CN102062868A - Positioning and back-tracking method for earthquake electromagnetic wave source in ionized layer - Google Patents
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Abstract
The invention discloses a positioning and back-tracking method for an earthquake electromagnetic wave source in an ionized layer, and relates to electromagnetic wave technology. By the method, a radiation source is positioned according to a received signal on a satellite. In the ionized layer, a route of an electromagnetic wave is determined by a Haselgrove differential equation at a similar high frequency; according to the equation, influences on the transmission route by the anisotropism and the dispersivity of the ionized layer are taken into consideration. The theory of the algorithm comprises that: an arithmetic solution of a ray equation is calculated by making use of the value technology; during calculation, the precision is controlled. In the actual operation, the actually measured electronic concentration of the ionized layer can be used. The effectiveness of the algorithm is verified by the actually measured data. The method can be applied to position of the radiation source in the ionized layer and also applied to position of a sound wave source in the ocean.
Description
Technical Field
The invention relates to the technical field of electromagnetic waves, in particular to a seismic electromagnetic wave source positioning and back tracking method in an ionosphere.
Background
As early as the fifties and sixties of the last century, people begin earthquake electromagnetic research, and after more than forty years of continuous efforts, people have acquired a large amount of electromagnetic abnormal phenomena related to earthquakes, and the research on the subject has important significance for short-term earthquake prediction. These electromagnetic precursors are present both on the ground and at high altitudes, but are also of greater interest mainly due to electromagnetic anomalies in the ionosphere and magnetic layers, mainly because anomalies in high altitudes are less subject to interference and pollution and are easier to detect and track by means of space and remote sensing techniques.
The earth's ionosphere is an important component of the near-earth space environment, and according to the Institute of Electrical and Electronics Engineers (IEEE) standard (1969), the ionosphere is "a portion of the earth's atmosphere in which particles and electrons are present in quantities large enough to affect the propagation of radio waves". By this definition, the ionosphere is approximately the entire space between above 60km above the ground to the top of the magnetic layer. The propagation of electromagnetic waves in the ionosphere is mainly related to the electron concentration profile of the ionosphere, the collision frequency of the ionosphere and the distribution of the magnetic field in the ionosphere.
Vector antennas have been developed for the direct measurement of individual components of electromagnetic fields in order to obtain the propagation direction of electromagnetic waves in space, these vector antennas recording in real time the amplitude and phase values of the individual components of the electric and magnetic fields. In order to extract wave propagation information (including polarization information and wave vector direction) from these raw measurement data, several efficient wave vector analysis algorithms (such as Means algorithm, SVD technique of spectrum matrix, etc.) have been developed.
Disclosure of Invention
The invention aims to disclose a seismic electromagnetic wave source positioning and back tracking method in an ionosphere, which is a high-precision and fast algorithm to search a radiation source of space radio waves.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for locating and backward tracing the source of earthquake electromagnetic wave in ionized layer features that the ray tracing of ionized layer is carried out by receiving the incoming wave direction, frequency and propagation medium of electromagnetic wave, and the ray equation is numerically solved to locate the radiation source; which comprises the following steps:
A) theoretical derivation:
(a) the equation describing the wave propagation path is a Hasegrove equation, the equation is rewritten into a form suitable for numerical solution, and the first-order partial derivative of the refractive index to each variable is solved;
(b) selecting a proper numerical method to solve the ray equation and deducing a specific iteration format;
B) computer programming, ionospheric ray tracing software:
(a) compiling computer software for calculating wave propagation in the ionized layer according to the theoretical derivation result in the step A);
(b) extracting the initial propagation direction of the wave from the measured data of the vector antenna;
(c) because the propagation path of the wave has reversibility, the initial direction of the receiving point is reversed, and backward tracking is carried out as one of the initial conditions of software calculation;
(d) setting other initial conditions calculated by the software: receiving the position of the point, the calculated tolerance, the tracked cutoff condition;
C) determining the epicenter position:
the tracked cut-off point is the wave source of the radiation source in space, and the mid-seismic position is determined by using the cut-off point.
In the method, the step B) directly carries out numerical solution on the three-dimensional Haselegorve equation so as to avoid the influence of the dispersion of the earth magnetic field and the ionized layer on the wave propagation path and enable the path to be more accurate.
The method, wherein step B) corrects the node values when the current node advances to the next node according to an integration algorithm to avoid accumulation of errors.
The method adopts a variable step length technology in the step B), the variable step length technology fully considers the spatial gradient of the refractive index of the medium, the step length is small at the place with large gradient, and the step length is large at the place with small gradient, so as to ensure the tracking precision.
The method, wherein the tracking cutoff condition in said step B) is the peak height at F2 level in the ionosphere.
In the step C), the epicenter position is determined by using the cut-off point, and after the cut-off point is tracked, the cut-off point is projected to the ground along the magnetic line of the earth magnetic field, and the projected point is the epicenter position.
The method is characterized in that a vector antenna is utilized to obtain multi-component electromagnetic field data, and frequency, incoming wave direction and polarization characteristic information are extracted according to a wave vector analysis algorithm.
The integration algorithm of the method is Runge-Kutter algorithm and Adams-Moulton algorithm.
The method, the step-length-changing technology, automatically adjusts the step length according to the gradient of the medium by the following formula:
where k is a constant of proportionality, the value of k is generally determined empirically and with the accuracy of the tracing, and in practice, a suitable value (generally between 10) may be selected by running the ray tracing program repeatedly-3And 10-5In between). When the gradient of the refractive index along the ray path is small, namely the change of the refractive index is gentle, the step length is large; conversely, when the refractive index changes dramatically along the ray path, the step size decreases automatically;
at the same time, an upper limit step is set for the step lengthmaxAnd lower limit stepminWhen the step length calculated according to the above formula is out of the range, the upper limit step length is set asThe lower limit step size is taken as the actual step size value.
The wave vector analysis algorithm of the method is an SVD technology of Means algorithm and spectrum matrix.
The method is a high-precision and rapid algorithm, effectively controls the tracking error and can accurately position the seismic area.
Drawings
FIG. 1 is a schematic diagram of a coordinate system calculated by a seismic electromagnetic wave source location and back tracking method in an ionosphere according to the present invention; wherein:
FIG. 1(a) is a spherical coordinate system used in the calculation of the present invention;
FIG. 1(b) is an enlarged view of the local coordinate system of point P;
FIG. 2 is a flow chart of ionospheric ray-tracing software for a method of locating and back-tracking a seismic electromagnetic wave source in the ionosphere according to the present invention.
Detailed Description
The invention discloses a method for positioning and backward tracking a seismic electromagnetic wave source in an ionosphere, which is a method for tracking high-altitude electromagnetic anomalies, and can track and obtain the spatial position of a radiation source generating the anomalies. These a priori information of the ionosphere must be obtained before the method of the present invention can be utilized. The method is a precondition and a basis for implementing the method by extracting the initial direction of the wave from the original measured data of the vector antenna by Means of the existing wave vector analysis algorithm (such as the Means algorithm, the SVD technology of the spectrum matrix, and the like), and the disclosed wave vector analysis algorithms are not a discussion range of the invention per se and are not repeated herein. Before applying the method of the invention, the following information has been obtained by default:
(a) the initial propagation direction of the wave is obtained through a wave vector analysis algorithm;
(b) three-dimensional structure information N (h, θ,
) Is known, where N is the ionosphere electron concentration in meters-3H is height (m), θ and
polar and azimuth angles, i.e. geographical latitude and longitude, respectively, in a calculated coordinate system (see below).
Fig. 1 is a schematic diagram of a coordinate system calculated by the seismic electromagnetic wave source positioning and back tracking method in the ionosphere according to the present invention. FIG. 1(a) is a spherical coordinate system used in the calculation of the present invention; FIG. 1(b) is an enlarged view of the local coordinate system of point P;
the coordinate system calculated by the method of the invention is as follows:
in order to represent the ray path and the propagation direction of the wave, a coordinate system must be established. A calculation coordinate system (spherical coordinate system) is established with the earth center O as the origin and the rotation axis of the earth as the z-axis, as shown in fig. 1 (a). In this coordinate system, a certain point P on the ray path is characterized by 3 parameters: r, θ, φ. To characterize the direction of wave propagation at point P (i.e. wave vector)
Direction) of the point P, a local rectangular coordinate system is established at the point P
In this coordinate system, it is possible to use,the direction indicates the direction of the OP connection line,
the direction represents the true south direction of point P, and
the direction represents the righteast direction of point P, see fig. 1 (b). Wave vector at point PThe direction of (a) can be determined by two parameters (theta) in a local rectangular coordinate systemk，φk) And may also be characterized by the elevation angle alpha and the azimuth angle beta of point P (these two angles will be used later). Elevation angle alpha is rotated from the horizontal to the wave vector
The angle of (1) is in the range of 0-90 degrees; the azimuth angle beta is rotated clockwise from the true north direction to
The projection angle on the horizontal plane ranges from 0 degree to 360 degrees. Thus, θk，φkAnd α, β is θk＝π/2-α，φk＝π-β。
In the high frequency approximation, the propagation path of the wave is described by a ray. When the influence of the earth magnetic field on the propagation of electromagnetic waves is considered, the ionosphere shows anisotropy, and the energy direction and the wave vector direction of rays do not completely coincide but form an included angle. In 1955, j.hasegrove derived a ray equation suitable for computer solution:
where r, θ, φ is the coordinate of a point P on the ray path in spherical coordinates, ρr，ρθ，ρφIs the refractive index of the P point along the wave vector direction in 3 components in the spherical coordinate system (satisfy) The argument t can be any parameter that increases monotonically along the ray path (since t is not explicitly included to the right of the equation), and n is the refractive index of the medium (mainly the ionosphere). Due to r, theta, phi and rhor，ρθ，ρφCoupled together, r, θ, φ cannot be found separately, but must be aligned aboveThe 6 equations of (a) are solved simultaneously.
The equation set (1 a-f) is an equation set formed by 6 first-order differential equations, and the principle of ray tracing is to solve the equations numerically and finally obtain a complete ray trajectory description. Prior to solving, the right side of equations (1 a-f) must be written as the quantities r, θ, φ, ρ to be solvedr，ρθ，ρφAnd explicit functions of the argument t. Mathematically, that is, the system of equations (1 a-f) is transformed into the following initial value problem:
for such initial value problems, more sophisticated algorithms have been developed mathematically, such as the classical fourth-order Runge-Kutter algorithm, Adams-Moulton prediction correction system, and so on. These algorithms are well known and are not described in detail in the present invention.
In ionosphere applications, the refractive index n is represented by the Appleton-Hartree equation (hereinafter abbreviated as the A-H equation):
YT＝Y sin Θ (3)
YL＝Y cos Θ
wherein
fNAnd fHRespectively plasma frequency of ionized layer and electron cyclotron frequency caused by geomagnetic field, f is frequency of tracked wave, theta is included angle between wave vector direction and geomagnetic field, YTAnd YLRespectively representing a lateral component of Y perpendicular to the wave vector and a longitudinal component parallel to the wave vector. In practical application, fNThe ionosphere detection data can be obtained by actually measured ionosphere detection data, and can also be obtained by an ionosphere experience mode; f. ofHObtained from empirical modes of the earth-magnetic field (e.g., international earth-magnetic field reference model IGRF, dipole model, etc.); f can be extracted from the measured data of the vector antenna (according to the existing wave vector analysis algorithm). And the signs in the denominator of equation (3) correspond to the normal mode and the extraordinary mode in ionospheric wave propagation, respectively. In thatThe refractive index at a given point in space is a function of direction only, which manifests as dielectric anisotropy, while ionospheric anisotropy is due to the earth's magnetic field. The following describes how to adjust the refractive index n and its partial derivatives
(eta represents 3 position coordinates r, theta, phi) is expressed as 6 to-be-solved quantities r, theta, phi and rhor，ρθ，ρφExplicit function of (2).
1. Refractive index n
The direction of the refractive index n represents the wave vector direction and therefore has the following expression:
in the above formula YηRepresenting Y in a spherical coordinate system3 components, the expressions of which will be given later. Will YT，YLBy substituting the expression of (a) into the formula a-H, the refractive index can be expressed as:
D＝2(1-X)-YT 2+R (8a，b，c)
2. partial derivative of
The following describes how the derivative of the square of the refractive index versus the position variable is expressed as an explicit function of the quantity to be sought:
and is also provided with
WhileAnd
it can be found from the electron concentration profile of the ionosphere and a magnetic field model, which will be given later.
3. Partial derivative of
4. Electron concentration model of ionosphere
In practical implementation, the electron concentration model adopts a Chapman function:
wherein f iscFor the critical frequency at the equator, 6.5MHz, 300km, 62km, H representing the height from the ground, may be used. In computing the coordinate system, the height may be expressed as:
h＝r-Re (17)
r represents the distance to the center of the earth, ReThe earth radius is taken as 6370 km. As appearing in the preceding formula (9)
Can be expressed as:
5. geomagnetic field model
The earth's magnetic field is approximated by a dipole model, the electron cyclotron frequency can be expressed as:
wherein,
an electron cyclotron frequency on the equatorial ground of about 0.85 MHz; theta is a polar angle of a calculation coordinate system, and is equivalent to geomagnetic complementary weft under a dipole model. (9) The partial derivative with respect to Y where formula occurs is:
(13) the various components of Y in the calculated coordinate system and their derivatives appear in the equation:
6. setting of initial conditions for tracking:
having expressed the system of equations (1 a-f) in the form of (2a), it is necessary to also give the initial conditions in the form of (2b), i.e., r, θ, φ, ρr，ρθ，ρφThe initial value of (c). The first 3 quantities represent the starting point of tracking, and are input into the spherical coordinate system0Coordinate (r) of0，θ0，φ0) Then the method is finished; the latter 3 quantities represent 3 components of the refractive index n in the local coordinate system (see fig. 1) in the direction of the incoming wave at the starting point. Suppose that the elevation angle and the azimuth angle of the incoming wave direction at the starting point are respectively alpha0，β0To back-track the source (in terms of reversibility of the ray path), the initial point of tracking isThe initial direction is set to-alpha0，-β0If the refractive index along this direction is normalized to 1, then 3 components can be expressed as:
ρr0＝sin(-α0)，ρθ0＝-cos(-α0)cos(-β0)，ρφ0＝cos(-α0)sin(-β0) (28)
since only the direction of the refractive index is considered here and not the magnitude of the refractive index, in the actual calculation, a correction should be made to the magnitude value of the above-mentioned initial value: calculating the (-alpha) along using the formula A-H0，-β0) The refractive index in the direction n is the corrected initial value
In fact, when the current node advances to the next node according to Runge-Kutter integral algorithm (or other similar integral algorithm), the rho corresponding to the next node is neededηThe value is corrected so that accumulation of errors is avoided.
7. Step-size-changing technique in tracking:
in many of the disclosed ray tracing algorithms, the fixed step is used in solving equation (1), when the electron concentration of the ionosphere along the ray path changes greatly (for example, at the reflection point of the ray), the fixed step easily causes the errors in the ray path and the wave vector direction to be large, and in severe cases, the square of the refractive index becomes negative (in the a-H formula, when the frequency of the wave is less than the plasma frequency of the ionosphere, the wave is cut off along some directions, and the square of the refractive index along the directions which cannot propagate is negative.) to solve this problem, the method of the present invention introduces a variable step technique, that is, during the integration process of the differential direction group (1), the step is automatically adjusted according to the gradient of the medium:
10、
where k is a constant of proportionality, the value of k is generally determined empirically and with the accuracy of the tracing, and in practice, a suitable value (generally between 10) may be selected by running the ray tracing program repeatedly-3And 10-5In between). When the gradient of the refractive index along the ray path is small, namely the change of the refractive index is gentle, the step length is large; conversely, when the refractive index changes dramatically along the ray path, the step size decreases automatically;
at the same time, an upper limit step is set for the step lengthmaxAnd lower limit stepminWhen the step calculated according to the above formula is out of this range, the upper limit step or the lower limit step is taken as the actual step value.
8. The tracked cutoff conditions are:
when the peak height of F2 layer of ionosphere (300-350 km is typical) is tracked, the tracking is stopped. The plasma frequency at the peak height of the F2 layer is a maximum where the electrokinetic properties are complex and various types of plasma instabilities excite electromagnetic waves with different propagation characteristics. It is reasonable to set the peak height of the F2 layer as the cutoff condition for tracking in the method of the present invention.
9. Positioning of ground wave source or epicenter:
after stopping tracking at layer F2, the magnetic lines along the cutoff point are mapped to the ground, and this point is the source of the epicenter or ground wave. A number of theoretical calculations indicate that the effect of the seismic epicenter on the ionosphere is mapped by the magnetic field lines. The angle reflecting the inclination of the magnetic line is the magnetic inclination angle I, and the relationship between the geomagnetic latitude Λ is tan I ═ 2tan Λ, and the larger the latitude, the larger the magnetic inclination angle is, meaning that the offset between the tracking cut-off point and the epicenter region of the F2 layer is smaller. Whereas in the low latitude or equatorial region, the tracking cut-off point for the F2 layer may be greatly offset from the actual epicenter region due to the smaller declination angle. For a detailed discussion of this problem, reference may be made to the monosphere procurators of earthquates, both of the U.S. pulines and K.Boyarchuk treatises, from which many of the theoretical bases of the method of the present invention may be derived, and further description is omitted here.
In summary, the present invention provides a method for locating and backward tracking a seismic electromagnetic wave source in an ionosphere, comprising the steps of:
(a) the equation describing the propagation path of the wave is the hasegrove equation, which is rewritten to a form suitable for numerical solution, the key being to find the first partial derivative of the refractive index for each variable. This step belongs to theoretical derivation work.
(b) And (4) selecting a proper numerical method to solve the ray equation and deducing a specific iteration format. This step also belongs to theoretical analysis work.
(c) And compiling computer software for calculating wave propagation in the ionized layer according to theoretical derivation results of the previous steps. This step belongs to the computer programming work.
(d) The initial propagation direction of the wave is extracted from the measured data of the vector antenna (using an existing, published wave vector analysis algorithm).
(e) Since the propagation path of the wave (i.e. the ray path) has reversibility, the initial direction of the receiving point is reversed (meaning "backward" tracing) as one of the initial conditions of the software calculation.
(f) Setting other initial conditions calculated by the software: the location of the receiver points, the tolerance of the calculations (reflecting the accuracy of the tracking), the cutoff condition for the tracking (height of the peak at layer F2 in the ionosphere), etc.
(g) The cutoff point of tracking is the source of the radiation source in space. For the actual earthquake epicenter prediction problem, the tracked cut-off point can be projected to the ground along the magnetic line of the earth magnetic field, and the projected point is the possible epicenter position calculated by the method.
The algorithm of the present invention has been implemented in the Fortran language. The user inputs the location (longitude, latitude and altitude), frequency, initial wave vector direction, tracking tolerance, and electron concentration profile of the receiving point, and the program can calculate the wave vector direction on the outgoing line path and the path using the algorithm proposed by the method of the present invention. In addition, the algorithm has very flexible universality, namely, a user can customize the electron concentration profile of the ionosphere (by using a later ionosphere model or measured data).
The ionospheric ray path calculated by the algorithm and the position of the wave source are located according to the ray path, and the verification of the measured data is obtained. The method of the invention can be applied not only to the positioning of radiation sources in the ionosphere, but also to the positioning of acoustic wave sources in the sea.
Referring to fig. 2, a flow chart of the ionospheric ray tracing software is shown, wherein arrows represent call relations.
Claims (10)
1. A seismic electromagnetic wave source positioning and backward tracking method in an ionosphere is characterized in that ray tracking of the ionosphere is carried out by utilizing the characteristics of the incoming wave direction, frequency and propagation medium of received electromagnetic waves, and numerical solution is carried out on a ray equation to position a radiation source; the method comprises the following steps:
A) theoretical derivation:
(a) the equation describing the wave propagation path is a Hasegrove equation, the equation is rewritten into a form suitable for numerical solution, and the first-order partial derivative of the refractive index to each variable is solved;
(b) selecting a proper numerical method to solve the ray equation and deducing a specific iteration format;
B) computer programming, ionospheric ray tracing software:
(a) compiling computer software for calculating wave propagation in the ionized layer according to the theoretical derivation result in the step A);
(b) extracting the initial propagation direction of the wave from the measured data of the vector antenna;
(c) because the propagation path of the wave has reversibility, the initial direction of the receiving point is reversed, and backward tracking is carried out as one of the initial conditions of software calculation;
(d) setting other initial conditions calculated by the software: receiving the position of the point, the calculated tolerance, the tracked cutoff condition;
C) determining the epicenter position:
the tracked cut-off point is the wave source of the radiation source in space, and the mid-seismic position is determined by using the cut-off point.
2. The method as set forth in claim 1, wherein step B) is performed by directly numerically solving the three-dimensional haselegprove equation to avoid the influence of the earth's magnetic field and the ionospheric dispersion on the wave propagation path, thereby making the path more accurate.
3. The method as claimed in claim 1, wherein the step B) corrects the node value to avoid accumulation of errors when advancing to the next node by the current node according to an integration algorithm.
4. The method of claim 1, wherein step B) employs a variable step size technique that takes into account the spatial gradient of the refractive index of the medium, where the gradient is large, the step size is small, and where the gradient is small, the step size is large, to ensure tracking accuracy.
5. The method of claim 1, wherein the tracking cutoff condition in step B) is the peak height at F2 in the ionosphere.
6. The method as claimed in claim 1, wherein in step C), the epicenter position is determined by using the cut-off point, and after the cut-off point is traced, the cut-off point is projected to the ground along the magnetic line of the earth's magnetic field, and the projected point is the epicenter position.
7. The method of claim 1, provided that multi-component electromagnetic field data is obtained using a vector antenna, and frequency, incoming wave direction and polarization characteristic information of the waves are extracted according to a wave vector analysis algorithm.
8. The method of claim 3, wherein the integration algorithm is Runge-Kutter algorithm, Adams-Moulton algorithm.
9. The method of claim 4, wherein the step size changing technique automatically adjusts the step size based on the gradient of the medium by:
in the formula, k is a proportionality constant, and when the gradient of the refractive index along the ray path is small, namely the change of the refractive index is gentle, the step length is large; conversely, when the refractive index changes dramatically along the ray path, the step size decreases automatically;
at the same time, an upper limit step is set for the step lengthmaxAnd lower limit stepminWhen the step calculated according to the above formula is out of this range, the upper limit step or the lower limit step is taken as the actual step value.
10. The method of claim 7, wherein the wave vector analysis algorithm is a Means algorithm, a spectral matrix SVD technique.
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| CN107422368A (en) * | 2016-05-23 | 2017-12-01 | 韩国地质资源研究院 | Prevent earthquake early warning system sends the epicentral location of wrong early warning from determining method by forcing the information of the adjacent observation station of association |
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| CN107422368A (en) * | 2016-05-23 | 2017-12-01 | 韩国地质资源研究院 | Prevent earthquake early warning system sends the epicentral location of wrong early warning from determining method by forcing the information of the adjacent observation station of association |
| CN107422368B (en) * | 2016-05-23 | 2019-06-04 | 韩国地质资源研究院 | Method is determined by the epicentral location for forcing the information for being associated with adjacent observation station to prevent earthquake early warning system from issuing wrong early warning |
| CN109683196A (en) * | 2018-11-15 | 2019-04-26 | 天津大学青岛海洋技术研究院 | A kind of ionosphere and seismic precursor correlative space-time characterisation analysis method |
| CN113406609A (en) * | 2021-06-04 | 2021-09-17 | 哈尔滨工业大学 | Method for detecting ionosphere burst abnormal structure by sky-wave radar |
| CN113406609B (en) * | 2021-06-04 | 2022-11-29 | 哈尔滨工业大学 | Method for detecting ionosphere burst abnormal structure by sky-wave radar |
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