CN105549007B - A kind of vertical survey ionogram inversion method based on overlapping multinomial model - Google Patents
A kind of vertical survey ionogram inversion method based on overlapping multinomial model Download PDFInfo
- Publication number
- CN105549007B CN105549007B CN201610004849.5A CN201610004849A CN105549007B CN 105549007 B CN105549007 B CN 105549007B CN 201610004849 A CN201610004849 A CN 201610004849A CN 105549007 B CN105549007 B CN 105549007B
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- msubsup
- msup
- layer
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 51
- 239000005433 ionosphere Substances 0.000 claims description 39
- 238000004364 calculation method Methods 0.000 claims description 23
- 238000007781 pre-processing Methods 0.000 claims description 19
- 238000005259 measurement Methods 0.000 claims description 16
- 238000013213 extrapolation Methods 0.000 claims description 7
- 238000001514 detection method Methods 0.000 claims description 6
- 238000010276 construction Methods 0.000 claims description 5
- 239000007787 solid Substances 0.000 claims description 2
- 238000004422 calculation algorithm Methods 0.000 abstract description 2
- 238000012821 model calculation Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 210000004204 blood vessel Anatomy 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000005562 fading Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Radar, Positioning & Navigation (AREA)
- Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Computer Networks & Wireless Communication (AREA)
- General Physics & Mathematics (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
- Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
Abstract
The invention discloses a kind of vertical survey ionogram inversion methods based on overlapping multinomial model, the described method comprises the following steps:Step A, measured data pre-processes;Step B, E layers of section are calculated as a result, using and overlapping multinomial model based on measured data pretreatment;Step C, based on measured data pre-processed results and E layers of section, estimate that parameter paddy is wideIt is deep with paddy, and build corresponding paddy layer parameter section;Step D, based on measured data pre-processed results and paddy layer section, F layers of section are calculated using overlapping multinomial model.Vertical survey ionogram inversion method disclosed in this invention based on overlapping multinomial model, the vertical survey ionogram inversion algorithm of fused data pretreatment and paddy layer section optimizing based on overlapping multinomial model thought is proposed, ionospheric inversion precision and stability can be effectively improved.
Description
Technical Field
The invention relates to the field of ionosphere research and application, in particular to a vertical ionogram inversion method based on an overlapped polynomial model.
Background
The ionospheric vertical sounding (vertical sounding for short) is the earliest sounding method used in the history of ionospheric research, and although there are many sounding techniques, the ionospheric vertical sounding is still the most important ionospheric sounding method. A vertical ionogram reflecting the relation between the ionosphere virtual height and the frequency can be obtained through ionosphere vertical detection. The virtual height obtained by vertical measurement is not the true reflection height of the electromagnetic wave in the ionosphere, and the true reflection height is obtained by inverting the vertical ionogram, namely inverting the ionosphere profile (the corresponding relation between the ionosphere height and the plasma frequency or the electron concentration) by utilizing the frequency-virtual height trace of the vertical ionogram. The inversion of the vertical ionogram is of great significance to research on ionosphere structure and ionosphere wave propagation problems, has been paid extensive attention all the time, and of course, has great difficulty in inversion.
At present, the inversion method of the relatively common vertical measurement ionogram is an ionosphere parameter inversion method developed based on the idea of a direct calculation method or a mode method, wherein Titheridge and the like disclose a method for inverting an ionosphere profile by using an overlapped polynomial based on the idea of the direct calculation method. The method has the disadvantages that the method is directly based on actual detection data, so that the data quality has a large influence on the precision of the method, a small amount of false height data loss can directly cause the oscillation of a calculated section, a large amount of data loss can bring large deformation and displacement of the section, and the loss of the actual detection false height data is inevitable due to the fading of detection equipment and an ionized layer; furthermore, some direct interpolation methods for detecting the false height data do not combine the ionosphere propagation characteristics, can perform better interpolation on a small amount of data missing near each layer of adjacent frequency, but can obtain completely wrong interpolation results on more or large amount of data missing and data missing near each layer of adjacent frequency, and further increase the calculation error of the profile. In addition, there is no specific reference to the "valley" in the ionospheric profile in this method, but this is not practical in a physical sense.
Disclosure of Invention
The invention aims to solve the technical problem of providing a vertical measurement ionogram inversion method based on an overlapped polynomial model.
The invention adopts the following technical scheme:
in a method for vertical ionogram inversion based on an overlapping polynomial model, the improvement comprising the steps of:
step A, preprocessing actually measured data;
b, calculating an E-layer profile by using an overlapping polynomial model based on the result of actual measurement data preprocessing;
step C, estimating the valley width of the parameters based on the pre-processing result of the measured data and the E-layer profileDepth of harmonyConstructing a corresponding valley layer parameter profile;
and D, calculating the F-layer section by using an overlapping polynomial model based on the pre-processing result of the measured data and the valley layer section.
Further, the step a specifically comprises:
step A1, constructing E-layer and valley-layer sections of parabolic model, polynomial modelLayer anda layer profile;
step A2, based on the established ionosphere model, combining with actually measured virtual height data, under the constraint condition that the profile is continuous and smooth, calculating the virtual height and the actually measured virtual height error and the minimum criterion according to the ionosphere model, and obtaining parameters for constructing the ionosphere model by a searching and iteration method;
and A3, carrying out extrapolation compensation pretreatment on the missing measured data by adopting the ionosphere model with the determined parameters to form complete and continuous virtual height data.
Further, the step B specifically includes:
step B1, calculating the E-layer average group refractive index based on the E-layer virtual height data preprocessing result:
symbolFor indicating at radio frequencyAnd plasma frequencyGroup refractive index ofGroup refractive indexHas the following form
(1)
Wherein,
(2)
(3)
(4)
(5)
(6)
(7)
(8)
in the formula,the magnetic rotation frequency is 300km above the vertical measuring station,is a magnetic inclination angle at 300km above the vertical survey station,in order to be the frequency of the electric wave,is the plasma frequency;
at the frequency of the electric waveAt the position of the air compressor, the air compressor is started,andgroup refractive index corresponding to plasma frequencyAll areValue is usedIndicate that to,InThe higher accuracy can be obtained by the following formulaThe value:
(9)
and is
(10)
At the frequency of the electric waveAnd plasma frequencyA group refractive index value of;
step B2, calculating the coefficients of the E-layer overlapping polynomial according to the preprocessing result of the E-layer virtual height data:
frequency ofAndthe solid high curve in between is shown as
(11)
This curve must give the plasma frequencyThe positive is indeed high, so there are
(12)
(13)
Wherein,,
Taking the derivative of equation (11)
(14)
Thereby at frequencyReduced virtual height (slave height) ofMeasured) was:
(15)
or
(16)
Wherein
(17)
Is like that
(18)
(19)
Wherein
(20)
(21)
Formula (12), formula (13), formula (16), formula (18) and formula (19) determineAndfive values, according to equation (11), frequencyTrue height ofComprises the following steps:
(22)
if the formula (12), the formula (13), the formula (16), the formula (18), the formula (19) and the formula (22) are satisfiedThe values can be determined, then the system of equations must be linearly related, thereby yielding constantsAndthe following relationships exist:
(23)
(24)
determining frequency by solving simultaneous equations (24)5 polynomial coefficients();
Derived from the above
(25)
WhereinWhen the temperature of the water is higher than the set temperature,are respectively equal to、And,are respectively equal to、、,
(26)
(27)
The integral in equation (25) is estimated by a 5-point gaussian relationship, whereSum weightComprises the following steps:
(28)
(29)
correspond to eachValues, which can be calculated first to give the correspondingAndthe value, for a given magnetic field strength and direction,is only dependent onAndfrom 5, there areThe corresponding value can calculate 5And 5, andvalue then for4 ofThe value is calculated by the following equation (30):
(30)
coefficient of performanceAndafter calculation, the simultaneous equations (24) can be solved to obtain the coefficientsWhen is coming into contact withComplete repetition of the above calculation procedure gives each frequencySince the simultaneous equation system (24) is a sick equation system to a certain extent, and the calculation accuracy can be greatly improved by the phase difference between equations before solving the equation system, the following simultaneous equation system is used in calculating the polynomial coefficients
(31)
Step B3, calculating the E-layer section by using an overlapping polynomial model based on the pre-processing result of the E-layer data:
frequency ofTrue height ofExpressed as:
(32)
in the formulaAndis the frequency of the electric wave、Andthe height of the blood vessel、Andreference toDetermined value by imaginary high data、Andand (3) calculating to obtain:
(33)
(34)
(35)。
further, the step C specifically includes:
step C1, valley widthDepth of harmonyEstimating:
after the E-layer profile is inverted by using an overlapping polynomial model based on the preprocessed E-layer data, the valley width of the valley layer parameter is estimated according to the maximum value of the E-layer profile, namely the real height corresponding to the E-layer adjacent frequencyDepth of harmonyThe specific expression is as follows:
,
(36)
whereinThe real height corresponding to the adjacent frequency of the E layer,
according to the estimated valley layer parameters, a three-segment valley layer is constructed, which specifically comprises the following steps:
(37)
whereinIs the E-layer adjacent frequency, coefficientAndbyAndtwo point determination, coefficientAndbyAnddetermining two points;
or adding "two-stage" grain layer, specifically
(38)
Wherein the coefficientsAndbyAndtwo point determination, coefficientAndbyAnddetermining two points;
c2, F-layer profile inversion:
(1) less than the maximum frequency of the F layerThe plasma frequency of (c) corresponds to a real height calculation:
when the valley layer parameter is valley widthDepth of harmonyAfter preliminary estimation, based onConstructing a three-section or two-section valley layer model and preprocessed data of the F layer, and calculating the frequency of the F layer smaller than the maximum frequency by using the overlapped polynomial model in the same step BThe plasma frequency of (a) corresponds to real height;
(2) maximum frequency of F layerCalculating the corresponding actual height:
calculating the maximum frequencyCorresponding actual heightNeed to determineFor a conventional size ionosphere, the values of (c) are:
(39)
in the formulaRepresenting frequency intervals(equal to),Representing a critical frequency of the layer;
(3) calculating the peak height of the F layer:
using critical frequenciesCalculating ionospheric peak heightBy fitting a parabolic through frequencyAndcorresponding actual heightAndthe method is realized by the following specific steps:
(40)
step C3, valley widthDepth of harmonyAnd finally determining:
the relationship between the ionosphere vertical incidence radio wave reflection real height and the detection recording virtual height is as follows:
(41)
whereinAt the frequency of radio waveAnd plasma frequencyCalculating corresponding virtual height data based on the relationship between the real height and the virtual height according to the inverted section, and calculating the actual virtual heightAnd calculating the error of the virtual height, specifically:
(42)
by optimizing the valley width and the valley depth within a certain rangeThe parameters of valley width and valley depth that reached the minimum were determined as the valley layer profile parameters.
Further, the step D specifically includes:
based on the actual measurement of the virtual height and the error of the calculated virtual height in the step CThe set of inverted F-layer profile data that reaches the minimum is determined to be the final F-layer profile.
The invention has the beneficial effects that:
the invention discloses a vertical ionogram inversion method based on an overlapped polynomial model, and provides a vertical ionogram inversion algorithm based on the idea of the overlapped polynomial model and integrating data preprocessing and valley layer profile optimization, wherein a polynomial ionosphere model is constructed firstly; then combining the actually measured virtual height data, and under the constraint condition of continuous and smooth profile, obtaining the coefficients of a polynomial ionosphere model by a searching and iteration method, thereby realizing effective extrapolation compensation pretreatment of missing actually measured data; based on the preprocessed E-layer virtual height data, solving a polynomial coefficient corresponding to each frequency through an ionosphere overlapping polynomial model, and directly calculating and determining an ionosphere profile of the E layer; a standard sectional type valley layer is added in a valley width and valley depth optimizing mode; and finally, solving a polynomial coefficient corresponding to each frequency by adopting an ionosphere overlapping polynomial model based on valley layer and preprocessed F layer virtual height data, and directly calculating and determining a final ionosphere profile, so that the ionosphere inversion precision and stability can be effectively improved.
Drawings
FIG. 1 is a flow chart of a vertical ionogram inversion method disclosed herein;
FIG. 2 is an example of inversion of a three-layer ionosphere containing "two-segment" valleys using the method disclosed herein;
FIG. 3 is an example of inversion of a three-layer ionosphere containing "three-segment" valleys using the method disclosed in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Embodiment 1, as shown in fig. 1, this embodiment discloses a vertical ionogram inversion method based on an overlapped polynomial model, which includes the following steps:
(1) an ionospheric profile mathematical model is constructed:
the invention models the ionosphere as comprising the E layer, the valley layer,A layer,The section of the E layer and the valley layer of the four-layer model of the layer is parabolic,layer andthe layer profile is polynomial. In order for the created electron concentration profile to satisfy the continuous smooth characteristic, plasma frequency (square) values and profile gradients calculated based on the ionospheric model above and below the connection point should be equal at the layer-to-layer connection point, respectively, according to which condition the internal relationship between the relevant parameters is defined.
(2) Acquiring and constructing ionosphere model parameters:
and acquiring final section parameters of each layer based on the errors and the minimum criterion of the virtual height and the actually measured virtual height obtained by model calculation:
1) obtaining E-layer profile parameters:
the three parameters for determining the E-layer profile are mainly、(or)、WhereinThe method can be automatically given by vertical measurement ionogram interpretation software, the error is less than 0.2MHz, the selection of E-layer calculation virtual height and the determination of model construction parameters are realized by adopting a region searching method in the method, and the method specifically comprises the following steps: the fact that the vertical ionization diagram is interpreted to obtain the actual trace of the E layer is assumed to havePoints corresponding to operating frequencies and virtual heights ofAndthe read E-layer critical frequency and minimum virtual height are respectively recorded asAndthen to the parameter、、In that、、(wherein、Andis a control quantity of a search range) to obtain different groups of parameters by a certain step value, and each group of parameters is obtained according to a calculation method of the virtual height of an E layer of a modelOf dotsAnd then calculating the actual measurement virtual height and calculating the error square sum of the virtual height by a model, and determining the group of parameters which minimize the error square sum as the parameters of the E-layer profile.
2) Acquiring valley layer profile parameters:
in thatIn the actual measurement trace of the layer, the sum of adjacent frequencies of the layer is greater than ELayer tracing minimum false heightData between corresponding frequencies are sensitive to valley layer parameters, so that in the inversion process of the valley layer parameters, the part of trace points are selected as corresponding actual measurement virtual heights of the valley layer and used for selecting corresponding calculation virtual heights of the valley layer and determining valley layer construction model parameters, and the assumption is commonPoints corresponding to operating frequencies and virtual heights ofAnd. In the method, the calculation is carried out by a least square methodLayer profile coefficients and by checking whether the calculated coefficients satisfyAnd the acquisition of the parameters of the valley layer profile is finally realized by searching and iterating due to the monotonous increasing characteristic of the layer profile.
3)Layer profile parameter
SelectingIn the actual measurement trace of the layer,layer trace frequency of least virtual height toIs used to determineLayer parameters, assumed to be commonData points corresponding to operating frequencies and virtual heights ofAnd. At the time of readingIn the case of (a) in (b),the layer profile is composed of polynomial coefficientsIt is fully determined that these coefficients can be calculated using methods similar to those used in inverting the valley layer parameters.
4)Layer profile parameters:
use of data in a layer survey trace for determiningLayer parameters, assumed to be commonData points corresponding to operating frequencies and virtual heights ofAnd. At the time of readingIn the case of (a) in (b),layer profile coefficient ofIs completely determined inAfter the layer parameters have been determined,layer andthe profile gradient at the layer intersection has also been determined, and thereforeThe determination of the layer construction model parameters is also a constraint optimization problem, and similar determination can be adoptedThe coefficients are calculated using methods used for layer parameters.
5) Finally determining the valley layer,A layer,Layer construction model parameters:
for underdevelopmentLayer, vertical measurement ionization picture interpretation software gives automaticallyRelative toDeviation of fully developed layerIs an unknown quantity which, in theory,has a value betweenThus, in determining the valley layer,A layer,When the layer parameter is, willIn thatInternal traversal, selecting the error between the calculated and measured virtual heights of all data pointsThe corresponding valley layer,A layer,Layer parameters as final valley layer,A layer,Layer parameters.
(3) Extrapolation compensation pretreatment of missing actual measurement virtual height data:
based on the constructed ionosphere model and parameters of each layer of constructed model acquired by combining measured data, extrapolation compensation of missing measured data is realized through model calculation, continuous preprocessing data in trend is formed, and high-quality data support is provided for subsequent high-practice calculation.
(4) Frequency of E layerThe actual height of (2) is calculated:
based on the results of the pre-processing of the measured data, it is assumed that E-layer is commonData points corresponding to operating frequencies and virtual heights ofAndcalculating the frequency based on an overlapping polynomial model of 5 coefficients() Corresponding actual height. The method specifically comprises the following steps:
1) calculating polynomial coefficients and average group refractive index
Extrapolation compensation preprocessing result based on measured data (operating frequency and virtual height are respectivelyAnd() Calculate each frequency using equation (31)() The corresponding 5 polynomial coefficients; use formula (1)Equation (8) for calculating the radio frequencyAnd plasma frequencyHas a group refractive index of(ii) a Calculation of radio wave frequency Using equations (9) and (10)At the position of the air compressor, the air compressor is started,andthe mean of the group refractive indices corresponding to the plasma frequency isThe value of (c).
2) Calculate the real height of the first three frequencies:
setting frequency、Corresponding actual height、Are all equal to the height of deficiencyIs calculated by equation (43)And then the frequency is obtained by the calculation of an overlapping polynomial of 5 coefficients represented by the formula (44)True height of。
(43)
(44)
3) Calculate the real height of the other frequencies of the E layer:
the real height is sequentially determined using overlapping polynomials of 5 coefficients represented by equation (32)() In the formulaObtained by calculation using the formula (33) to the formula (35).
(5) Presetting valley layer parameters and calculating the F layer real height:
based on the results of the measured data preprocessing, it is assumed that the F layer is commonData points corresponding to operating frequencies and virtual heights ofAnd. Estimating valley width according to the above-mentioned valley layer parameter estimation methodDepth of harmonyAnd constructing corresponding valley layer parameter profiles, and calculating frequency by adopting an overlapped polynomial model with 5 coefficients() Corresponding actual height. The method specifically comprises the following steps:
1) setting valley layer parameters
Presetting the valley width according to the formula (36)Depth of harmonyAnd constructing a valley profile using the model of equation (37) or equation (38).
2) Calculating polynomial coefficients and average group refractive index
The method is the same as the above E layer calculation, and the method used thereinValue set to E-layer critical frequency。
3) Calculating the real height of the first three frequencies
Setting frequency、Corresponding actual height、Respectively equal to the frequency of the model of the valley layer profile、Extrapolated value、(ii) a Calculated by the following equation (45)And then the frequency is obtained by the calculation of an overlapping polynomial of 5 coefficients represented by the formula (44)True height of。
(45)
(46)
(47)
(48)
4) Calculating F-layer less than maximum frequencyCorresponding to the plasma frequency of
The real height is sequentially determined using overlapping polynomials of 5 coefficients represented by equation (32)() In the formulaObtained by calculation using equations (33) and (34), calculated by (49)The value of (c).
(49)
5) Calculating the maximum frequencyCorresponding to the actual height
Calculation using equation (31)Corresponding 5 polynomial coefficients; combined with measured critical frequencyCalculated using equation (39)A value of (d); the maximum frequency is then calculated using an overlapping polynomial of 5 coefficients represented by equation (32)Corresponding to the actual heightThe value of (c).
6) Calculating ionospheric peak height
Combined with measured critical frequencyCalculating ionospheric peak height using equation (40)The value of (c).
(6) Error of calculating and actually measuring virtual height data
According to the section inverted by the steps, corresponding virtual height data is calculated by using an equation (41), and then the actual virtual height is calculated according to an equation (42)Sum model computing pseudo-heightThe error between.
(7) Determining a final profile
Set the valley widthDepth of harmonyIn that、And (3) obtaining different combination parameters by a certain step value in the range, repeating the steps (5) and (6) for each group of parameters to obtain errors of the actually measured virtual height and the calculated virtual height, and determining the group of valley layer parameters and the section with the minimum errors as final valley layer parameters and sections.
Two examples of inversion using the method of the present invention are shown in fig. 2 and 3, where the inverted profile of fig. 2 contains a "two-segment" valley layer and the inverted profile of fig. 3 contains a "three-segment" valley layer. Wherein the measured data is the interpretation result of vertical ionization chart interpretation software, which is a typical three-layer (E layer, B layer, C layer,layer andlayer) of,Ionospheric echo tracing with insufficiently developed layers. In the invention, effective extrapolation compensation (black circle points) is realized for missing measured data based on the ionosphere model; using the invention based on overlapping polynomialsThe vertical ionogram inversion method obtains a smoother and more accurate ionosphere profile (black dashed line), and is significantly superior to a profile inversion result (black solid line) only adopting measured data and a profile inversion result (black dotted line) of direct interpolation of the measured data. The defects that more or a large amount of data are lost, data near adjacent frequencies of each layer are lost, and section calculation errors are greatly increased and even wrong due to direct interpolation of a large amount of lost data without combination of ionosphere propagation characteristics in a polynomial inversion method are overcome; and the actually existing 'valley layer' is reasonably considered in the inversion profile, so that the ionosphere inversion accuracy and stability are higher.
Claims (1)
1. A vertical ionogram inversion method based on an overlapping polynomial model is characterized by comprising the following steps: step A, pre-processing measured data, wherein the step A specifically comprises the following steps:
step A1, constructing E-layer and valley-layer sections of parabolic model, F of polynomial model1Layer and F2A layer profile;
step A2, based on the established ionosphere model, combining with actually measured virtual height data, under the constraint condition that the profile is continuous and smooth, calculating the virtual height and the actually measured virtual height error and the minimum criterion according to the ionosphere model, and obtaining parameters for constructing the ionosphere model by a searching and iteration method;
a3, carrying out extrapolation compensation pretreatment on missing measured data by adopting an ionosphere model with determined parameters to form complete and continuous virtual height data;
b, based on the result of the actual measurement data preprocessing, calculating the E-layer profile by using an overlapped polynomial model, wherein the step B specifically comprises the following steps:
step B1, calculating the E-layer average group refractive index based on the E-layer virtual height data preprocessing result:
symbol mu'ijFor indicating at radio frequency fiAnd plasma frequency fjHas a group refractive index mu' of the following form
<mrow> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mfrac> <msub> <mi>G</mi> <mi>o</mi> </msub> <msub> <mi>&mu;</mi> <mi>o</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
<mrow> <msub> <mi>&mu;</mi> <mi>o</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>X</mi> <mi>o</mi> </msub> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>X</mi> <mi>o</mi> </msub> <mo>=</mo> <msubsup> <mi>f</mi> <mi>N</mi> <mn>2</mn> </msubsup> <mo>/</mo> <msup> <mi>f</mi> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>G</mi> <mi>o</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&mu;</mi> <mi>o</mi> </msub> <msub> <mi>n</mi> <mi>o</mi> </msub> </mfrac> <mo>{</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msub> <mi>X</mi> <mi>o</mi> </msub> <msup> <mi>tan</mi> <mn>2</mn> </msup> <mi>&theta;</mi> </mrow> <msup> <mi>M</mi> <mn>2</mn> </msup> </mfrac> <mo>&lsqb;</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>X</mi> <mi>o</mi> </msub> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&gamma;&mu;</mi> <mi>o</mi> <mn>4</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mfrac> <mo>-</mo> <mfrac> <mn>2</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&gamma;&mu;</mi> <mi>o</mi> <mn>4</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>&rsqb;</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mi>&gamma;</mi> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <msup> <mi>tan</mi> <mn>2</mn> </msup> <mi>&theta;</mi> </mrow> <mrow> <msubsup> <mi>Y</mi> <mi>o</mi> <mn>2</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>&theta;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
YO=fH/j (6)
<mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&mu;</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mfrac> <mrow> <mn>2</mn> <msup> <mi>tan</mi> <mn>2</mn> </msup> <mi>&theta;</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>&gamma;&mu;</mi> <mi>o</mi> <mn>4</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>&mu;</mi> <mi>o</mi> </msub> <msub> <mi>n</mi> <mi>o</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mi>M</mi> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <msup> <mi>tan</mi> <mn>2</mn> </msup> <mi>&theta;</mi> <mo>/</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&gamma;&mu;</mi> <mi>o</mi> <mn>4</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&rsqb;</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
in the formula (f)HThe magnetic rotation frequency is 300km above the vertical survey station, theta is the magnetic inclination angle 300km above the vertical survey station, f is the radio frequency, f is the magnetic rotation frequencyNIs the plasma frequency;
at radio frequency fiF ofjAnd fj-1Average of group refractive index mu' corresponding to plasma frequencyIndicating that, for j 2, 3, 4., (i-1),where i is 4, 5, 6.., n, a high degree of accuracy can be obtained by the following formulaThe value:
<mrow> <mover> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> <mi>j</mi> <mo><</mo> <mi>i</mi> <mo>-</mo> <mn>3</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
and is
<mrow> <mover> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>+</mo> <mn>4</mn> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mi>i</mi> <mo>-</mo> <mn>3</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
μ′i,j-1/2At a radio frequency fiAnd plasma frequencyA group refractive index value of;
step B2, calculating the coefficients of the E-layer overlapping polynomial according to the preprocessing result of the E-layer virtual height data:
frequency fi-2And fi+1The solid high curve in between is shown as
<mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>(</mo> <mfrac> <msub> <mi>f</mi> <mi>N</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>f</mi> <mi>N</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>f</mi> <mi>N</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>f</mi> <mi>N</mi> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>4</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
This curve must give the plasma frequency fN=fi-2、fi-1The positive is indeed high, so there are
<mrow> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>3</mn> </msubsup> <mo>+</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>4</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>a</mi> <mn>3</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <mo>+</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
Wherein a isi-2=fi-2/fi,ai-1=fi-1/fi,
Taking the derivative of equation (11)
<mrow> <mi>d</mi> <mi>h</mi> <mo>=</mo> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <msub> <mi>ka</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
Thereby at frequency fi-1Reduced virtual height of (d), from height hi-2The measurement is as follows:
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mi>d</mi> <mi>h</mi> <mo>=</mo> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <msub> <mi>ka</mi> <mi>k</mi> </msub> <msubsup> <mo>&Integral;</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>df</mi> <mi>N</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
or
h″i-1,i-2=0+a1b11+a2b12+a3b13+a4b14(16)
Wherein
<mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>k</mi> <msubsup> <mo>&Integral;</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>df</mi> <mi>N</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
Is like that
h″i,i-2=0+a1b21+a2b22+a3b23+a4b24(18)
h″i+1,i-2=0+a1b31+a2b32+a3b33+a4b34(19)
Wherein
<mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>k</mi> <msubsup> <mo>&Integral;</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> <mo>(</mo> <mrow> <msubsup> <mi>f</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mi>k</mi> </msubsup> </mrow> <mo>)</mo> <msub> <mi>df</mi> <mi>N</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>b</mi> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>k</mi> <msubsup> <mo>&Integral;</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> <mo>(</mo> <mrow> <msubsup> <mi>f</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mi>k</mi> </msubsup> </mrow> <mo>)</mo> <msub> <mi>df</mi> <mi>N</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
Formula (12), formula (13), formula (16), formula (18) and formula (19) define a0、a1、a2、a3And a4Five values, according to equation (11), frequency fiTrue height h ofiComprises the following steps:
hi=a0+a1+a2+a3+a4(22)
if the value a satisfying the formula (12), the formula (13), the formula (16), the formula (18), the formula (19) and the formula (22) can be obtained, the system of equations must be linearly related, thereby obtaining the constant pi1、pi2、pi3、pi4And pi5The following relationships exist:
pi1hi-2+pi2hi-1+pi3h″i-1,i-2+pi4h″i,i-2+pi5h″i+1,i-2=hi(23)
<mrow> <mfenced open = "" close = "}"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>11</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>21</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>31</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>12</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>22</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>32</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>3</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>13</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>23</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>33</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>4</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>14</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>24</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>34</mn> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
determining the frequency f by solving a simultaneous system of equations (24)i5 polynomial coefficients pim,m=1,2,3,4,5;
Derived from the above
<mrow> <msub> <mi>b</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>k</mi> <mo>(</mo> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> <mo>/</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msub> <mi>t</mi> <mi>m</mi> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mi>t</mi> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mi>N</mi> </msub> <mo>/</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>
Where j is 1, 2, 3, f is equal to fi-1、fiAnd fi+1Mu' are respectively equal to
<mrow> <mi>t</mi> <mo>=</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msubsup> <mi>f</mi> <mi>N</mi> <mn>2</mn> </msubsup> <mo>/</mo> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>/</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow>
The integral in equation (25) is estimated by a 5-point Gaussian relationship, where xrAnd the weight value wrComprises the following steps:
x1=0.04691008 x2=0.23076534 x3=0.5 x4=0.76923466 x5=0.9530899 (28)
w1=0.11846344 w2=0.23931434 w3=0.28444444
w4=0.23931434 w5=0.11846344 (29)
for each value of j, the corresponding f and t can be calculated firstmThe value of μ't depends only on f and t for a given magnetic field strength and direction, from 5 tr=xrtmThe values correspond to 5 values of μ't, and 5Value, then 4 b for k ═ 1, 2, 3, 4jkThe value is calculated by the following equation (30):
after the coefficients a and b are calculated, the simultaneous equations (24) can be solved to obtain the coefficient pi1,pi2,pi3,pi4,pi5When i is 3, 4, 5.., n-1, a complete repetition of the above calculation procedure can give each frequency fiSince the simultaneous equation system (24) is a sick equation system to a certain extent, and the calculation accuracy can be greatly improved by the phase difference between equations before solving the equation system, the following simultaneous equation system is used in calculating the polynomial coefficients
pi1+pi2=1
(ai-2-1)pi1+(ai-1-1)pi2+b11pi3+b21pi4+b31pi5=0
<mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>12</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>11</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>22</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>21</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>32</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>31</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow>
<mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>3</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>13</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>12</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>23</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>22</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>b</mi> <mn>33</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>32</mn> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow>
<mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>4</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>3</mn> </msubsup> <mo>)</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo>(</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>4</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <mo>)</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>b</mi> <mn>14</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>13</mn> </msub> <mo>)</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>b</mi> <mn>24</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>23</mn> </msub> <mo>)</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>4</mn> </mrow> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>b</mi> <mn>34</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>33</mn> </msub> <mo>)</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>
Step B3, calculating the E-layer section by using an overlapping polynomial model based on the pre-processing result of the E-layer data:
frequency fiTrue height of (h)iExpressed as:
hi=pi1hi-2+pi2hi-1+pi3h"i-1,i-2+pi4h"i,i-2+pi5h"i+1,i-2(32)
in the formula h ″)i-1,1-2、h″i,i-2And h'i+1,1-2Is the frequency f of the electric wavei-1、fiAnd fi+1Of (b) is of virtual height h'i-1、h′iAnd h'i+1Reference hi-2A determined value which is given by a false high data h ″i-1,i-3、h″i,i-3And h'i+1And (3) calculating to obtain:
h″i-1,i-2=h″i-1,i-3-μ′i-1,i-2(hi-2-hi-3) (33)
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>3</mn> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>-</mo> <mover> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>h</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>3</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mn>2</mn> </mrow> </msubsup> <mover> <msubsup> <mi>&mu;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mo>&prime;</mo> </msubsup> <mo>&OverBar;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>35</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
step C, estimating a parameter valley width W based on the actual measurement data preprocessing result and the E-layer profilevAnd valley depth FvAnd constructing a corresponding valley layer parameter profile, wherein the step C specifically comprises the following steps:
step C1, valley width WvAnd valley depth FvEstimating:
after the E-layer profile is inverted by using an overlapping polynomial model based on the preprocessed E-layer data, the valley parameter valley width W is estimated according to the maximum value of the E-layer profile, namely the real height corresponding to the E-layer adjacent frequencyvAnd valley depth FvThe specific expression is as follows:
<mrow> <msub> <mi>W</mi> <mi>v</mi> </msub> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mn>40</mn> <mo>,</mo> <msub> <mi>F</mi> <mi>v</mi> </msub> <mo>=</mo> <mn>0.008</mn> <msubsup> <mi>W</mi> <mi>v</mi> <mn>2</mn> </msubsup> <mo>/</mo> <mrow> <mo>(</mo> <mrow> <mn>20</mn> <mo>+</mo> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mrow>
wherein HMaxThe real height corresponding to the adjacent frequency of the E layer,
according to the estimated valley layer parameters, a three-segment valley layer is constructed, which specifically comprises the following steps:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mi>h</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.15</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>C</mi> <mi>E</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mi>v</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.15</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.8</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> <mi>h</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.8</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>37</mn> <mo>)</mo> </mrow> </mrow>
wherein f isCEFor E-layer adjacent frequency, coefficient q1And p1From [ f ]CE,HMax]And [ fCE-Fv,HMax+0.15Wv]Two points are determined, coefficient q2And p2From [ f ]CE-Fv,HMax+0.8Wv]And [ fCE,HMax+Wv]Determining two points;
or adding "two-stage" grain layer, specifically
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mi>h</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.4</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> <mi>h</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>0.4</mn> <msub> <mi>W</mi> <mi>v</mi> </msub> <mo>&le;</mo> <mi>h</mi> <mo>&le;</mo> <msub> <mi>H</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>W</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>38</mn> <mo>)</mo> </mrow> </mrow>
Wherein the coefficient q1And p1From [ f ]CE,HMax]And [ fCE-Fv,HMax+0.4Wv]Two points are determined, coefficient q2And p2From [ f ]CE-Fv,HMax+0.4Wv]And [ fCE,HMax+Wv]Determining two points;
c2, F-layer profile inversion:
(1) less than the maximum frequency F of the F layernThe plasma frequency of (c) corresponds to a real height calculation:
when the valley layer parameter is valley width WvAnd valley depth FvAfter preliminary estimation, based on the construction of a three-section or two-section valley layer model and F layer pretreatmentAfter processing data, calculating the F layer less than the maximum frequency F by using an overlapped polynomial model in the same step BnThe plasma frequency of (a) corresponds to real height;
(2) maximum frequency F of F layernCalculating the corresponding actual height:
calculating the maximum frequency fnCorresponding real height hnH "needs to be determinedn+1,n-2For a conventional size ionosphere, the values of (c) are:
<mrow> <msubsup> <mi>h</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>h</mi> <mi>n</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>&Delta;</mi> <mi>f</mi> </mrow> <mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>f</mi> <mi>n</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>39</mn> <mo>)</mo> </mrow> </mrow>
where Δ f denotes the frequency interval fn+1-fn=fn-fn-1,fcRepresenting a critical frequency of the layer;
(3) calculating the peak height of the F layer:
using a critical frequency fcCalculating ionospheric peak height hcBy fitting a parabolic through frequency fn-2And fnCorresponding real height hn-2And hnThe method is realized by the following specific steps:
<mrow> <msub> <mi>h</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>h</mi> <mi>n</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mo>{</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msubsup> <mi>f</mi> <mi>c</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> </mrow> <mrow> <msubsup> <mi>f</mi> <mi>c</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <mn>1</mn> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>40</mn> <mo>)</mo> </mrow> </mrow>
step C3, valley width WvAnd valley depth FvAnd finally determining:
the relationship between the ionosphere vertical incidence radio wave reflection real height and the detection recording virtual height is as follows:
<mrow> <msubsup> <mi>h</mi> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msub> <mi>h</mi> <mi>i</mi> </msub> </msubsup> <msup> <mi>&mu;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> <mi>d</mi> <mi>h</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>41</mn> <mo>)</mo> </mrow> </mrow>
where μ' (f)i,fN) At a radio wave frequency fiAnd plasma frequency fNCalculating corresponding virtual height data based on the relationship between the real height and the virtual height according to the inverted profile in the step, and calculating the actually measured virtual height h'iAnd calculating the error of the virtual height, specifically:
<mrow> <mi>&epsiv;</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>h</mi> <mi>i</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>h</mi> <mi>i</mi> <mo>&prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>42</mn> <mo>)</mo> </mrow> </mrow>
determining the parameters of the valley width and the valley depth which enable epsilon to reach the minimum as the profile parameters of the valley layer by an optimizing mode in a certain range of the valley width and the valley depth;
step D, based on the pre-processing result of the measured data and the valley layer profile, calculating the F layer profile by using an overlapped polynomial model, wherein the step D specifically comprises the following steps:
and C, determining the final F-layer profile based on the set of inverted F-layer profile data which minimizes the errors epsilon of the actually measured virtual height and the calculated virtual height in the step C.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610004849.5A CN105549007B (en) | 2016-01-05 | 2016-01-05 | A kind of vertical survey ionogram inversion method based on overlapping multinomial model |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610004849.5A CN105549007B (en) | 2016-01-05 | 2016-01-05 | A kind of vertical survey ionogram inversion method based on overlapping multinomial model |
Publications (2)
Publication Number | Publication Date |
---|---|
CN105549007A CN105549007A (en) | 2016-05-04 |
CN105549007B true CN105549007B (en) | 2018-05-22 |
Family
ID=55828316
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201610004849.5A Active CN105549007B (en) | 2016-01-05 | 2016-01-05 | A kind of vertical survey ionogram inversion method based on overlapping multinomial model |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN105549007B (en) |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN109614585B (en) * | 2018-12-03 | 2023-01-24 | 中国电波传播研究所(中国电子科技集团公司第二十二研究所) | Novel ionosphere region reconstruction method |
CN111103573B (en) * | 2019-10-19 | 2021-09-17 | 中国电波传播研究所(中国电子科技集团公司第二十二研究所) | Refraction correction method for measuring TDOA (time difference of arrival) based on satellite external radiation source radar |
Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
RU2008105018A (en) * | 2008-02-11 | 2009-08-20 | Оао "Радиоавионика" (Ru) | METHOD FOR CONSTRUCTING SUB-SURFACE OBJECT IMAGE |
CN106134480B (en) * | 2009-09-18 | 2013-04-17 | 中国电子科技集团公司第二十二研究所 | F1 layer is not exclusively grown ionospheric model and inversion method |
CN105005682A (en) * | 2015-06-17 | 2015-10-28 | 中国电子科技集团公司第二十二研究所 | Retrieval method for vertical exploration ionogram |
CN105160156A (en) * | 2015-08-10 | 2015-12-16 | 中国电子科技集团公司第二十二研究所 | Vertical measurement ionogram inversion method integrated with data pre-processing |
CN105184039A (en) * | 2015-06-17 | 2015-12-23 | 中国电子科技集团公司第二十二研究所 | Ionosphere vertical section modeling and parameter inversion method |
-
2016
- 2016-01-05 CN CN201610004849.5A patent/CN105549007B/en active Active
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
RU2008105018A (en) * | 2008-02-11 | 2009-08-20 | Оао "Радиоавионика" (Ru) | METHOD FOR CONSTRUCTING SUB-SURFACE OBJECT IMAGE |
CN106134480B (en) * | 2009-09-18 | 2013-04-17 | 中国电子科技集团公司第二十二研究所 | F1 layer is not exclusively grown ionospheric model and inversion method |
CN105005682A (en) * | 2015-06-17 | 2015-10-28 | 中国电子科技集团公司第二十二研究所 | Retrieval method for vertical exploration ionogram |
CN105184039A (en) * | 2015-06-17 | 2015-12-23 | 中国电子科技集团公司第二十二研究所 | Ionosphere vertical section modeling and parameter inversion method |
CN105160156A (en) * | 2015-08-10 | 2015-12-16 | 中国电子科技集团公司第二十二研究所 | Vertical measurement ionogram inversion method integrated with data pre-processing |
Also Published As
Publication number | Publication date |
---|---|
CN105549007A (en) | 2016-05-04 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US20130046489A1 (en) | Magnetometer bias and anomaly detector | |
WO2021169883A1 (en) | Ultrasonic gas meter flow measurement algorithm | |
CN108492329B (en) | Three-dimensional reconstruction point cloud precision and integrity evaluation method | |
KR101979184B1 (en) | Apparatus and method for cycle slip detection of multi-frequency gnss carrier phase by using estimation of ionospheric delay rate | |
CN105549007B (en) | A kind of vertical survey ionogram inversion method based on overlapping multinomial model | |
WO2019242045A9 (en) | Method for calculating virtual source two-dimensional wavefront construction seismic wave travel time | |
WO2013025639A1 (en) | Magnetometer bias and anomaly detector | |
CN108776340A (en) | Forward-orbit interference synthetic aperture radar sea surface flow field inversion method based on genetic algorithm | |
CN110956249B (en) | Stratified medium inversion method based on resampling optimization particle swarm algorithm | |
CN105160156B (en) | A kind of vertical survey ionogram inversion method of fused data pretreatment | |
CN105005682B (en) | One kind, which is hung down, surveys ionogram inversion method | |
Fang et al. | Estimation of ultrasonic signal onset for flow measurement | |
CN113567979B (en) | Multi-temporal InSAR phase unwrapping method based on simulated annealing algorithm | |
CN105184039B (en) | A kind of modeling of ionosphere vertical section and parameter inversion method | |
Yu et al. | A review on acoustic reconstruction of temperature profiles: From time measurement to reconstruction algorithm | |
CN108519588A (en) | A kind of multifrequency phase unwrapping method and device | |
Bu et al. | Improved calibration method for refraction errors in multibeam bathymetries with a wider range of water depths | |
CN105550514B (en) | A kind of method for building up and system of the rate pattern based on dual path integration | |
CN112731520A (en) | Full waveform inversion method and system based on structure tensor diffusion filtering | |
CN107918144B (en) | Anisotropic medium preliminary wave ray-tracing procedure and system | |
CN110261472B (en) | Method for measuring and reconstructing hearth section flow field by using wavelet basis function through acoustic wave method | |
CN109655888B (en) | Quantitative selection method and system for smooth floating reference surface in seismic data processing | |
Mohammad-Djafari | Image reconstruction of a compact object from a few number of projections | |
Gaullier et al. | Introducing shape constraints into object-based traveltime tomography | |
CN105701276B (en) | A kind of improved ionosphere vertical section modeling method |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |