1

STATE OF ISRAEL מדינת ישראל

THE MINISTRY OF NATIONAL INFRASTRUCTURES משרד התשתיות הלאומיות

Office of the Chief Scientist המדען הראשי

מדויק ( יגרדיומטר) ניטור גיאומגנטי קיום וקידום

בהר עמרם, ש בלוך"במצפה הגיאופיסי ע

ח מסכם"דו

ES-16-14' ח מס"דו

יני שורקעמרכז מחקר גר של הפרויקט חוקר ראשי ,ר בוריס גינזבורג'ד :יםמחבר

של הפרויקט חוקר ראשי ,ר ניצן זלומונסקי'ד מהנדס הפרויקט , אסף יניב' מר כנהוהנדסת תמ ,אביבית נוימן' גב

2014 מאי

2

PUBLICATION DOCUMENTATION PAGE

3. Recipient Accession No. 2. 1. Publication No. ES-16-14

5. Publication Date

2114מאי 29

4.Title and Subtitle מדויק במצפה ( גרדיומטרי) ניטור גיאומגנטי קיום וקידוםבהר עמרם, ש בלוך"הגיאופיסי ע

טיפול : כולל פעילויות עיקריות במחקרח תיאר "דווויסות , ותחזוקה בציוד המותקן במצפה הגיאופיסי

הורדת נתונים , מדי נטייה מדויקיםובדיקות התקנה של עיבוד נתונים מוקדם , ממכשירי מדידה הנמצאים במצפה

סנכרון ואינטגרציה של הנתונים , של תוצאות ניטוראנליזה של , השונים לבסיס נתונים אחוד מהערוצים

.הנתונים

6. Performing Organiz. Code

8. Performing Organiz. Rep. No. ג "ממ 7. Author (s): ןאביבית נוימ,אסף יניב, זלומונסקיניצן , בוריס גינזבורג

10. Project/ Task / Work Unit No. 23 3005 9. Performing Organization Name and Address יבנה 81811, ג שורק"ממ

11. Contract No. 012-11-240

13. Type of report and period covered 2111-2114 תושנ, מסכםח "דו

12.Sponsoring Organigation (s) Name and

Address משרד האנרגיה והמיםירושלים 91361, 36148. ד.ת 14. Sponsoring Organiz. Code

15. Supplementary Notes

16. Abstract The aim of the long-term precise magnetic observations with the help of a supersensitive potassium

magnetometer/gradiometer (SuperGrad) project is to search for new capabilities of the SuperGrad

instrument (GEM Systems) in application to tectonic dynamics. SuperGrad was installed in the geophysical

tunnel at the southern part of the Arava Desert. Three total field magnetic sensors of SuperGrad were placed

so as to get gradient data both in north-south and east-west directions. Monitoring of the gradiometer

differences was carried out together with vector measurements of the Earth‟s magnetic field by means of a

declination-inclination magnetometer (dIdD). Magnetic measurements were supplemented with precise

ground tilt measurements.

During the project the following activity items were performed:

Maintenance of the instruments installed at Har Amram geophysical observatory;

Checking, installation, tuning and putting into operation of the instruments for ground tilt measurements;

Acquisition and storage of the data.

Preparation of the data for integration into joint data base comprising different geophysical channels

Analysis of the magnetic field/gradient data together with other data registered at the magnetic

observatory (ground tilt, temperature etc.). מילות מפתח. 17

ות מדידות מגנטי, מתקדם יניטור גיאומגנט-ניטור גיאופיסי רב, מדידות נטית קרקע, מדויקות

ערוצי

17. Keywords

Advanced magnetic monitoring, precise magnetic

measurements, ground tilt measurements, multi-sensor

geophysical monitoring

20. Security Class

(This Page) ס"בלמ

19. Security Class

(This Report) ס "בלמ

18. Availability Statement

22. Price 21. No. of Pages 41

3

תקציר

גיאופיסי מדידות מדויקות של השדה המגנטי של כדור הארץ הן חלק אינטגראלי בניטורמטרת . בדרום הערבה –ש בלוך שנמצא בהר עמרם "משולב לטווח ארוך במצפה הגיאופיסי ע

המיוצר על ידי ( סופרגרד)מדויק -גרדיומטר סופר/רת מגנטומטרהניטור הגיאומגנטי בעזהיא חיפוש אנומליות בהתנהגות השדה המגנטי של כדור (GEM Systems)חברה קנדית

הסופרגרד שהותקן מכשיר. דינמיות אזוריות-הארץ הקשורות לפעילויות גיאו הגיאופיסית הוא בעל שלושה גלאים הפרוסים בתצורה המאפשרת במנהרה

מדידות מדויקות של השדה . דרום-מערב וגם בכיוון צפון-גרדיאנטים בכיוון מזרח מדידתזמניות של מרכיבי השדה הגיאומגנטי -מלוות במדידות בו (total field)המגנטי השלם

(. declination-inclination magnetometer dIdD)מגנטומטר מסוג מבוצעות על ידי . ע מבוצעות על ידי מדי נטייה שהותקנו במנהרהמדידות מדויקות של נטית הקרק

:במהלך הפרויקט ביצענו את העבודות הבאות טיפול ותחזוקה בציוד המותקן במצפה הגיאופיסי בהר עמרם

וויסות ובדיקות התקנה של מדי נטייה מדויקים

הורדת נתונים ממכשירי מדידה הנמצאים במצפה

עיבוד נתונים מוקדם של תוצאות ניטור

סנכרון ואינטגרציה של הנתונים מהערוצים השונים לבסיס נתונים אחוד

אנליזה של הנתונים.

Abstract

The aim of the long-term precise magnetic observations with the help of a supersensitive

potassium magnetometer/gradiometer (SuperGrad) project is to search for new capabilities of

the SuperGrad instrument (GEM Systems) in application to tectonic dynamics. SuperGrad

was installed in the geophysical tunnel at the southern part of the Arava Desert. Three total

field magnetic sensors of SuperGrad were placed so as to provide gradient data both in north-

south and east-west directions. Monitoring of the gradiometer differences was carried out

together with vector measurements of the Earth‟s magnetic field by means of a declination-

inclination magnetometer (dIdD). Magnetic measurements were supplemented with precise

ground tilt measurements.

During the whole project the following activity items were performed:

Maintenance of the instruments installed at Har Amram geophysical observatory;

Checking, installation, tuning and putting into operation of the instruments for ground

tilt measurements;

Acquisition and storage of the data;

Preparation of the data for integration into joint data base comprising different

geophysical channels;

Analysis of the magnetic field/gradient data together with other data registered at the

magnetic observatory.

4

Maintaining and advancing precise geomagnetic

(gradiometer) monitoring at the Bloch Geophysical

Observatory (Har Amram).

Final report

Content

1. Introduction 5

2. Ground tilt measurements 7

a) Seika SBG2U/NG2U 11

b) Volksmeter VMII-2RU-GPS

c) Sherborne T233-0001-1 inclinometer 12

d) Wireless data communication channel 14

3. Magnetic field monitoring and data processing 15

3.1. Three-predictor model 17

3.2. Two-predictor model 18

3.3. Analysis of seasonal variability in regression coefficients 20

a) Temperature stability

b) dIdD stability

c) Ground tilt

d) Other possible reasons for the bias in the estimation of

regression coefficients

3.4. Data processing summary 23

4. Conclusion 24

5. References 24

Appendix1. Yearly ground tilt data acquired by the measurement

system based on Seika tilt sensor.

Appendix 2 Yearly ground tilt data acquired by the measurement

system based on VLL tilt sensor.

Appendix 3. Yearly ground tilt data acquired by the measurement

system based on Sherborne T233-0001-1 tilt sensor. 16

Appendix 4 Code for calculation of regression coefficients 39

5

1. Introduction

The aim of the long-term precise magnetic observations with the help of a supersensitive

potassium magnetometer/gradiometer (SuperGrad) project is to search for new capabilities of

the SuperGrad instrument (GEM Systems) in application to tectonic dynamics. SuperGrad

was installed in the geophysical tunnel at the southern part of the Arava Desert. Three total

field magnetic sensors of SuperGrad were placed so as to get gradient data both in north-south

and east-west directions. Monitoring of the gradiometer differences was carried out together

with vector measurements of the Earth‟s magnetic field by means of a declination-inclination

magnetometer (dIdD).

Research objectives & expected significance

The research objectives of the project:

Application of modern magnetometer instrumentation with pT sensitivity for magnetic

monitoring of active faults.

To obtain magnetic field/gradient monitoring database in the Arava Rift region.

Databases of so high precision and sampling rate are unique for geomagnetic

observatories.

Using the tilt meters to obtain a first data set on earth tide induced geodynamics at the

site. This will serve as a baseline for comparison with expected model earth-tide

deformation and to identify eventual locally induced earth-tide influences in the SG

time series

To search for a relation between seismic activity and anomalous behavior of Earth

magnetic field / gradient specific features for Arava Rift region.

To integrate precise ground tilt measurements as a part of multi-sensor geophysical

monitoring.

To analyze a correlation between anomaly signatures in monitoring data in the frame

of multi-sensor approach to analysis of geodynamic associated phenomena.

The scientific significance is:

Collection of high precision monitoring data for investigation of tectonomagnetic

effect in wide frequency bandwidth.

Revelation of relation between seismic activity and anomalous behavior of Earth

magnetic field / gradient together with other geophysical fields for Arava Rift region.

Multisensor approach in active fault monitoring.

Equipment layout in the geophysical tunnel is shown in Figure 1.

Specific activity items in the course of the project included: Support and technological improvement of precise geomagnetic monitoring at

Bloch observatory

Integration of precise ground tilt measurement into multi-sensor monitoring

Regular data acquisition

Data management and data integration into unified database

Analysis of the magnetic field/gradient data together with other data registered

at the magnetic observatory

6

SG3

N S

W

SG1

SG2

SG3

Flux

DIDD

R

n

SM

1 SM

2

172 m

35 m

Figure 1. Equipment layout in the geophysical tunnel

Flux – fluxgate magnetometer

SG1,2,3 – SuperGrad sensors

DIDD – component Overhauser magnetometer

DAQ – control and data acquisition equipment

Rn – radon sensors

DAQ – control and data acquisition equipment

SM1,2 – seismometer sensors

DAQ – control and data acquisition equipment

DAQ DA

Q DA

Q

20 m 20 m 36 m 43 m 18 m 35 m

DA

Q

DAQ

Tilt-

meter (Seika)

Tilt-meters

(Volksmeter

and

Sherborne)

battery compartment

Normally closed door

Normally opened door

compartment for sesmo calibration

7

2. Ground tilt measurements

Continuous measurements of ground tilt are implemented by three tilt meters: Seika

SBG2U/NG2U, Volksmeter VMII-2RU-GPS, and Sherborne (T233-0001-1 Schaevitz

D/Axis) inclinometer.

a) Seika SBG2U/NG2U

The NG2U is a liquid based inclinometer sensor with integrated electronics. It features

an analog DC output. The sensor electronics require only minimal power and are in

conjunction with the capacitive primary transformer characterized by high accuracy and

high long-term stability. The measurement technique enables a linear relationship between

the angle to be measured and the output signal.

An electronics box contains two signal conditioners with a 0 ... 5V output signal each

and a highly stable supply voltage. A signal conditioner includes an active low pass filter,

whose upper cut-off frequency / settling time can be adjusted to suit the measurement task,

and noise voltage filters to guarantee the EMC.

Details of the tilt measurement setup based on Seika tilt sensor are given in Fig. 2 - 4.

Sensor SBG2U/NG2U has two analog outputs which are sampled by 16-bit A/D converter

(ADAM-4017) located at the distance of about three meters from the sensor. Since the

remaining part of the data acquisition system is installed 30 meters away, the data are

translated as RS-422 code and then converted to RS-232 format by ADAM-4520

converter. Sampling rate of A/D converter was chosen as 1 Sample/sec. Data acquisition

software averages the data, decimates them down to 1 Sample/minute, and stores in a

memory.

In the beginning of the project we used a usual desktop PC for sensor control and data

storage. However, in the process of project implementation it turned out that reliability of

this computer type is low because of fan failures in specific environmental conditions of

the site. That is why in the course of the project we changed all the desktop PC‟s in tilt

data acquisition systems for small fanless computers of fitPC type (see Fig. 2d).

System running during 2012 revealed that at least two types of standard UPS devices

featured unreliable operation under observatory conditions. Therefore, we decided to build

our own power supply system based on standard power supply and back-up battery. This

device, though having no special advanced features as in computerized UPS, provides

reliable long-term operation. The power supply system is shown in Fig.3.

Dedicated software for the system control and data acquisition and storage was written

using LabView package. Front panel of graphical user interface is shown in Fig. 5.

All the data acquired were arranged as yearly files. Graphical presentation of the data

acquired in the course of the project is given in Appendix 1 both in the form of time series

and Fourier transforms.

8

Some of these Fourier graphs allow distinguishing weak peaks at specific periods of 1 day

and half a day. This, probably, can be attributed to the tidal phenomena at Red Sea which is

about 15 km to the South from the observatory site. We shall see even more pronounced

manifestations of these 1-day changes by analyzing the data acquired by more precise tilt

meters Volksmeter VMII-2RU-GPS, and Sherborne.

6/9/2013 23:15 0.679100 0.808283 6/9/2013 23:16 0.680050 0.808700 6/9/2013 23:17 0.679667 0.809017 6/9/2013 23:20 0.679158 0.808283 6/9/2013 23:21 0.679325 0.808633 6/9/2013 23:22 0.680058 0.809133 6/9/2013 23:23 0.680600 0.808575 6/9/2013 23:24 0.680467 0.808575

d)

Figure 2. Seika tilt meter. a) example of data acquired, b) sensor picture,

c) sensor installation, d) fitPC used for system control and data acquisition.

a) b)

c) d)

Figure 3. Power supply system with back-up battery.

9

Backup

battery

Figure 4. Block-diagram of the tilt measurement setup based on Seika tilt sensor.

PC

Com 1

ADAM 4520

Com

DB 9

+

PSU +15 V

Matching box

+Vs

Data+

Data-

Red

Green

9 White

9

Black

ADAM 4017

Data+

Data-

+Vs

Vin1-

Vin1+

Vin0-

Vin0+

Seika SBG2/U 0.5 – 4.5 V

C1 +/- 10

C2 +/- 10

+Vs

Black

Black

White

9

Green

9

11

Figure 5. LabView VI front panel of the software for Seika tilt system control and data acquisition.

11

b) Volksmeter VMII-2RU-GPS

The VolksMeter uses Symmetric Differential Capacitor (SDC) array sensor to detect and

measure minute accelerations and tilts. The sensor consists of two fixed printed circuit boards

holding the transmitting and receiving capacitor plates and a moving Faraday shield array,

mounted on the end of a pendulum. When subjected to accelerations or tilts, the shield array

on the pendulum moves relative to the fixed plates and changes the amount of receiving plate

that is exposed to or shielded from the transmitting plates. This, in turn, changes the overall

capacitance of the sensor. A magnetic eddy damper, located below the sensor plates, damps

oscillations of the pendulum. A direct Capacitance-To-Digital-Converter (CDC) chip converts

the current capacitance of the sensor array to a 24-bit number. An interface board in the

VolksMeter controls the CDC chip and formats the acquired data for transmission to the

support computer. Sensor of VMII-2RU-GPS tilt meter is shown in Fig.6.

Example of data format is as follows:

07/31/12,10:12:01,CH1,-2049

07/31/12,10:12:01,CH2,-243

07/31/12,10:13:01,CH1,-2049

07/31/12,10:13:01,CH2,-244

07/31/12,10:14:01,CH1,-2049

07/31/12,10:14:01,CH2,-243

Figure 6. Sensor of VMII-2RU-GPS tilt meter.

12

All the data acquired were arranged as yearly files. Graphical presentation of the data

acquired in the course of the project is given in Appendix 2 both in the form of time series and

Fourier transforms.

One-day cycle peak at Fourier graphs is clearly seen for both 2012 and 2013 observation

periods.

c) Sherborne T233-0001-1 inclinometer.

To improve the quality of tilt data gathered at the tunnel, we‟ve purchased one more

instrument for precise ground tilt measurements.

The Schaevitz inclinometer produced by Sherborne Sensors is self-contained and designed

to operate from a standard DC power source. Its output is in the form of an analogue DC

signal directly proportional to the sine of the angle of tilt. In the level (horizontal) position,

the DC output is zero. When tilted in one direction, the inclinometer output is 0 to +5 volts

full scale and in the opposite direction 0 to −5 volts full scale. The heart of this closed loop,

gravity referenced sensor is a flexure supported torque-balance system; rugged enough to

withstand severe shock and vibration and still maintain excellent accuracy. The electronics

and sensor are housed within the sealed housing permitting operation in hostile environments.

Picture of the T233-0001-1 inclinometer is shown in fig. 7.

Figure 7. T233-0001-1 tiltmeter

As the inclinometer tilts through an angle Φ, the Paddle “A” (Fig. 8) tends to move in the

direction of tilt due to gravity. This resultant motion is converted by a position sensor “B” to

an error signal input to the servo amplifier, which develops a restoring current to the torque

motor “C”. Because of the servo action, an equal and opposite torque to that produced by

gravity is produced so that the pendulous mass no longer moves and is restored to its original

position. The torque motor current is directly proportional to the angle of tilt; the current is

routed through a stable resistor, R0 in order to provide a voltage signal. Stops are provided on

13

both sides of the paddle to limit its travel when the inclinometer is not powered. When power

is applied, the paddle automatically moves to its null position.

Sherborne tiltmeter installed in Bloch observatory is shown in fig. 9.

Figure 9. T233-0001-1 tilt meter; installed on the same platform as VMII-2RU-GPS sensor.

Figure 8. Block- diagram of T233-0001-1 D/Axis inclinometer

14

Format of the data acquired by Sherborne tiltmeter is given here:

24/02/2014 16:43:06 -0.088039 0.472658

24/02/2014 16:44:06 -0.088038 0.472654

24/02/2014 16:45:06 -0.088038 0.472651

24/02/2014 16:46:06 -0.088038 0.472653

24/02/2014 16:47:06 -0.088036 0.472659

24/02/2014 16:48:06 -0.088038 0.472649

24/02/2014 16:49:06 -0.088038 0.472660

24/02/2014 16:50:06 -0.088038 0.472655

All the data acquired were arranged as yearly files. Graphical presentation of the data

acquired in the course of the project is given in Appendix 3 both in the form of time series and

Fourier transforms.

As in the case of other tilt meters, one-day cycle peak at Fourier graphs is clearly seen for

both 2013 and 2014 observation periods.

d) Wireless data communication channel

In the beginning of 2012 Geophysical Institute of Israel installed cellular communication

within Bloch geophysical observatory (Har Amram). Basing on this new installation it is

possible to get access to the instrument running in the tunnel by means of 3G wireless router

installed inside the tunnel. The data from the instruments could be requested and accessed

from any Internet point. It gives an opportunity both to have full information of instrument

health and to get the data on-the-fly.

Block diagram of wireless data channel is shown in fig. 10.

Figure 10. Up to four PC's can be connected to a single wireless router.

Home computer Router at the

observatory site

PC1

PC2

PC4

PC3

Internet

15

Picture of 3G router is shown in fig. 11.

Figure 11. Wireless 3G router with four Ethernet inputs.

3. Magnetic field monitoring and data processing

In the course of the project continuous precise geomagnetic (gradiometer) monitoring was

implemented. Data were stored locally on PC supporting SuperGrad instrument. Data files

were transferred to office PC approximately once per month and integrated in data base. Data

quality was periodically checked.

Magnetic components monitoring was implemented continuously by DIDD magnetometer

during reported period. Data were checked and corrected for occasional spikes and

irregularities.

The point of the short-based magnetic gradiometer with highly sensitive magnetic sensors

is to cancel signals of remote sources like diurnal variations and micro-pulsations but to sense

the sources of local/regional origin that could be governed by geodynamic activity. In our

case, the separation between magnetic sensors – gradiometer base – is about dozens of meters

(see Figure 1). Over such short distances, both diurnal variations and micro-pulsations are

essentially homogeneous. It turned out, however, that the gradiometer time series contain

residuals of external variations.

Synchronous monitoring of supersensitive total field and vector magnetometers allowed us

to understand the influence of the external magnetic field on gradiometer readings. A

comparison between the gradiometer and the external field components time series showed

their obvious correlation. The closest correlation was observed with declination changes. In

this case, the correlation coefficient was estimated as being more than 0.95. As it was shown

16

(Shirman & Ginzburg, 2004), the main reason for such phenomenon is the non-parallelism of

the Earth‟s magnetic field vectors at the points of the sensors‟ location. The „cleaning‟

procedure based on a mutual regression analysis of the gradiometer and vector magnetometer

time series was found to be an effective tool for reduction of the influence of the external

homogeneous variation. Figure 12 illustrates the result of such reduction. Presented here are

typical 10-day records at the summer period. High correlation between the Y-component of

the external magnetic field (Figure 12a) and the gradiometer readings (Figure 12b, c) is

clearly seen. Various methods of the „cleaning‟ procedure are discussed below.

The dIdD vector magnetometer measures X (north), Y (east), and Z (downward)

components of the Earth‟s magnetic field. SuperGrad sensors measure the total magnetic field

Fk (in our case k=1, 2, 3 for a three-sensor system). Within the bounds of the test site, the

magnetic field vector may deviate slightly from the field direction at the dIdD point.

Declination Dk and inclination Ik angles specify the field direction at the SuperGrad sensor

locations.

Total field gradiometer time series

are calculated from the total magnetic field Fik measured by any of the SuperGrad sensors k

where i is the sample number.

Figure 12. Example of the 10-day record a) Y-component of the Earth‟s magnetic field; b), c)

raw gradient time series; d), e) corrected readings.

i

k

i

k

i

kk FFG 2121

17

According to Shirman and Ginzburg (2004), misalignment of magnetic field vectors in the

points of the SuperGrad sensor locations results in the dependence of gradiometer readings on

the homogeneous component variations of the Earth‟s magnetic field:

dGk1k2=b1k1k2·dX+ b2k1k2·dY+ b3k1k2·dZ+k1k2 (1)

where dX, dY, dZ are the centered vectors of magnetic field component data, dGk1k2 is the

centered vector of gradiometer readings, is a vector of residuals, and coefficients b are as

follows:

)()( k2k10k1k2 IIIsinb1

)()( k2k10k1k2 DDIoscb2 (2)

)()( k2k10k1k2 IIIcosb3

where I0 is the mean inclination angle at the reference point.

3.1. Three-predictor model

Angles of misalignment in Eq. (2) are not known a priori and in many instances could not

be measured with satisfactory accuracy. In this case linear model (1) may be treated as a

linear regression of dGk1k2 onto dX, dY, dZ (predictors). In matrix notation, Eq. (1) takes the

form:

dG = βP +

ndZ

2dZ

1dZ

ndY

2dY

1dY

ndX

2dX

1dX

P (3)

where β is a vector of the true coefficient and n is the number of readings in the data set series.

In the simplest case of the ordinary least squares (OLS) method, an estimation b = (b1, b2, b3)

of coefficients β in Eq. (3) is obtained as follows (Draper & Smith, 1998):

b = (PTP)

-1PTdG (4)

where PT

is the transpose of the matrix P.

Residuals in the linear regression model (3) represent gradiometer data corrected for non-

parallelism of magnetic vectors at measurement points. Figures 5d and e present these

„cleaned‟ or corrected gradiometer series Gcorri

k1k2 = ik1k2

Pb-dGε (5)

Misalignment angles and therefore regression coefficients in (4) are expected to be time

independent since they are influenced only by the rocks‟ magnetization. Processing of

18

monitoring data for the period of 2003-2011 indeed shows an absence of a long term trend in

coefficient values.

With the help of Eq. (2) we can calculate the non-parallelism angles of the Earth‟s magnetic

field in the points of sensor locations based on the mean values of regression coefficients.

Table 2. Non-parallelism angles of the Earth‟s magnetic field in the points of sensor locations

Misalignment in D Misalignment in I

Sensors 1 & 2 28' 3'26''

Sensors 1 & 3 14' 2'45''

We see that declination differences are substantially larger than inclination ones. This

result is a direct consequence of the fact that local magnetic field inhomogeneity is governed

mainly by the rocks‟ remnant magnetization oriented almost in an E-W direction as

mentioned above. Note that declination differences (D2-D1) and (D3-D1) differ by a factor 2,

which is also a ratio of spatial separation between these sensors in an E-W direction (see

Figure 1). This means a presence of a constant D-gradient along the Y-axes within the bounds

of the tunnel.

Though the annual mean values of regression coefficients are highly stable over a

monitoring period of about 10 years, their current values feature small but distinct season

changes. We show these by the example of the coefficient b212 since it has the maximum

value of all the coefficients. Figure 13a shows the graph of the coefficient b212 temporal

changes during one year of monitoring. Each point in the plot is obtained by calculation of

regression coefficients according to Eq. (4) for ten-day data series. We see that seasonal

changes of about+/- 1.5% take place in the course of the year. Similar changes are observed

during the whole monitoring period.

Figure 13. Seasonal changes of regression coefficient b212. Each point is calculated over a 10-day

data set. a) Three predictor model; b) two predictor model.

19

3.2. Two-predictor model

First, let us note that the non-parallelism of magnetic vectors at every pair of measurement

points is governed by only two parameters - (Ik1-Ik2) and (Dk1-Dk2). In fact, this means that the

three-predictor regression equation (3) contains redundancy which could, in principle, cause

errors in estimation of our physical model (1-2) parameters. We need, therefore, to rewrite

Eqs. (1) and (2) as follows:

dGk1k2=(Ik1-Ik2)·[-sinI0·dX+cosI0·dZ]+cosI0·(Dk1-Dk2)·dY+k1k2 (6)

This means that the three-predictor regression equation (Eq. (3)) can be replaced by a two-

predictor model in the following manner:

dG = ΒR +

nn dY

dY

dY

dC

dC

dC

..

2

1

2

1

R (7)

Here dC=-sinI0·dX+cosI0·dZ is a centered projection of the Earth‟s magnetic field

variation onto a direction orthogonal to the mean total magnetic field vector in the plane of

magnetic meridian.

Similar to Eq. (4), the OLS estimation of B=(B1,B2) is given by

B = (RTR)

-1RTdG (8) It is interesting to compare gradiometer data corrected by the three-predictor model (3)

with two-predictor (7). An example is given in Figure 14. We see that some useful signals can

be erroneously depressed by the three-predictor model due to its superfluous degree of

freedom. However, periodical season changes of regression coefficients around their annual

average values remain for the two-predictor model as well, - see Figure 13b.

21

Figure 15. 10-day gradiometer record Gcorr12 after correction - top: three predictor and

bottom: two predictor methods. Signals erroneously suppressed by three-predictor model are

clearly seen.

Computer program for calculation of the regression coefficients according to aforementioned

formulas is given in Appendix 4.

3.3 Analysis of seasonal variability in regression coefficients

a) Temperature stability The temperature inside inner tunnel compartments is very stable. According to our

measurements, yearly temperature variation in the vicinity of the DIDD location (see Figure

1b) does not exceed +/- 0.3 C. The compartment of the SuperGrad sensors location is even

deeper into the rock massif and has an additional thermal baffle separating it from the

entrance. As noted above, the magnetic SuperGrad system has very high temperature and

long-term stability. Stability of the dIdD magnetometer is lower, mainly due to the

temperature sensitivity of its coil system. However, such low yearly temperature variations do

not seem to exert direct influence on magnetometer readings.

b) dIdD stability The stability of the dIdD Overhauser vector magnetometer was controlled by absolute

measurements according to the requirements (Jankovski & Sucksdorf, 1996). As shown in

Figure 2, yearly variations were negligible in dIdD baselines.

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 14399

40

20

0

20

40

nevBZi

i

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 14399

40

20

0

20

40

nevB1i

i

pT

pT10-day record

21

Our dIdD instrument is an early version of a GEM vector magnetometer with an

unsuspended Overhauser sensor. Therefore, the seasonal tilt of the dIdD pillar may, in

principal, be a plausible reason for seasonal changes in regression coefficients in Eq. (2). To

get a quantitative estimation of this effect, we performed computer simulation of the influence

of the dIdD frame angular position on regression coefficients. Our results showed that in order

to get an observed seasonal variability in regression coefficients of +/-1.5%, we need to

assume an approximate 10 tilt of the pillar which is, of course, unfeasible.

c) Ground tilt Ground tilt may cause changes in regression coefficients only when it differs at the

gradiometer sensor locations. For the case of the b212 coefficient vertical component of the

anomaly magnetic field, a difference in ground tilt in the east-west direction may be

responsible for the change in declination differences. Simple estimation shows that impossible

tilts of about 1 are needed to explain the observed variability in the appropriate regression

coefficient.

d) Other possible reasons for the bias in the estimation of regression

coefficients There are several reasons that could lead to bias in the estimation of regression

coefficients.

a) Dependence between predictors: If predictors C and Y in Eq. (7) are nearly linearly

dependent, then matrix RTR in Eq. (8) is close to singular, giving rise to unstable estimates of

regression coefficients. C and Y are projections of the Earth‟s magnetic field variation onto

directions orthogonal to the mean total magnetic field vector – one in the plane of the

magnetic meridian and the other in an easterly direction. For our case, dC and dY are not

linearly dependent but correlated. The correlation coefficient calculated on our obtained data

set features a mean annual value of about 0.5. However, there is a considerable spread in the

course of the year so that the correlation coefficient can take values from 0.2 to 0.8.

Modifications of the OLS regression, such as ridge regression (Draper & Smith, 1998), exist

to evaluate and remove possible bias in parameters estimation due to the dependence between

predictors.

b) Influence of outliers: The standard method of OLS regression assumes a normal

distribution of the residual ε in Eqs. (3) and (7). In practice, departures from this assumption

occur. In fact, these departures are just the „useful‟ signals we are searching for to correlate

with the regional geodynamic activity. Except for these „useful‟ signals, there are different

kinds of instrumental spikes, local interferences, and disturbances unavoidable in any

magnetic observatory. A least square analysis weights each observation equally in getting

parameter estimates.

22

However, observations containing different kinds of „signals‟, which are not conditioned

by the linear model in Eq. (7), should be down-weighted for estimation of regression

coefficients. There are several, so called, robust methods of linear regression that enable the

observations to be weighted unequally.

c) Non-linearity of the model: If the linear model in Eq. (7) is not exactly true and there are

other unaccounted terms, for instance, higher orders of predictors dC, dY, then estimations of

regression coefficients could be somewhat biased.

d) Influence of dIdD noise: In the OLS regression method, it is assumed that predictors (R

in Eq. (7)) are measured exactly while output variable (dG in Eq. (7)) is subject to the random

error ε with normal distribution.

If this is not true and random error in measurements of predictors (magnetic field

components in our case) should be accounted for, then the OLS estimate of regression

coefficients will be biased (Draper & Yang, 1996).

In our case, the contribution of dIdD magnetometer noise is significant. Moreover, the

variance of C and Y components features seasonal changes, see Figure 16. This means that

the „signal/noise‟ ratio for estimation of regression coefficients is liable to seasonal variations

as well. Various methods of line regression when all the variables are subject to error have

been suggested. Among these are the geometric mean functional relationship (GMFR),

maximum likelihood estimation (MLE), method of moments, and others. Further details can

be found in Draper & Smith (1998).

Figure 16. Root-mean-square deviation values of the Earth‟s magnetic field components

during 1 year of monitoring. Each point is calculated over a 10-day data set.

0

10

20

30

40

50

60

70

80

1 4 7 10 13 16 19 22 25 28 31 34 37

Y-component

C-component

nT

Time

23

Detailed analysis of possible reasons for the bias in the estimation of regression

coefficients as described in this section is a subject of further research.

3.4. Data processing summary We analyzed details of the data processing of precise total-field short-based magnetic

gradiometer monitoring aimed at searching for the magnetic manifestation of regional

geodynamics. The intention of the method is to cancel signals of remote sources like diurnal

variations and micro-pulsations while sensing the sources of local/regional origin that could

be governed by geodynamic activity.

It was shown that gradiometer time series contain residuals of external variations even with

a very short gradiometer base of dozens of meters. Over such short distances both diurnal

variations and micro-pulsations are essentially homogeneous. This phenomenon can be

explained by the non-parallelism of magnetic field vectors at the points of magnetic sensor

locations. This misalignment is, in turn, caused by magnetization (for the most part, remnant)

of the surrounding rocks.

A „cleaning‟ procedure based on mutual regression analysis of the gradiometer and vector

magnetometer time series was found to be an effective tool for reducing the influence of an

external homogeneous variation.

According to our model, regression coefficients depend on misalignment angles only and

therefore are expected to be highly stable in time. As our results show, indeed, there is no

long term trend in regression coefficient values, which also verifies instrumentation stability.

Though annual mean values of regression coefficients are highly stable over the

monitoring period of about 8 years, their current values feature small but distinct season

changes.

Our estimations show that either geophysical phenomena or instrumental errors are

unlikely responsible for these changes. We believe that possible bias in estimation of

regression coefficients may cause their small periodical seasonal changes. Further research of

the subject will be a target of our future work.

24

4. Conclusion.

Task items of the project were:

Support and technological improvement of precise geomagnetic monitoring at Bloch

observatory

Integration of precise ground tilt measurement into multi-sensor monitoring

Regular data acquisition

Data management and data integration into unified database

In the course of the project the following activity items were performed:

Maintenance of the instruments installed at Har Amram geophysical observatory;

Checking, installation, tuning and putting into operation of the instruments for ground

tilt measurements;

Acquisition and storage of the data.

Analysis of the magnetic field/gradient data together with other data registered at the

magnetic observatory

All the task items of the project have been successfully fulfilled in accordance with Project

program and timetable.

5. References

Alexandrov, E., Balabas, M., Pazgalev, A., Vershovskii, A., & Yakobson, N. (1996) Double-

resonance atomic magnetometers: from gas discharge to laser pumping. Laser Physics 6, 244 – 251.

Draper, N., & Yang, Y. (1997) Generalization of the geometric mean functional relationship.

Computational Statistics & Data Analysis, 23, 355-372.

Draper, N. R. & Smith, H (1998) Applied Regression Analysis, 3rd

ed, NY., Wiley & Sons.

Jankovski, J. & Sucksdorff, C. (1996) IAGA Guide for Magnetic Measurements and Observatory

Practice, Warsaw.

Pankratz, L. W., Sauter, E. A., Kormendi, A., & Hegymegi, L. (1999) The US–Hungarian delta I

delta D quasi-absolute spherical coil system. Geophys. Trans. 42, 195–202.

Rybakov, M. & Goldshmidt, V. (1996) Gravity and magnetic investigations in the Har Amram area

(Southern Israel). Report. 844/486/96 The Geophysical Institute of Israel, Lod, Israel.

Shirman, B. & Ginzburg, B. (2004) Influence of local field inhomogeneity on the accuracy of

precise total magnetic field monitoring. Meas. Sci. Technol. 15, 2370-2374.

25

Appendix 1. Yearly ground tilt data acquired by the measurement system based on Seika tilt sensor.

26

27

28

29

Appendix 2. Yearly ground tilt data acquired by the measurement system based on VLL tilt sensor.

Tilt data obtained by VMII-2RU-GPS tilt meter during 2012

31

Figure 6. Tilt data obtained by VMII-2RU-GPS tilt meter during 2012

Fourier spectrum of the Tilt data obtained by VMII-2RU-GPS tilt meter during 2012

31

Tilt data obtained by VMII-2RU-GPS tilt meter during 2013. Interpolated data are designated

by blue bars at the bottom of the graphs.

32

Fourier spectrum of the part of tilt data obtained by VMII-2RU-GPS tilt meter during 2013. One-

day cycle peak is marked.

33

Tilt data obtained by VMII-2RU-GPS tilt meter during 2014.

34

Fourier spectrum of tilt data obtained by VMII-2RU-GPS tilt meter during 2014. One-day cycle

peak and its second harmonic are marked.

35

Appendix 3. Yearly ground tilt data acquired by the measurement system based on Sherborne

T233-0001-1 tilt sensor.

Tilt data obtained by Sherborne tilt meter T233-0001-1 during 2013.

36

Fourier spectrum of the part of tilt data obtained by Sherborne tilt meter T233-0001-1 during 2013.

One-day cycle peak and its second harmonic are marked.

37

Tilt data obtained by Sherborne tilt meter T233-0001-1 during 2014.

38

Fourier spectrum of tilt data obtained by Sherborne tilt meter T233-0001-1 during 2014. One-day

cycle peak and its second harmonic are marked.

39

DIDD

0 1 2 3 4 5

0

1

"04/05/11" "00:00" 3.207 31160.11 29977.127 43238.626

"04/05/11" "00:01" 3.206 31161.116 29977.088 ...

D DIDD2

HC DIDD3

BZ DIDD4

BX HC cos D

180

1000 BY HC sin D

180

1000 BZ BZ 1000

SG12 SG1

dltBX BX mean BX( ) dltBY BY mean BY( ) dltBZ BZ mean BZ( )

dltSG12 SG12 mean SG12( )

Y dltSG12 X0

dltBM X1

dltBY regression SG12 on dltBM, dltBY

B0 XT

X 1

XT

Y B - vector of coefficients for 2-predictor model

B01.066 10

3

6.017 103

Result0 B00

B01

Result0 1.06557E-0036.017E-003( )

nevB0i

dltSG12i

B00

dltBMi

B01

dltBYi

S0 stdev nevB0( )

S0 3.717

SG0 1 2 3 4

0 43035678.309 61283.563 -103624.898 "04/05/11" ...

Y1 dltBM X10

dltSG12 X11

dltBY regression dltBM on SG12, dltBY

BV1 X1T

X1 1

X1T

Y1

BV18.588 10

2

5.124 100

B1

1

BV10

BV11

BV10

B11.1644 10

3

5.966 103

nevB1i

dltSG12i

B10

dltBMi

B11

dltBYi

S1 stdev nevB1( )

S1 3.886

Y2 dltBY X20

dltSG12 X21

dltBM regression dltBY on SG12, dltBM

BV2 X2T

X2 1

X2T

Y2

Appendix 4 Code for calculation of regression coefficients

41

BV21.658 10

2

1.752 101

B2

BV21

BV20

1

BV20

B21.0565 10

3

6.0309 103

nevB2i

dltSG12i

B20

dltBMi

B21

dltBYi

S2 stdev nevB2( )

S2 3.722

B0

B00

B10

B20

1

3 B

1B0

1B1

1B2

1

1

3

B1.0944 10

3

6.0046 103

B01

6.017E-003 B11

5.966E-003

B21

6.031E-003Result B

0B

1

Result 1.0944E-0036.0046E-003( )

nevBi

dltSG12i

B0

dltBMi

B1

dltBYi

S stdev nevB( )

S 3.732

N.R. Draper, Y. Yang "Generalization of the geometric mean functional relationship",

Computational Statististics & Data Analysis , 23, (1997) 355-372

Fuller, W.A. Measurement error models (Wiley, NY, 1987)

S0 0

1

M0

M 1

i

X0

iX

0 i

106

S1 1

106

1

M0

M 1

i

X1

iX

1 i

S0 1

1

M0

M 1

i

X0

iX

1 i

S

1 0 S

0 1

01

1000

1

M0

M 1

i

X0

iX

0 i

S196269594.173

128228756.162

128228756.162

247787486.52

1

1

1000

1

M0

M 1

i

X1

iX

1 i

SY0

1

M0

M 1

i

X0

iY( )

i

SY1

1

M0

M 1

i

X1

iY( )

i

0 14.0451 15.773

SY0

981756 .396 Result 0 1( )

B00

1.0656E-003 Result 14.045 15.773( )

BFULLER S1

SY0

SY1

B01

6.017E-003ResultComb B0

1B1

1B2

1BFULLER

0BFULLER

1

BFULLER1.0498E-003

6.0494E-003

ResultComb 6.017E-0035.966E-0036.0309E-0031.0498E-0036.0494E-003( )

41

0 1440 2880 4320 5760 7200 8640 10080 11520 12960 14400400

200

0

200

400

dltSG12i

i

0 1309.091 2618.182 3927.273 5236.364 6545.455 7854.545 9163.636 10472.72711781.81813090.909 1440040000

20000

0

20000

40000

60000

dltBXi

i

0 1309.091 2618.182 3927.273 5236.364 6545.455 7854.545 9163.636 10472.72711781.81813090.909 1440060000

40000

20000

0

20000

40000

60000

dltBYi

i

0 1309.091 2618.182 3927.273 5236.364 6545.455 7854.545 9163.636 10472.72711781.81813090.909 1440040000

30000

20000

10000

0

10000

20000

dltBZi

i

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 1439930

20

10

0

10

20

nevB0i

i

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 1439930

20

10

0

10

20

nevB1i

i

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 1439930

20

10

0

10

20

nevB2i

i

0 1309 2618 3927 5236 6545 7854 9163 10472 11781 13090 1439930

20

10

0

10

20

nevBi

i