rus
Issue #8/2021
G. I. Dolgikh, S. S. Budrin, S. G. Dolgikh, V. A. Chupin
Direction Finding of Geospheric Disturbances by Laser Strainmeters
Direction Finding of Geospheric Disturbances by Laser Strainmeters
DOI: 10.22184/1993-7296.FRos.2021.15.8.656.665
Two methods of direction finding of geosphere sources of oscillations and waves of infrasonic and low-frequency sound ranges by laser strainmeters are considered. The first method is based on the assumption that the recorded wave disturbances refer to surface waves of the Rayleigh type. In this case, a two- coordinate laser strainmeter is used, which consists of adjacent one- coordinate laser strainmeters with mutually perpendicular measuring arms. In the second case, the triangulation method is used. This method uses a minimum of three spatially separated laser strainmeters.
Two methods of direction finding of geosphere sources of oscillations and waves of infrasonic and low-frequency sound ranges by laser strainmeters are considered. The first method is based on the assumption that the recorded wave disturbances refer to surface waves of the Rayleigh type. In this case, a two- coordinate laser strainmeter is used, which consists of adjacent one- coordinate laser strainmeters with mutually perpendicular measuring arms. In the second case, the triangulation method is used. This method uses a minimum of three spatially separated laser strainmeters.
Теги: direction finding spatially separated laser strainmeters triangulation two-coordinate laser strainmeter двухкоординатный лазерный деформограф пеленгование пространственно-разнесенные лазерные деформографы триангуляция
Direction Finding of Geospheric Disturbances by Laser Strainmeters
G. I. Dolgikh, S. S. Budrin, S. G. Dolgikh, V. A. Chupin
V. I. Il’ichev Pacific Oceanological Institute Far Eastern Branch Russian Academy of Sciences, Vladivostok, Russia
Two methods of direction finding of geosphere sources of oscillations and waves of infrasonic and low-frequency sound ranges by laser strainmeters are considered. The first method is based on the assumption that the recorded wave disturbances refer to surface waves of the Rayleigh type. In this case, a two- coordinate laser strainmeter is used, which consists of adjacent one- coordinate laser strainmeters with mutually perpendicular measuring arms. In the second case, the triangulation method is used. This method uses a minimum of three spatially separated laser strainmeters.
Keywords: two-coordinate laser strainmeter, spatially separated laser strainmeters, direction finding, triangulation
Article received: 17.11.2021
Article accepted: 02.12.2021
INTRODUCTION
The problems of monitoring and determining the location of various sources of anthropogenic and natural origin using laser interference methods are solved using an integrated approach that takes into account both the directivity and the spatial distribution of measuring systems. In our case, several methods can be used to solve the problem of detecting and determining the location of oscillating sources. The first method consists in using an orthogonal system of laser strainmeters, the second method is based on the use of three or more spaced laser strainmeters having the same directivity.
The first method is based on the assumption of a known polarization of the recorded wave processes. Such well-known polarization signals include seismoacoustic signals arising at the water-bottom boundary as a result of the transformation of sonar signals generated in the water by a low-frequency underwater sound projector and moving underwater and surface objects. For the first time, the ability to track the movement of a source of geospheric disturbances using a laser strainmeter was described in paper [1], in which a record of a 105‑meter laser strainmeter was given, containing seismoacoustic waves modulated by gravitational sea waves generated at the “water-bottom” boundary by a moving surface vessel. Variations in the modulation parameters in this record can be used to estimate the change in the direction of the ship’s movement. Another type of amplitude modulation of underwater noise emission from sea vessels is currently widely used in practice for their classification [2]. In paper [3], it was shown that in the low-frequency region, seismoacoustic surface waves become the dominant mechanism for the transfer of acoustic energy in the shallow-water shelf zone of the sea.
Experimental studies of comparative levels of acoustic noise recorded by hydrophones and bottom geophones [3] have shown that on the shallow shelf at frequencies below 25 Hz, a decrease is observed in the spectrum of hydrophone records, and an increase in the level of spectral components in the spectrum of geophone records. This behavior depends on the ratio of sonar wavelength to sea depth. At depths less than half the length of the hydroacoustic wave, conditions arise under which almost all of the hydroacoustic energy is transformed into elastic vibrations of the bottom, recorded by a coastal laser strainmeter [4]. These depths have been called critical depths. In the earth’s crust, these disturbances propagate mainly in the form of Rayleigh-type surface waves. This condition can be used for registration and direction finding of such disturbances with a two-coordinate laser strainmeter consisting of two one-coordinate laser strainmeters with almost mutually perpendicular measuring arms installed at Mys Shul’tsa [5].
Not always recorded disturbances can be represented in the form of the Rayleigh-type surface waves. For example, deformation jumps recorded by distant laser strainmeters [6] and which are an unconditional indicator of the occurrence of seabed movements [7] leading to a tsunami cannot be attributed to Rayleigh-type surface waves in any way. Therefore, it is impossible to use the polarization properties of surface waves for their direction finding. For this, the triangulation method, which is based on the use of three or more spatially separated laser strainmeters, is fitting better. This system includes strainmeters described in work [8]. In the second part of the article, using the example of a recording of deformation disturbances of various origins, the features of the triangulation method of direction finding by these laser strainmeters will be considered.
DIRECTION FINDING OF DEFORMATION DISTURBANCES BY A TWO-COORDINATE LASER STRAINMETER
On June 3, 2014, with the help of an orthogonal system of laser strainmeters, directions «north-south» and «west-east», installed at the Mys Shul’tsa Marine Experimental Station, it was possible for a long time to escort the ferry from the moment it began to move from the port of Zarubino to the maximum possible observation distance. The primary information on the trajectory of the ferry was taken from the resource http://marinetraffic.com, which provides publicly available data on the position of vessels registered in the Automatic Identification System (AIS). Figure 1 shows spectrograms of synchronous recordings of two strainmeters.
The spectrograms shown in Fig. 1 have a duration of 7 h from two “north-south” and “west-east” strainmeters in the range of 20.5–22 Hz. The time on the spectrograms is counted from the beginning of the recording – 8:00 UTC. The arrows on the spectrograms indicate the times corresponding to the position of the vessel at the points marked on the trajectory of the ferry, shown in Fig. 2.
As can be seen from Figs. 1 and 2, the frequency tracks of the ferry are very clearly visible on the spectrograms of both strainmeters up to the turning point 7, after which they become less contrasting, but they can be traced very confidently up to the marker point 9–12:00 UTC, corresponding to the distance of the vessel from Mys Shul’tsa at 156 km. Taking into account the directive pattern of laser strainmeters [14, 17], the possibility of using a two-coordinate laser strainmeter to determine the direction of a moving vessel was investigated. When performing calculations, in accordance with [1, 5], it was assumed that the main displacements of the abutments of the strainmeters are caused by the Rayleigh-type surface waves. When calculating, we will take into account only the wave component oriented along the direction of wave propagation. First, we will carry out the calculations under the condition that the angle of direction to the source is between the “north-south” and “west-east” axes of the laser strainmeters (marker point position 1). The projections of the components oriented in the direction of wave propagation on the “north-south” and “west-east” axis of the laser strainmeters will be equal:
, (1)
, (2)
where: γ1 is the angle of direction to the source, measured from the north direction clockwise, A(1,1) and A(2,1) are the amplitudes at the frequency of the analyzed signal, obtained during spectral processing of the records of “north-south” and “west-east” laser strainmeters, when the ferry is at point 1, A(1) and A(2) are the “true” amplitude of the displacement of the particles of the medium, reduced to the length of the base of the “north-south” and “west-east” laser strainmeters, when the ferry is at point 1, α1 and α2 are the angles between axes of the “north-south” and “west-east” laser strainmeters and the north direction (198°).
Taking into account that Α(1) / Α(2) = 2,8, and expanding the cosines in equations (1) and (2), we have:
, (3)
where:
. (4)
When substituting (4) into (3) after simple transformations, we obtain:
. (5)
Further calculations are carried out under the condition that the angle of direction to the source is east of the axis of the “north-south” laser strainmeter (position of marker points 2–11). In this case, the projection of the component oriented in the direction of wave propagation on the axis of the laser strainmeters will be equal to:
, (6)
, (7)
where: γ1 and γi + 1 are the angles of direction to the source, measured from the north direction for i + 1 point, A(1, i + 1) and A(2, i + 1) are the amplitudes at the frequency of the analyzed signal, obtained by spectral processing of records of “north-south” and “west-east” laser strainmeters, when the ferry is at the marker point (i + 1), A(1) and A(2) are the “true” amplitude of displacement of the medium particles, reduced to the length of the base of the “north-south” and “west-east” laser strainmeters, when the ferry is at i + 1 point. Solving the system of equations (6) and (7) and taking into account the fact that A(1) / A(2) = 2.8, we obtain:
, (8)
After analyzing the calculation results, some errors were revealed in the values of the angles with the real direction of the source movement; this may be due to the propagation of signals from the ferry to the laser strainmeter. Let’s consider two possible cases of propagation:
The signal emitted by the ferry is captured by the sound channel and propagates through it to a depth of 35 m (approximately half the wavelength at a frequency of 21.5 Hz at a speed of 1500 m / s), and then the signal to the laser strainmeter propagates only along the “water-bottom” boundary in the form of a Rayleigh wave of the surface type of cylindrical divergence. Of course, the signal emitted by the ferry on the shelf begins to interact with the bottom earlier, but we do not know the depth of the location of the axis of the sound channel, so we will assume that the signal emitted by the ferry propagates along the “water-bottom” boundary to the laser strainmeter starting from a depth of 35 m, and does not propagate through the water.
In the absence of a sound channel, the signal generated by the ferry, according to the law of spherical divergence, propagates to the bottom, and then the signal to the laser strainmeter propagates along the “water-bottom” boundary in the form of a Rayleigh wave of the surface type of cylindrical divergence. Despite this, the method of determining the direction to the source using a system of orthogonal laser strainmeters gives quite good results.
DIRECTION FINDING OF DEFORMATION DISTURBANCES BY TRIANGULATION METHOD
Now we will consider a method for detecting an oscillation source using a spatially spaced system of several laser strainmeters. At the moment we have such a system consisting of three laser strainmeters. Laser strainmeters are located at Mys Shul’tsa, Primorsky Krai; Mys Svobodny, Sakhalin; Krasnokamensk, Trans-Baikal Territory. This method, the triangulation method is not new and is widely used in modern life, including in geolocation systems, but its use for finding a source using laser interference devices is discussed for the first time.
Let’s assume that we have a source of fluctuations of a natural or anthropogenic nature in the waters of the Sea of Japan. The sources of these vibrations can be underwater explosions, earthquakes, typhoons, abnormally large waves, etc. Let’s assume that vibrations from the source penetrate into the upper layer of the earth’s crust and propagate to the receiving points at an average speed of 2 km / s. Let’s set an arbitrary point on the map in the Sea of Japan, where the oscillating source is supposedly located. The distances from the source to the receiving points are as follows: Source – Mys Shul’tsa – 640 km, Source – Mys Svobodny – 1484 km, Source – Krasnokamensk – 1818 km. Then the time of arrival to each receiving point: Source – Mys Shul’tsa – 640 / 2 = 320 s, Source – Mys Svobodny – 1484 / 2 = 742 s, Source – Krasnokamensk – 1818 / 2 = 909 s. Considering that the oscillations will come to the point Mys Shul’tsa first, then we consider this point as the zero mark, then the propagation times to the remaining points will be as follows: Mys Shul’tsa – 0 s, Mys Svobodny – 742–320 = 422 s, Krasnokamensk – 909–320 = 589 s.
Let’s calculate the direction to the source along the Mys Shul’tsa – Mys Svobodny propagation path. To do this, draw 2 circles with the center at the point Mys Shul’tsa point with a radius of 1000 and 1200 km. We calculate the distance taking into account the propagation time from Mys Shul’tsa to Mys Svobodny 422 · 2 = 844 km. Next, draw 2 circles with the center at the point Mys Svobodny with a radius of 1000 + 844 = 1 844 km and 1200 + 844 = 2044 km. At the intersections of the circles, draw 2 directions to the source (green lines).
As you can see from Fig. 3, two directions to the source were received, one of them being true and the other false. A false direction to the source will be excluded in further calculations.
Let’s calculate the direction to the source along the Mys Shul’tsa – Krasnokamensk propagation path. Draw 2 circles with the center at the Mys Shul’tsa point with a radius of 1000 and 1200 km. The arrival time of the wave from Mys Shul’tsa to Krasnokamensk is 589 s. The distance taking into account the propagation time from Mys Shul’tsa to Krasnokamensk 589 · 2 = 1 178 km. We draw 2 circles with the center at the Krasnokamensk point with a radius of 1000 + 1178 = 2178 km and 1200 + 1178 = 2378 km. At the intersections of the circles, draw 2 directions to the true source (red lines).
In Fig. 4, two directions intersect, respectively, they are true, the other two directions are removed as false.
We calculate the direction to the source along the Mys Svobodny – Krasnokamensk propagation path. Draw 2 circles with the center at the Mys Svobodny point with a radius of 1000 and 1200 km. We calculate the distance taking into account the propagation time (589 – 422 = 167 s) from Mys Svobodny to Krasnokamensk 167 · 2 = 334 km. We draw 2 circles with the center at the Krasnokamensk point with a radius of 1000 + 334 = 1334 km and 1200 + 334 = 1534 km. At the intersections of the circles, draw the direction to the true source (purple line).
In Fig. 5 it can be seen that the directions intersect at one point, this intersection point will be the location of the source.
CONCLUSION
This paper presents several methods for determining the direction and location of oscillating sources of natural and anthropogenic origin, using systems consisting of several laser strainmeters.
When using an orthogonal system of directed laser strainmeters, the error in determining the direction to the source ranges from 0.2% to 16.5%. At the same time, as expected, the maximum errors are associated with the movement of the ferry in shallow water (the length of the hydroacoustic wave at a frequency of 20 Hz is about 75 m). The use of the third axis – the vertical one – can reduce the error. A significant contribution to the error is made by the features of the transformation of hydroacoustic waves at the “water-bottom” boundary and the conversion of their energy into the energy of Rayleigh-type waves propagating along the “water-bottom” boundary, as well as various other waves (longitudinal and transverse, Stoneley and Love waves). Taking into account all the features is possible only with accurate knowledge of the structure of the seabed and characteristics of the seabed rocks, the angle of inclination of the seabed, etc., which the author does not currently have. After carrying out a number of experimental works to determine the elastic parameters of the seabed and build its acoustic model, it is possible to more accurately solve the problem of the direction finding of a surface vessel. The advantage of this method is finding the system of laser strainmeters at one point, which is an advantage over distributed systems of strainmeters.
Spatially separated systems of laser strainmeters have higher accuracy in determining the location of the source, and with the use of a larger number of measuring stations distributed in space, the accuracy will increase. The main error in this method is the isotropy and composition of the propagation medium of the recorded oscillations. For example, for Rayleigh waves in different materials, the propagation velocity can vary within wide limits, which can create significant errors in determining the location of the source. It is also possible that geological anomalies can be found on the path of propagation of oscillations from one measurement point to another, which will not allow the use of this method. In this regard, the installation of laser strainmeters should be carried out in places with a previously known and well-studied geological structure along the directions of propagation of oscillations from one measurement point to another.
Source of financing. The research was carried out at the expense of the Ministry of Science and Higher Education (the topic of the state assignment “Studying the fundamental principles of the origin, development, transformation, and interaction of hydroacoustic, hydrophysical and geophysical fields in the World Ocean”).
Information about the authors
Grigory Ivanovich Dolgikh, Doctor of Physical and Mathematical Sciences, Academician of the Russian Academy of Sciences, dolgikh@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0002-2806-3834
Stanislav Grigorievich Dolgikh, Cand. of Physical and Mathematical Sciences, sdolgikh@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-9828-5929
Vladimir Alexandrovich Chupin, Cand. of Physical and Mathematical Sciences, chupin@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-5103-8138
Sergey Budrin, ss_budrin@mail.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-7462-9459
G. I. Dolgikh, S. S. Budrin, S. G. Dolgikh, V. A. Chupin
V. I. Il’ichev Pacific Oceanological Institute Far Eastern Branch Russian Academy of Sciences, Vladivostok, Russia
Two methods of direction finding of geosphere sources of oscillations and waves of infrasonic and low-frequency sound ranges by laser strainmeters are considered. The first method is based on the assumption that the recorded wave disturbances refer to surface waves of the Rayleigh type. In this case, a two- coordinate laser strainmeter is used, which consists of adjacent one- coordinate laser strainmeters with mutually perpendicular measuring arms. In the second case, the triangulation method is used. This method uses a minimum of three spatially separated laser strainmeters.
Keywords: two-coordinate laser strainmeter, spatially separated laser strainmeters, direction finding, triangulation
Article received: 17.11.2021
Article accepted: 02.12.2021
INTRODUCTION
The problems of monitoring and determining the location of various sources of anthropogenic and natural origin using laser interference methods are solved using an integrated approach that takes into account both the directivity and the spatial distribution of measuring systems. In our case, several methods can be used to solve the problem of detecting and determining the location of oscillating sources. The first method consists in using an orthogonal system of laser strainmeters, the second method is based on the use of three or more spaced laser strainmeters having the same directivity.
The first method is based on the assumption of a known polarization of the recorded wave processes. Such well-known polarization signals include seismoacoustic signals arising at the water-bottom boundary as a result of the transformation of sonar signals generated in the water by a low-frequency underwater sound projector and moving underwater and surface objects. For the first time, the ability to track the movement of a source of geospheric disturbances using a laser strainmeter was described in paper [1], in which a record of a 105‑meter laser strainmeter was given, containing seismoacoustic waves modulated by gravitational sea waves generated at the “water-bottom” boundary by a moving surface vessel. Variations in the modulation parameters in this record can be used to estimate the change in the direction of the ship’s movement. Another type of amplitude modulation of underwater noise emission from sea vessels is currently widely used in practice for their classification [2]. In paper [3], it was shown that in the low-frequency region, seismoacoustic surface waves become the dominant mechanism for the transfer of acoustic energy in the shallow-water shelf zone of the sea.
Experimental studies of comparative levels of acoustic noise recorded by hydrophones and bottom geophones [3] have shown that on the shallow shelf at frequencies below 25 Hz, a decrease is observed in the spectrum of hydrophone records, and an increase in the level of spectral components in the spectrum of geophone records. This behavior depends on the ratio of sonar wavelength to sea depth. At depths less than half the length of the hydroacoustic wave, conditions arise under which almost all of the hydroacoustic energy is transformed into elastic vibrations of the bottom, recorded by a coastal laser strainmeter [4]. These depths have been called critical depths. In the earth’s crust, these disturbances propagate mainly in the form of Rayleigh-type surface waves. This condition can be used for registration and direction finding of such disturbances with a two-coordinate laser strainmeter consisting of two one-coordinate laser strainmeters with almost mutually perpendicular measuring arms installed at Mys Shul’tsa [5].
Not always recorded disturbances can be represented in the form of the Rayleigh-type surface waves. For example, deformation jumps recorded by distant laser strainmeters [6] and which are an unconditional indicator of the occurrence of seabed movements [7] leading to a tsunami cannot be attributed to Rayleigh-type surface waves in any way. Therefore, it is impossible to use the polarization properties of surface waves for their direction finding. For this, the triangulation method, which is based on the use of three or more spatially separated laser strainmeters, is fitting better. This system includes strainmeters described in work [8]. In the second part of the article, using the example of a recording of deformation disturbances of various origins, the features of the triangulation method of direction finding by these laser strainmeters will be considered.
DIRECTION FINDING OF DEFORMATION DISTURBANCES BY A TWO-COORDINATE LASER STRAINMETER
On June 3, 2014, with the help of an orthogonal system of laser strainmeters, directions «north-south» and «west-east», installed at the Mys Shul’tsa Marine Experimental Station, it was possible for a long time to escort the ferry from the moment it began to move from the port of Zarubino to the maximum possible observation distance. The primary information on the trajectory of the ferry was taken from the resource http://marinetraffic.com, which provides publicly available data on the position of vessels registered in the Automatic Identification System (AIS). Figure 1 shows spectrograms of synchronous recordings of two strainmeters.
The spectrograms shown in Fig. 1 have a duration of 7 h from two “north-south” and “west-east” strainmeters in the range of 20.5–22 Hz. The time on the spectrograms is counted from the beginning of the recording – 8:00 UTC. The arrows on the spectrograms indicate the times corresponding to the position of the vessel at the points marked on the trajectory of the ferry, shown in Fig. 2.
As can be seen from Figs. 1 and 2, the frequency tracks of the ferry are very clearly visible on the spectrograms of both strainmeters up to the turning point 7, after which they become less contrasting, but they can be traced very confidently up to the marker point 9–12:00 UTC, corresponding to the distance of the vessel from Mys Shul’tsa at 156 km. Taking into account the directive pattern of laser strainmeters [14, 17], the possibility of using a two-coordinate laser strainmeter to determine the direction of a moving vessel was investigated. When performing calculations, in accordance with [1, 5], it was assumed that the main displacements of the abutments of the strainmeters are caused by the Rayleigh-type surface waves. When calculating, we will take into account only the wave component oriented along the direction of wave propagation. First, we will carry out the calculations under the condition that the angle of direction to the source is between the “north-south” and “west-east” axes of the laser strainmeters (marker point position 1). The projections of the components oriented in the direction of wave propagation on the “north-south” and “west-east” axis of the laser strainmeters will be equal:
, (1)
, (2)
where: γ1 is the angle of direction to the source, measured from the north direction clockwise, A(1,1) and A(2,1) are the amplitudes at the frequency of the analyzed signal, obtained during spectral processing of the records of “north-south” and “west-east” laser strainmeters, when the ferry is at point 1, A(1) and A(2) are the “true” amplitude of the displacement of the particles of the medium, reduced to the length of the base of the “north-south” and “west-east” laser strainmeters, when the ferry is at point 1, α1 and α2 are the angles between axes of the “north-south” and “west-east” laser strainmeters and the north direction (198°).
Taking into account that Α(1) / Α(2) = 2,8, and expanding the cosines in equations (1) and (2), we have:
, (3)
where:
. (4)
When substituting (4) into (3) after simple transformations, we obtain:
. (5)
Further calculations are carried out under the condition that the angle of direction to the source is east of the axis of the “north-south” laser strainmeter (position of marker points 2–11). In this case, the projection of the component oriented in the direction of wave propagation on the axis of the laser strainmeters will be equal to:
, (6)
, (7)
where: γ1 and γi + 1 are the angles of direction to the source, measured from the north direction for i + 1 point, A(1, i + 1) and A(2, i + 1) are the amplitudes at the frequency of the analyzed signal, obtained by spectral processing of records of “north-south” and “west-east” laser strainmeters, when the ferry is at the marker point (i + 1), A(1) and A(2) are the “true” amplitude of displacement of the medium particles, reduced to the length of the base of the “north-south” and “west-east” laser strainmeters, when the ferry is at i + 1 point. Solving the system of equations (6) and (7) and taking into account the fact that A(1) / A(2) = 2.8, we obtain:
, (8)
After analyzing the calculation results, some errors were revealed in the values of the angles with the real direction of the source movement; this may be due to the propagation of signals from the ferry to the laser strainmeter. Let’s consider two possible cases of propagation:
The signal emitted by the ferry is captured by the sound channel and propagates through it to a depth of 35 m (approximately half the wavelength at a frequency of 21.5 Hz at a speed of 1500 m / s), and then the signal to the laser strainmeter propagates only along the “water-bottom” boundary in the form of a Rayleigh wave of the surface type of cylindrical divergence. Of course, the signal emitted by the ferry on the shelf begins to interact with the bottom earlier, but we do not know the depth of the location of the axis of the sound channel, so we will assume that the signal emitted by the ferry propagates along the “water-bottom” boundary to the laser strainmeter starting from a depth of 35 m, and does not propagate through the water.
In the absence of a sound channel, the signal generated by the ferry, according to the law of spherical divergence, propagates to the bottom, and then the signal to the laser strainmeter propagates along the “water-bottom” boundary in the form of a Rayleigh wave of the surface type of cylindrical divergence. Despite this, the method of determining the direction to the source using a system of orthogonal laser strainmeters gives quite good results.
DIRECTION FINDING OF DEFORMATION DISTURBANCES BY TRIANGULATION METHOD
Now we will consider a method for detecting an oscillation source using a spatially spaced system of several laser strainmeters. At the moment we have such a system consisting of three laser strainmeters. Laser strainmeters are located at Mys Shul’tsa, Primorsky Krai; Mys Svobodny, Sakhalin; Krasnokamensk, Trans-Baikal Territory. This method, the triangulation method is not new and is widely used in modern life, including in geolocation systems, but its use for finding a source using laser interference devices is discussed for the first time.
Let’s assume that we have a source of fluctuations of a natural or anthropogenic nature in the waters of the Sea of Japan. The sources of these vibrations can be underwater explosions, earthquakes, typhoons, abnormally large waves, etc. Let’s assume that vibrations from the source penetrate into the upper layer of the earth’s crust and propagate to the receiving points at an average speed of 2 km / s. Let’s set an arbitrary point on the map in the Sea of Japan, where the oscillating source is supposedly located. The distances from the source to the receiving points are as follows: Source – Mys Shul’tsa – 640 km, Source – Mys Svobodny – 1484 km, Source – Krasnokamensk – 1818 km. Then the time of arrival to each receiving point: Source – Mys Shul’tsa – 640 / 2 = 320 s, Source – Mys Svobodny – 1484 / 2 = 742 s, Source – Krasnokamensk – 1818 / 2 = 909 s. Considering that the oscillations will come to the point Mys Shul’tsa first, then we consider this point as the zero mark, then the propagation times to the remaining points will be as follows: Mys Shul’tsa – 0 s, Mys Svobodny – 742–320 = 422 s, Krasnokamensk – 909–320 = 589 s.
Let’s calculate the direction to the source along the Mys Shul’tsa – Mys Svobodny propagation path. To do this, draw 2 circles with the center at the point Mys Shul’tsa point with a radius of 1000 and 1200 km. We calculate the distance taking into account the propagation time from Mys Shul’tsa to Mys Svobodny 422 · 2 = 844 km. Next, draw 2 circles with the center at the point Mys Svobodny with a radius of 1000 + 844 = 1 844 km and 1200 + 844 = 2044 km. At the intersections of the circles, draw 2 directions to the source (green lines).
As you can see from Fig. 3, two directions to the source were received, one of them being true and the other false. A false direction to the source will be excluded in further calculations.
Let’s calculate the direction to the source along the Mys Shul’tsa – Krasnokamensk propagation path. Draw 2 circles with the center at the Mys Shul’tsa point with a radius of 1000 and 1200 km. The arrival time of the wave from Mys Shul’tsa to Krasnokamensk is 589 s. The distance taking into account the propagation time from Mys Shul’tsa to Krasnokamensk 589 · 2 = 1 178 km. We draw 2 circles with the center at the Krasnokamensk point with a radius of 1000 + 1178 = 2178 km and 1200 + 1178 = 2378 km. At the intersections of the circles, draw 2 directions to the true source (red lines).
In Fig. 4, two directions intersect, respectively, they are true, the other two directions are removed as false.
We calculate the direction to the source along the Mys Svobodny – Krasnokamensk propagation path. Draw 2 circles with the center at the Mys Svobodny point with a radius of 1000 and 1200 km. We calculate the distance taking into account the propagation time (589 – 422 = 167 s) from Mys Svobodny to Krasnokamensk 167 · 2 = 334 km. We draw 2 circles with the center at the Krasnokamensk point with a radius of 1000 + 334 = 1334 km and 1200 + 334 = 1534 km. At the intersections of the circles, draw the direction to the true source (purple line).
In Fig. 5 it can be seen that the directions intersect at one point, this intersection point will be the location of the source.
CONCLUSION
This paper presents several methods for determining the direction and location of oscillating sources of natural and anthropogenic origin, using systems consisting of several laser strainmeters.
When using an orthogonal system of directed laser strainmeters, the error in determining the direction to the source ranges from 0.2% to 16.5%. At the same time, as expected, the maximum errors are associated with the movement of the ferry in shallow water (the length of the hydroacoustic wave at a frequency of 20 Hz is about 75 m). The use of the third axis – the vertical one – can reduce the error. A significant contribution to the error is made by the features of the transformation of hydroacoustic waves at the “water-bottom” boundary and the conversion of their energy into the energy of Rayleigh-type waves propagating along the “water-bottom” boundary, as well as various other waves (longitudinal and transverse, Stoneley and Love waves). Taking into account all the features is possible only with accurate knowledge of the structure of the seabed and characteristics of the seabed rocks, the angle of inclination of the seabed, etc., which the author does not currently have. After carrying out a number of experimental works to determine the elastic parameters of the seabed and build its acoustic model, it is possible to more accurately solve the problem of the direction finding of a surface vessel. The advantage of this method is finding the system of laser strainmeters at one point, which is an advantage over distributed systems of strainmeters.
Spatially separated systems of laser strainmeters have higher accuracy in determining the location of the source, and with the use of a larger number of measuring stations distributed in space, the accuracy will increase. The main error in this method is the isotropy and composition of the propagation medium of the recorded oscillations. For example, for Rayleigh waves in different materials, the propagation velocity can vary within wide limits, which can create significant errors in determining the location of the source. It is also possible that geological anomalies can be found on the path of propagation of oscillations from one measurement point to another, which will not allow the use of this method. In this regard, the installation of laser strainmeters should be carried out in places with a previously known and well-studied geological structure along the directions of propagation of oscillations from one measurement point to another.
Source of financing. The research was carried out at the expense of the Ministry of Science and Higher Education (the topic of the state assignment “Studying the fundamental principles of the origin, development, transformation, and interaction of hydroacoustic, hydrophysical and geophysical fields in the World Ocean”).
Information about the authors
Grigory Ivanovich Dolgikh, Doctor of Physical and Mathematical Sciences, Academician of the Russian Academy of Sciences, dolgikh@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0002-2806-3834
Stanislav Grigorievich Dolgikh, Cand. of Physical and Mathematical Sciences, sdolgikh@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-9828-5929
Vladimir Alexandrovich Chupin, Cand. of Physical and Mathematical Sciences, chupin@poi.dvo.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-5103-8138
Sergey Budrin, ss_budrin@mail.ru; V. I. Ilyichev Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia.
ORCID: 0000-0001-7462-9459
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