MERMAIDs over OBSs and moored hydrophones is their significantly lower operational costs. First, due to the small weight and size, the MERMAIDs can be deployed from virtually any platforms. Second, since the data are sent to us by satellite, no costly recovery operations are envisaged, and the robot will be abandoned once its battery is depleted. The early ideas on the possibility of using drifting underwater robots for seismic data collections were laid out by Frederik Simons and colleagues (Simons et al. in 2006). The first MERMAID prototype was constructed and tested by Simons et al. [2009]. The above authors have successfully demonstrated the possibility of recording teleseismic P-waves in the oceans with the underwater floats by detecting one P-wave generated by a magnitude Mw = 5.9 event at reasonably teleseismic distance (46.5°).

MERMAID at the surface and during descent MERMAID mission (adopted from www.argo.ucsd.edu)

What are the major challenges?

One of the major challenges of the project is to ensure that MERMAID functions as long as possible before the battery is depleted (currently, we are aiming at 2.5 years). The solution to this problem is not trivial as oceans are full of acoustic signals generated by the sources other than teleseismic P-waves, e.g. ships, air gun exploration campaigns, T-waves, whales, etc. All these signals are potentially detectable by a STA/LTA algorithm. Since diving and surfacing are the most energy consuming operations, it is of great importance for the overall success of the mission to ensure that the robot surfaces only in the case of a P-wave detection. I am working on the development of a new probabilistic scheme that will allow the automatic recognition of teleseismic P-waves while keeping to minimum the probability of false recognitions.

Wavelet transform

As a primary tool for signal analysis, I am using wavelet transform. Wavelet transform is a signal analysis technique which has received a lot of interest in the last decade due to its high versatility and applicability to a wide range of problems, such as pattern recognition, signal compression, denoising, etc. As opposed to the Fourier transform, wavelet transform allows to obtain information on both the frequency and time content of the signal (i.e. we can find at what time which frequencies arrive in a given signal). In this regard, wavelet transformation is analogous to the traditional analysis based on spectrograms (also known as short-time Fourier analysis). As compared to spectrogram analysis, wavelet transform has one big advantage - it is non-redundant meaning that the resulting wavelet transform has exactly the same number of points as the original signal. Recall that in case of spectrogram analysis, the original signal is split into overlapping time windows which are subsequently Fourier transformed. The non-redundancy of the wavelet transform makes it ideally suited for our purposes because it reduces to a minimum the required amount of calculations, thus allowing to conserve power and extend the life-time of the robot. Another important advantage of the wavelet transform is that it allows to compress the original signal and thus reduce the amount of data transfered via satellite.

In wavelet transform, an analyzed signal is expanded in the space defined by the set of functions called wavelets and the set of wavelet coefficients is obtained. Each wavelet coefficient is a function of two variables, time and scale, with each scale corresponding to a certain frequency band. As a rule of thumb, each subsequent scale corresponds to a frequency band whose central frequency is half of the center frequency of the previous scale. Thus, higher scales correspond to lower frequencies. The magnitudes of the wavelet coefficients are proportional to the signal's power and thus can be used as a measure of the signal's power at a given moment of time and at a given scale (frequency band). The result of the wavelet transform is frequently represented by means of a scalogram, which depicts the absolute values of the wavelet coefficients as a function of time and scale. The figure below compares a teleseismic P-wave signal and its wavelet transform with three other signals most likely to be encountered by the MERMAID during its mission.

Sample scalograms of the signals produced by: (a) air guns, (b) ships, (c) teleseismic P-waves, (d) T-waves. Each pixel in the scalogram represents a particular wavelet coefficient. Note that for P-waves, most of the power is concentrated at the scales 5 and 6, which in our case correspond to the frequency range between 0.3 and 1.25 Hz, ax expected for teleseismic P-waves generated by earthquakes of high magnitude. The scalograms were calculated with a wavelet basis known as CDF(2,4), abbreviated by the names of its creators Cohen, Daubechies and Feauveau ( Cohen et al., 1992). As McGuire et al. [2008] and Simons et al [2009] found, this wavelet construction provides a very good compromise between computational effort and the performance of the wavelets.

Recognition method

As can be seen from the figure above, the power of the teleseismic P-waves is distributed significantly differently among scales as compared to the signals of other types. To quantify this difference, we create a statistical model for the signals of a given type by analyzing the power distribution among scales for as many signals of the same origin as possible. This process is illustrated in the figure below.

Calculation of the statistical model. First, wavelet coefficients are computed for a detected signal within a time window whose limits are defined by the moments of trigger and detrigger given by STA/LTA detection algorithm. Next, the amount of power in each scale is estimated by computing averages Wk of the absolute values of the wavelet coefficients. To obtain the relative power distribution among scales, the scale averages are normalized by norm L1 to produce normalized scale averages. This procedure is repeated for as many signals of the same origin as possible. By combining the normalized scale averages for all signals, the set of distributions is obtained, one distribution for each scale.

The resulting distributions of scale averages, one distribution for each scale, constitute the statistical model which describes how on average the power of the signals of a certain type is distributed among different scales. The distributions obtained from the continuous records of seven ocean bottom hydrophones, deployed in the Ligurian sea during the Grosmarin experiment (April-September 2008; Dessa et el., 2011), are shown below. Note that virtually all distributions are non-symmetric. We find that they are the best described by the log-normal probability distribution law.

Statistical models obtained from the Grosmarin data for four types of signals. Note the non-symmetric shape of almost all distributions.

More informative way to represent the statistical models is shown in the figure below. Here, the statistical characteristics for all models are combined in a single graph. The most important message which follows from this figure is that the statistical model for teleseismic P-waves is significantly different from any other types of signals. This marked difference gives us the possibility of an automatic recognition.

Description of the statistical models obtained from the Grosmarin data for four types of signals. Center points denote the medians of each distribution; boxes delimit 25% and 75% quantiles, while vertical lines indicate 5% and 95% quantiles.

Once the statistical model is developed, the recognition is performed by comparing the scale averages W0k calculated for a detected signal with corresponding distributions. For each scale k we estimate the probability of making a mistake by rejecting the detected signal as not belonging to the model while it does. This type of error is known in statistics as a Type I error. The high values of the probability of committing a Type I error are taken as indication that the signal belongs to the model. To combine the results from several scales, instead of multiplying the probabilities (which we found to be too restrictive) we calculate a weighted average of probabilities to obtain a single recognition criterion C, varying between 0 and 1. The detected signal is then accepted as the one belonging to the model if the recognition criterion exceeds a certain recognition threshold C0 : C > C0 .

In addition to the recognition criterion C, we also calculate the signal-to-noise ratio (SNR) for the detected signal. It will be shown below that its value can be used to improve the performance of the recognition routine. SNR is again estimated with the help of the wavelet transform. It is calculated as a ratio of the sum of the absolute values of the detected signal's wavelet coefficients to the sum of the wavelet coefficients calculated for the ambient noise record preceding the detected signal (see figure below).

Calculation of the SNR. Note that we use scale averages before they are normalized by the norm L1 (see also the figure with the details on the statistical model calculations).

Results

Test of the recognition method on the Grosmarin data

Once the methodology is developed, it is necessary to decide which numerical value of the recognition threshold C0 should be adopted as an indicator of a teleseismic P-wave detection with high degree of certainty. To this end, we have simulated MERMAID's mission by running a STA/LTA detection algorithm on the complete database of the Grosmarin experiment and testing each detected signal with our recognition method. As explained above, the SNR was also calculated. The results of the test are represented in figure below (left), which shows the positions of all detected signals (the P-waves on top panel and all other signals on bottom panel) in the C-SNR space.

GROSMARIN HAITI
Recognition results of the Grosmarin data. With the choice of thresholds C0 = 0.15 and SNR0 = 2.25, 94% of the P-waves recorded during the experiment were recognized correctly with no false positive recognitions. Recognition results on the Haiti data. With the same choice of the thresholds used for the Grosmarin data, 74% of all P-waves were recognized correctly with only two false positives. One of these false positives is most likely due to small magnitude local earthquake, whose origin we were not able to identify. The higher SNR false positive it due to a sharp spike most likely originating from an electronic noise. The frequency content of such sharp-spike signals has a lot of power at low frequencies and thus recognized as a P-wave with a high recognition criterion. The work is under way to ensure the recognition of such signals as well.

The value of this figure is that it allows to visualize the choice of the thresholds C0 and SNR0. Any signal within the region defined by these thresholds in C-SNR plane (gray area on both panels) will be recognized as a P-wave. Therefore, in order to minimize the number of false recognitions (signals of other origins recognized as a P-wave) and maximize the number of the correct recognitions, we have to define such thresholds that the gray region on the top panel contains as many points as possible, while the same region on the bottom panel should not contain any points. Such regions exist and allowed us to recognize correctly 94% of all detected P-waves while having zero false recognitions.

Test on the independent data set

Since the Grosmarin signals on which the recognition was tested were also used in the creation of the statistical model for the P-waves, we decided to run another test on the independent data set. To this end, we used the continuous 3-month-long records of the ocean bottom hydrophone installed near the coast of Haiti after the devastating earthquake in January 2010. The hydrophone and the instrument response of the electronics are identical to those used in the Grosmarin experiment, thus ensuring the compatibility of the statistical model. The results are presented in the above figure. With the choice of the thresholds determined from the Grosmarin data, a recognition rate of 74% of all teleseismic P-waves is achieved with only two false positives (see figure caption).

Latest results

A major event recorded by two MERMAIDs during the last mission is recognized correctly !

During the two-week-long test in the Mediterranean sea, two MERMAIDs were continuously recording pressure variation and detected a magnitude 7 event whose details are given below. When analyzed with the recognition method, both signals are rated with a high recognition criterion C meaning that this event would be positively identified had the MERMAIDs been on an actual mission.

EVENT

2011/06/24 at 03:09:40
Fox islands, Aleutian islands
Mw=7.3, Δ = 85°, Depth = 46.8 km

Recognition results:

Recognizing the false positive from the Haiti OBH

For the latest results on the work of how to rule out some of the noise signals which are difficult to distinguish with the recognition method presented above, click here.

Test missions

For the latest results on the test missions conducted so far with two MERMAIDs, click here.

Our collaborators

Jean-Olivier Irisson
Ph.D., Maître de Conférence
UPMC Univ Paris 06, UMR 7093, LOV, Observatoire océanologique, F-06234, Villefranche-sur-Mer, France
CNRS, UMR 7093, LOV, Observatoire océanologique, F-06234, Villefranche-sur-Mer, France
Web-page: http://jo.irisson.com/

Frederik J. Simons
Ph.D., Assistant Professor of Geosciences
321B Guyot Hall, Princeton University, USA
Web-page: http://www.princeton.edu/geosciences/people/simons/

References

Dessa, J.-X., S. Simon, M. Lelièvre, M.-O. Beslier, A. Deschamps, N. Béthoux, S. Solarino, F. Sage, E. Eva, G. Ferretti, O. Bellier, and C. Eva, "The Grosmarin Experiment: Three dimensional crustal structure of the North Ligurian margin from refraction tomography and preliminary analysis of microseismic measurements", Bull. Soc. Géol. France, in press, (2011).

Cohen, A., I. Daubechies, and J. Feauveau, "Biorthogonal bases of compactly supported wavelets", Comm. Pure Appl. Math., 45, 485-560, (1992).

McGuire, J. J., F. J. Simons, and J. A. Collins, "Analysis of seafloor seismograms of the 2003 Tokachi-Oki earthquake sequence for earthquake early warning", Geophys. Res. Lett., 35, L14310, (2008).

Simons, F. J., G. Nolet, J. M. Babcock, R. E. Davis, and J. A. Orcutt "A future for drifting seismic networks", EOS Trans. AGU, 31, 305-307, (2006).

Simons, F. J., G. Nolet, P. Georgief, J. M. Babcock, L. A. Regier, and R. E. Davis, "On the potential of recording earthquakes for global seismic tomography by low-cost autonomous instruments in the oceans", J. Geophys. Res., 114, B05307, (2009).

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