CN105549007B

CN105549007B - A kind of vertical survey ionogram inversion method based on overlapping multinomial model

Info

Publication number: CN105549007B
Application number: CN201610004849.5A
Authority: CN
Inventors: 鲁转侠; 柳文; 蔚娜; 杨龙泉; 冯静; 郭文玲; 师燕娥
Original assignee: China Research Institute of Radio Wave Propagation CRIRP
Current assignee: China Research Institute of Radio Wave Propagation CRIRP
Priority date: 2016-01-05
Filing date: 2016-01-05
Publication date: 2018-05-22
Anticipated expiration: 2036-01-05
Also published as: CN105549007A

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

Vertical measurement ionogram inversion method based on overlapping polynomial model

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. 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;

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:

symbol mu'_ijFor indicating at radio frequency f_iAnd plasma frequency f_jHas 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>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>

Y_O＝f_H/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 frequency_NIs the plasma frequency;

at radio frequency f_iF of_jAnd f_j-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 f_iAnd plasma frequencyA group refractive index value of;

frequency f_i-2And f_i+1The solid high curve in between is shown as

This curve must give the plasma frequency f_N＝f_i-2、f_i-1The positive is indeed high, so there are

Wherein a is_i-2＝f_i-2/f_i，a_i-1＝f_i-1/f_i，

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 f_i-1Reduced virtual height of (d), from height h_i-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 f_iTrue height h of_iComprises the following steps:

h_i＝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 p_i1、p_i2、p_i3、p_i4And p_i5The following relationships exist:

p_i1h_i-2+p_i2h_i-1+p_i3h″_i-1，i-2+p_i4h″_i，i-2+p_i5h″_i+1，i-2＝h_i(23)

determining the frequency f by solving a simultaneous system of equations (24)_i5 polynomial coefficients p_im，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 f_i-1、f_iAnd f_i+1Mu' are respectively equal to

The integral in equation (25) is estimated by a 5-point Gaussian relationship, where x_rAnd the weight value w_rComprises 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 first_mThe value of μ't depends only on f and t for a given magnetic field strength and direction, from 5 t_r＝x_rt_mThe values correspond to 5 values of μ't, and 5Value, then 4 b for k ═ 1, 2, 3, 4_jkThe 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 p_i1，p_i2，p_i3，p_i4，p_i5When i is 3, 4, 5.., n-1, a complete repetition of the above calculation procedure can give each frequency f_iSince 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

p_i1+p_i2＝1

(a_i-2-1)p_i1+(a_i-1-1)p_i2+b₁₁p_i3+b₂₁p_i4+b₃₁p_i5＝0

frequency f_iTrue height of (h)_iExpressed as:

h_i＝p_i1h_i-2+p_i2h_i-1+p_i3h"_i-1，i-2+p_i4h"_i，i-2+p_i5h"_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 wave_i-1、f_iAnd f_i+1Of (b) is of virtual height h'_i-1、h′_iAnd h'_i+1Reference h_i-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(h_i-2-h_i-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 profile_vAnd valley depth F_vAnd constructing a corresponding valley layer parameter profile, wherein the step C specifically comprises the following steps:

step C1, valley width W_vAnd valley depth F_vEstimating:

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 frequency_vAnd valley depth F_vThe specific expression is as follows:

wherein H_MaxThe real height corresponding to the adjacent frequency of the E layer,

wherein f is_CEFor E-layer adjacent frequency, coefficient q₁And p₁From [ f ]_CE，H_Max]And [ f_CE-F_v，H_Max+0.15W_v]Two points are determined, coefficient q₂And p₂From [ f ]_CE-F_v，H_Max+0.8W_v]And [ f_CE，H_Max+W_v]Determining two points;

or adding "two-stage" grain layer, specifically

Wherein the coefficient q₁And p₁From [ f ]_CE，H_Max]And [ f_CE-F_v，H_Max+0.4W_v]Two points are determined, coefficient q₂And p₂From [ f ]_CE-F_v，H_Max+0.4W_v]And [ f_CE，H_Max+W_v]Determining two points;

c2, F-layer profile inversion:

(1) less than the maximum frequency F of the F layer_nThe plasma frequency of (c) corresponds to a real height calculation:

when the valley layer parameter is valley width W_vAnd valley depth F_vAfter 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 B_nThe plasma frequency of (a) corresponds to real height;

(2) maximum frequency F of F layer_nCalculating the corresponding actual height:

calculating the maximum frequency f_nCorresponding real height h_nH "needs to be determined_n+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 f_n+1-f_n＝f_n-f_n-1，f_cRepresenting a critical frequency of the layer;

(3) calculating the peak height of the F layer:

using a critical frequency f_cCalculating ionospheric peak height h_cBy fitting a parabolic through frequency f_n-2And f_nCorresponding real height h_n-2And h_nThe method is realized by the following specific steps:

step C3, valley width W_vAnd valley depth F_vAnd finally determining:

<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，f_N) At a radio wave frequency f_iAnd plasma frequency f_NCalculating 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.