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

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

Technical field

The present invention relates to PROGRESS OF IONOSPHERIC RESEARCH IN and application field more particularly to a kind of vertical survey electricity based on overlapping multinomial model From figure inversion method.

Background technology

Ionospheric vertical sounding（It referred to as hangs down and surveys）Technology is the detection method used earliest in PROGRESS OF IONOSPHERIC RESEARCH IN history, although There are numerous Detection Techniques at present, but the ionosphere survey technology that hangs down is still most important ionospheric probing method.Pass through ionosphere Vertical sounding can obtain the vertical survey ionogram of reflection Ionospheric virtual height and frequency relation.The virtual height surveyed and obtained of hanging down not is electromagnetism True reflection height of the ripple in ionosphere, true reflection height obtains needs and surveys ionogram progress inverting to hanging down, i.e., using vertical Survey ionogram frequency-virtual height trace inverting Ionospheric Profile（Layer height and plasma frequency or electron concentration it is corresponding Relation）.The inverting for surveying ionogram of hanging down is of great significance to studying ionospheric structure and ionosphere wave propagation problem, all the time It is subject to very extensive attention, certainly, inverting also has sizable difficulty.

At present, the more universal vertical survey ionogram inversion method of application is developed based on direct computing method or type method thought Ionospheric Parameters inversion method, wherein, a kind of overlapping multinomial is disclosed based on direct computing method thought, Titheridge etc. The method of inverting Ionospheric Profile in this method, calculates its true reflection height, each by the measurement virtual height on look-in frequency In frequency, consider to determine 5 multinomial coefficients above and below calculating the two-part observed case of frequency, so that it is determined that ionizing Layer section.The shortcoming of this method is to be directly based upon actual detection data, thus the quality of data is affected to its precision, A small amount of virtual height shortage of data can directly result in reference section and vibrate, and substantial amounts of shortage of data will bring the big amplitude variation of section Shape and displacement, and due to detecting devices and ionospheric fading, the missing of actual detection virtual height data is inevitable；Further more, Some direct interpolation methods to detecting virtual height data, are not associated with ionospheric propagation characteristic, non-each layer are faced a small amount of near frequency Shortage of data can play preferable interpolation, but the shortage of data faced more or mass data missing and each layer near frequency may Full of prunes interpolation result is obtained, more increases the calculation error of section.In addition, for the " paddy in Ionospheric Profile Layer " is not also specifically related in this method, but this does not meet actual conditions from physical significance.

The content of the invention

It is anti-that the technical problems to be solved by the invention are just to provide a kind of vertical survey ionogram based on overlapping multinomial model Drill method.

The present invention adopts the following technical scheme that：

A kind of vertical survey ionogram inversion method based on overlapping multinomial model, it is improved in that the method bag Include 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.

Further, the step A is specially：

Step A1, the E layers of parabolic model and paddy layer section are built, multinomial modelLayer andLayer section；

Step A2, the ionospheric model based on foundation, with reference to actual measurement virtual height data, in the constraints of section continuous and derivable Under, virtual height and actual measurement virtual height error and minimum criteria are calculated according to ionospheric model, is built by the method for search, iteration The parameter of ionospheric model；

Step A3, extrapolation compensation pretreatment carries out missing measured data using the ionospheric model of definite parameter, is formed Complete continuous virtual height data.

Further, the step B is specifically included：

Step B1, E layers of average group refractive index are calculated based on E layers of virtual height data prediction result：

SymbolFor representing in wave frequencyAnd plasma frequencyThe group refractive index at place, group refractive indexWith following form

(1)

Wherein,

(2)

(3)

(4)

(5)

(6)

(7)

(8)

In formula,For hang down survey station overhead 300km at gyro-frequency,For hang down survey station overhead 300km at magnetic dip angle,For electricity Wave frequency rate,For plasma frequency；

In wave frequencyPlace,WithBetween the corresponding group refractive index of plasma frequencyAverage useTable Show, for,In, it is higher that accuracy can be obtained by the following formula Value：

(9)

And

(10)

It is in wave frequencyAnd plasma frequencyThe group refractive index value at place；

Step B2, E layers of overlapping multinomial coefficient are calculated based on E layers of virtual height data prediction result：

FrequencyWithBetween the high curve of reality be expressed as

(11)

This curve must be able to provide plasma frequencyOn it is just really high, therefore have

(12)

(13)

Wherein,,

It differentiates to formula (11)

(14)

So as in frequencyThe reduction virtual height at place（From heightMeasurement）For：

(15)

Or

(16)

Wherein

(17)

It is similar to have

(18)

(19)

Wherein

(20)

(21)

Formula (12), formula (13), formula (16), formula (18) and formula (19) determineWithFive values, According to formula (11), frequencyIt is real highFor：

(22)

If meet formula (12), formula (13), formula (16), formula (18), formula (19) and formula (22)Value can be obtained, then Equation group must be linearly related, it follows that constantWithThere are following relations：

(23)

(24)

Frequency is determined by solving Simultaneous Equations (24)5 multinomial coefficients（）；

It can be obtained by deriving above

(25)

WhereinWhen,Respectively equal to、With,Respectively equal to、、,

(26)

(27)

Integration in formula (25) estimated by the Gaussian dependence formula of 5 points, whereinAnd weightsFor：

(28)

(29)

It is corresponding eachValue, can be calculated corresponding firstWithValue, for given magnetic field intensity and direction,Value be only dependent uponWith, from 5Value can accordingly calculate 5Value and 5Value, then for4Value is calculated by the following formula (30)：

(30)

CoefficientWithAfter calculating, Simultaneous Equations (24) can be solved and obtain coefficient, when, each frequency can be provided by repeating more than calculating process completely5 multinomial coefficients, here due to Simultaneous Equations (24) are an ill-conditioned linear systems to a certain extent, before solving equations, by being differed between equation Its accuracy in computation can be greatly improved, so using following Simultaneous Equations during evaluator coefficient

(31)

Step B3, E layers of section are calculated using overlapping multinomial model based on E layer datas pre-processed results：

FrequencyThe real height at placeIt is expressed as：

(32)

In formulaWithIt is wave frequency、WithThe virtual height at place、WithWith reference toDefinite value passes through virtual height data、WithIt calculates and obtains：

(33)

(34)

(35)。

Further, the step C is specifically included：

Step C1, Gu KuanIt is deep with paddyIt estimates：

It is maximum according to E layers of section after using the complete E layers of section of overlapping multinomial model inverting based on E layer datas after pretreatment Value, i.e. E layers is faced the corresponding real height of frequency, and estimation paddy layer parameter paddy is wideIt is deep with paddy, expression is：

,

(36)

WhereinFace the corresponding real height of frequency for E layers,

According to the paddy layer parameter of estimation, structure " three-segment type " paddy layer is specially：

(37)

WhereinFace frequency, coefficient for E layersWithByWith 2 points determine, coefficientWithByWith2 points determine；

Or increase " two segment types " paddy layer, it is specially

(38)

Wherein coefficientWithByWith2 points determine, coefficient WithByWith2 points determine；

Step C2, F layers of profile inversion：

（1）Less than F layers peak frequencyPlasma frequency corresponding real high calculate：

When paddy layer parameter paddy is wideIt is deep with paddyAfter tentatively estimating, based on structure three-segment type or two segment type paddy layer models and F Data after layer pretreatment calculate F layers using the overlapping multinomial model of same step B and are less than peak frequencyPlasma frequency It is corresponding real high；

（2）F layers of peak frequencyCorresponding real high calculating：

Calculate peak frequencyIt is corresponding real highIt needs to be determined thatValue, have for the ionosphere of stock size：

(39)

In formulaRepresent frequency interval（It is equal to）,The critical frequency of expression layer；

（3）F range upon range of mountains is high to be calculated：

Use critical frequencyCalculate ionosphere peak height, frequency is passed through by parabola of fitWithCorresponding It is real highWithIt realizes, is embodied as：

(40)

Step C3, Gu KuanIt is deep with paddyIt is final to determine：

The real height of ionosphere vertical incidence radio wave attenuation and the relation of detection record virtual height are：

(41)

WhereinFor in electric wave wave frequency rateAnd plasma frequencyLocate corresponding group refractive index, according to upper The section of step inverting is stated, corresponding virtual height data are calculated based on the relation between real high and virtual height, then calculate actual measurement virtual heightWith the error for calculating virtual height, it is specially：

(42)

It is wide with by way of optimizing in paddy depth a certain range paddy, it will makeThe paddy for reaching minimum is wide and paddy depth parameter determines For paddy layer sectional parameter.

Further, the step D is specially：

Based on make in step C actual measurement virtual height and calculate virtual height errorReach minimum F layers of cross-sectional data of that group of inverting, really It is set to final F layer sections.

The beneficial effects of the present invention are：

Vertical survey ionogram inversion method disclosed in this invention based on overlapping multinomial model, it is proposed that based on overlapping more The vertical survey ionogram inversion algorithm of fused data pretreatment and the paddy layer section optimizing of item formula model thought, builds multinomial first Formula ionospheric model；Then in conjunction with actual measurement virtual height data, under the constraints of section continuous and derivable, pass through search, iteration Method obtains the coefficient of multinomial ionospheric model, so as to fulfill effective extrapolation compensation pretreatment of missing measured data；It is based on Pretreated E layers of virtual height data, multinomial model is overlapped by ionosphere, solves the corresponding multinomial coefficient of each frequency, Directly calculate Ionospheric Profile E layers definite；Paddy is wide and paddy depth optimizing by way of increase standard scores segmentation paddy layer；Last base In paddy layer and pretreated F layers of virtual height data, multinomial model is overlapped using ionosphere, it is corresponding multinomial to solve each frequency Formula coefficient directly calculates and determines final Ionospheric Profile, can effectively improve ionospheric inversion precision and stability.

Description of the drawings

Fig. 1 is the vertical flow chart for surveying ionogram inversion method disclosed in this invention；

Fig. 2 is to carry out inverting to three layers of ionosphere of a layer containing " two segment types " paddy using the method disclosed in the present Example；

Fig. 3 is to carry out inverting to three layers of ionosphere of a layer containing " three-segment type " paddy using the method disclosed in the present Example.

Specific embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.

Embodiment 1, as shown in Figure 1, present embodiment discloses a kind of vertical survey ionogram based on overlapping multinomial model is anti- Method is drilled, the described method comprises the following steps：

（1）Build Ionospheric Profile mathematical model：

The present invention by ionosphere modeling be comprising E layer, paddy layer,Layer,Four layer models of layer, E layers are with paddy layer section Parabolic type,Layer andLayer section is polynomial type.In order to which the Electron density profile for making foundation meets continuous and derivable characteristic, Layer and the plasma frequency at the tie point of layer, calculated respectively based on tie point above and below ionospheric model（Square）Value And section gradient should be equal, according to this condition, limits the internal relation between relevant parameter.

（2）Obtain structure ionosphere model parameters：

The virtual height and the error and minimum criteria of actual measurement virtual height being calculated based on model obtain the final section ginseng of each layer Number：

1）Obtain E layers of sectional parameter：

Determine E layers of section three parameters be mainly、（Or）、, whereinIonogram can be surveyed by hanging down Interpretation software provides automatically, and error is less than 0.2MHz, and a kind of method of range searching is used to realize E layers of calculating virtual height in this method Selection and structure model parameter determine, be specially：Have assuming that hanging down and surveying the E layers actual measurement trace that ionization map interpretation obtainsIt is a Point, corresponding working frequency and virtual height are respectivelyWith, the E layers of reading face frequency and minimum virtual height is denoted as respectively With, then to parameter、、、、（Wherein、WithIt is search range controlled quentity controlled variable）Different groups of parameters, each group of ginseng are obtained with certain stepping value Several computational methods according to model E layer virtual height obtainA point, then calculate actual measurement virtual height and model calculate virtual height Error sum of squares, error sum of squares is made to reach that group of minimum parameter and is determined as E layers of sectional parameter.

2）Obtain paddy layer sectional parameter：

Layer actual measurement trace in, face more than E layer frequency withLayer trace minimum virtual heightBetween corresponding frequency Data are more sensitive to paddy layer parameter, therefore, in the refutation process of paddy layer parameter, select this part tracing point as paddy layer phase Virtual height should be surveyed, paddy layer is corresponding to calculate virtual height and definite paddy layer building model parameter for choosing, it is assumed that sharedIt is a, Corresponding working frequency and virtual height are respectivelyWith.It is calculated in this method by least square methodLayer section coefficient, And pass through whether the coefficient for checking and calculating meetsPaddy layer section is realized in the characteristic of layer section monotonic increase, final search, iteration The acquisition of parameter.

3）Layer sectional parameter

It choosesIn layer actual measurement trace,The corresponding frequency of layer trace minimum virtual height arrivesBetween data for determiningLayer parameter, it is assumed that sharedA data point, corresponding working frequency and virtual height are respectivelyWith.It is having readIn the case of,Layer section is by multinomial coefficientIt determines completely, the side used during similar inverting paddy layer parameter can be used Method calculates these coefficients.

4）Layer sectional parameter：

Data in layer actual measurement trace are used to determineLayer parameter, it is assumed that sharedA data point, corresponding work Frequency and virtual height are respectivelyWith.It is having readIn the case of,Layer section is by coefficientIt determines completely,After layer parameter determines,Layer withLayer point of intersection section gradient have also determined that, thereforeLayer building model parameter is really Fixed is equally a constrained optimization problem, and similar determine can be usedThe method used during layer parameter calculates these coefficients.

5）Final definite paddy layer,Layer,Layer building model parameter：

For not reaching full growthLayer hangs down and surveys what ionization map interpretation software provided automaticallyCompared withLayer reaches full growth When deviationIt is a unknown quantity, theoretically,Value between, therefore, definite paddy layer,Layer,It, will during layer parameter Interior traversal, selection make all data point calculation virtual heights with actual measurement virtual height error and MinimumCorresponding paddy layer,Layer,Layer parameter as final paddy layer,Layer,Layer parameter.

（3）Missing actual measurement virtual height Data Extrapolation compensation pretreatment：

The parameter for each layer building model that ionospheric model and combination measured data based on above-mentioned structure obtain, leads to It crosses model calculating and realizes that the extrapolation of missing measured data compensates, continuous preprocessed data in formation trend is that follow-up reality is high Calculate the data supporting that high quality is provided.

（4）E layers of frequencyReal high calculate：

Result based on measured data pretreatment, it is assumed that E layers sharedA data point, corresponding working frequency and virtual height RespectivelyWith, based on the overlapping multinomial model of 5 coefficients, calculate frequency（）It is corresponding real high。 Specially：

1）Evaluator coefficient and average group refractive index

It is extrapolated based on measured data and compensates the result of pretreatment（Working frequency and virtual height are respectivelyWith（））, each frequency is calculated using formula (31)（）Corresponding 5 multinomial coefficients；Use formula (1)-formula (8) wave frequency is calculatedAnd plasma frequencyThe group refractive index at place is；Electric wave frequency is calculated using formula (9) and (10) RatePlace,WithBetween the average of the corresponding group refractive index of plasma frequency beValue.

2）Calculate the real high of first three frequency：

Setpoint frequency、Corresponding is real high、It is equal to virtual height, calculated with formula (43) Value, then by formula (44) represent 5 coefficients overlapping polynomial computation obtain frequencyIt is real high。

(43)

(44)

3）Calculate the real height of E layers of other frequencies：

The overlapping multinomial of 5 coefficients represented using formula (32) is sequentially determined real height（）, formula InIt is calculated and obtained using formula (33)-formula (35).

（5）Preset paddy layer parameter simultaneously calculates F layers real high：

Result based on measured data pretreatment, it is assumed that F layers sharedA data point, corresponding working frequency and virtual height RespectivelyWith.It is wide according to above-mentioned paddy layer parameter evaluation method estimation paddyIt is deep with paddy, and build corresponding paddy layer parameter and cut open Face calculates frequency using the overlapping multinomial model of 5 coefficients（）It is corresponding real high.Specially：

1）Paddy layer parameter is set

It is wide according to formula (36) preset paddyIt is deep with paddyValue, and use formula (37) or formula (38) model construction paddy layer section.

2）Evaluator coefficient and average group refractive index

Method is calculated with above-mentioned E layers, wherein useValue is arranged to E layers and faces frequency。

3）Calculate the real high of first three frequency

Setpoint frequency、Corresponding is real high、Paddy layer section model is respectively equal to built in frequency、Extrapolation Value、；It is calculated to following formula (45)Value, 5 coefficients then represented by formula (44) Overlapping polynomial computation obtains frequencyIt is real high。

(45)

(46)

(47)

(48)

4）It calculates F layers and is less than peak frequencyPlasma frequency it is corresponding real high

The overlapping multinomial of 5 coefficients represented using formula (32) is sequentially determined real height（）, formula InIt is calculated and obtained using formula (33) and (34), calculated by (49)Value.

(49)

5）Calculate peak frequencyIt is corresponding real high

It is calculated using formula (31)Corresponding 5 multinomial coefficients；With reference to actual measurement critical frequency, calculated using formula (39)Value；Then the overlapping polynomial computation peak frequency of 5 coefficients represented using formula (32)It is corresponding real high's Value.

6）Calculate ionosphere peak height

With reference to actual measurement critical frequency, ionosphere peak height is calculated using formula (40)Value.

（6）Calculate the error with actual measurement virtual height data

According to the section of above-mentioned steps inverting, corresponding virtual height data are calculated using formula (41), are then counted according to formula (42) Calculate actual measurement virtual heightVirtual height is calculated with modelBetween error.

（7）Determine final section

Set paddy wideIt is deep with paddy 、In the range of with certain stepping Value obtains various combination parameter, and each group of parameter repeats above step（5）With（6）It obtains actual measurement virtual height and calculates the mistake of virtual height Difference, makes that error reaches minimum that group of paddy layer parameter and section is determined as final paddy layer parameter and section.

Fig. 2 and Fig. 3 gives two inverting examples using the method for the present invention, and Fig. 2 invertings section contains " two segment types " paddy layer, Fig. 3 invertings section is containing " three-segment type " paddy layer.Wherein measured data is the sentence read result hung down and survey ionization map interpretation software, this is one Typical three layers（E layers,Layer andLayer）、The underdeveloped Ionospheric Echo trace of layer.In the present invention, based on structure electricity Absciss layer model realizes missing measured data effective extrapolation compensation（Black is punctuated）；Using the present invention is based on overlapping multinomials Vertical survey ionogram inversion method obtain more smooth and accurate Ionospheric Profile（Black dash line）, it is significantly better than and only adopts With the profile inversion result of measured data（Solid black lines）And the profile inversion result of the direct interpolation of measured data（Black dotted line）. Overcome the shortage of data and be not associated with electricity that more in multinomial inversion method or mass data lacks, each layer faces near frequency The defects of section calculation error caused by the direct interpolation of a large amount of missing datas of absciss layer propagation characteristic significantly increases or even is wrong；And " the paddy layer " of physical presence is reasonably considered in inverting section so that ionospheric inversion precision and stability higher.

Claims

1. a kind of vertical survey ionogram inversion method based on overlapping multinomial model, which is characterized in that the described method includes following Step：Step A, measured data pre-processes, and the step A is specially：

Step A1, the E layers of parabolic model and paddy layer section, the F of multinomial model are built₁Layer and F₂Layer section；

Step A2, the ionospheric model based on foundation, with reference to actual measurement virtual height data, under the constraints of section continuous and derivable, Virtual height and actual measurement virtual height error and minimum criteria are calculated according to ionospheric model, structure electricity is obtained by the method for search, iteration The parameter of absciss layer model；

Step A3, extrapolation compensation pretreatment carries out missing measured data using the ionospheric model of definite parameter, is formed complete Continuous virtual height data；

Step B, it is based on measured data pretreatment to calculate E layers of section, the step B tools as a result, using and overlapping multinomial model Body includes：

Symbol μ '_ijFor representing in wave frequency f_iWith plasma frequency f_jThe group refractive index μ ' at place, group refractive index μ ' tools There is 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 formula, f_HFor gyro-frequency at the survey station overhead 300km that hangs down, θ is magnetic dip angle at vertical survey station overhead 300km, and f is wave frequency, f_NFor plasma frequency；

In wave frequency f_iPlace, f_jAnd f_j-1Between the corresponding group refractive index μ ' of plasma frequency average useIt represents, it is right In j=2,3,4 ..., (i-1),It is higher can to obtain accuracy by the following formula by middle i=4,5,6 ..., n 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

<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-1/2}It is in wave frequency f_iAnd plasma frequencyThe group refractive index value at place；

Frequency f_i-2And f_i+1Between the high curve of reality be expressed as

This curve must be able to provide plasma frequency f_N=f_i-2、f_i-1On it is just really high, therefore have

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

It differentiates to formula (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>

So as in frequency f_i-1The reduction virtual height at place, from height h_i-2It is measured as：

<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>

It is similar to have

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) determine a₀、a₁、a₂、a₃And a₄Five values, according to formula (11), Frequency f_iThe high h of reality_iFor：

h_i=a₀+a₁+a₂+a₃+a₄ (22)

It can be obtained if meeting a values of formula (12), formula (13), formula (16), formula (18), formula (19) and formula (22), then equation Group must be linearly related, it follows that constant p_i1、p_i2、p_i3、p_i4And p_i5There are following relations：

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)

Frequency f is determined by solving Simultaneous Equations (24)_i5 multinomial coefficient p_im, m=1,2,3,4,5；

It can be obtained by deriving 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>

Wherein j=1, when 2,3, f is respectively equal to f_i-1、f_iAnd f_i+1, μ ' is respectively equal to

Integration in formula (25) estimated by the Gaussian dependence formula of 5 points, wherein x_rAnd weight w_rFor：

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)

Corresponding each j values, can be calculated corresponding f and t first_mValue, for given magnetic field intensity and direction, the value of μ ' t F and t are only dependent upon, from 5 t_r=x_rt_mValue can accordingly calculate 5 μ ' t value and 5 Value, then for k=1,2,3,44 b_jkValue is calculated by the following formula (30)：

After coefficient a and b are calculated, Simultaneous Equations (24) can be solved and obtain coefficient p_i1, p_i2, p_i3, p_i4, p_i5, work as i=3,4, 5 ..., n-1, each frequency f can be provided by repeating more than calculating process completely_i5 multinomial coefficients, here due to simultaneous Equation group (24) is an ill-conditioned linear systems to a certain extent, can by being differed between equation before solving equations Its accuracy in computation is greatly improved, so using following Simultaneous Equations during evaluator coefficient

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_iThe high h of reality at place_iIt is expressed 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)

H in formula "_I-1,1-2、h″_{I, i-2}With h "_I+1,1-2It is wave frequency f_i-1、f_iAnd f_i+1The virtual height h ' at place_i-1、h′_iWith h '_i+1With reference to h_i-2Definite value passes through virtual height data h "_{I-1, i-3}、h″_{I, i-3}With h '_i+1It calculates and obtains：

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, based on measured data pre-processed results and E layers of section, the wide W of estimation parameter paddy_vWith paddy depth F_v, and build corresponding paddy Layer parameter section, the step C are specifically included：

Step C1, the wide W of paddy_vWith paddy depth F_vIt estimates：

After the complete E layers of section of overlapping multinomial model inverting being used based on E layer datas after pretreatment, E layers of section maximum of foundation, i.e., E layers are faced the corresponding real height of frequency, the wide W of estimation paddy layer parameter paddy_vWith paddy depth F_v, expression is：

Wherein H_MaxFace the corresponding real height of frequency for E layers,

Wherein f_CEFace frequency, coefficient q for E layers₁And p₁By [f_CE, H_Max] and [f_CE-F_v, H_Max+0.15W_v] 2 points determine, coefficient q₂With p₂By [f_CE-F_v, H_Max+0.8W_v] and [f_CE, H_Max+W_v] 2 points determine；

Or increase " two segment types " paddy layer, it is specially

Wherein coefficient q₁And p₁By [f_CE, H_Max] and [f_CE-F_v, H_Max+0.4W_v] 2 points determine, coefficient q₂And p₂By [f_CE-F_v, H_Max+ 0.4W_v] and [f_CE, H_Max+W_v] 2 points determine；

Step C2, F layers of profile inversion：

(1) it is less than F layers of peak frequency f_nPlasma frequency corresponding real high calculate：

As the wide W of paddy layer parameter paddy_vWith paddy depth F_vAfter tentatively estimating, based on structure three-segment type or two segment type paddy layer models and F layers of pre- place Data after reason calculate F layers using the overlapping multinomial model of same step B and are less than peak frequency f_nPlasma frequency it is corresponding It is real high；

(2) F layers of peak frequency f_nCorresponding real high calculating：

Calculate peak frequency f_nThe corresponding high h of reality_nIt needs to be determined that h "_{N+1, n-2}Value, have for the ionosphere of stock size：

<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>

Δ f represents frequency interval f in formula_n+1-f_n=f_n-f_n-1, f_cThe critical frequency of expression layer；

(3) F range upon range of mountains is high calculates：

Use critical frequency f_cCalculate ionosphere peak height h_c, frequency f is passed through by parabola of fit_n-2And f_nCorresponding is real high h_n-2And h_nIt realizes, is embodied as：

Step C3, the wide W of paddy_vWith paddy depth F_vIt is final to determine：

<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>

Wherein μ ' (f_i, f_N) it is in electric wave wave frequency rate f_iWith plasma frequency f_NLocate corresponding group refractive index, according to above-mentioned step The section of rapid inverting calculates corresponding virtual height data based on the relation between real high and virtual height, then calculates actual measurement virtual height h '_iWith The error of virtual height is calculated, is specially：

<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>

Paddy is wide and paddy depth a certain range in by way of optimizing, reaching ε, minimum paddy is wide and paddy depth parameter is determined as paddy Layer sectional parameter；

Step D, based on measured data pre-processed results and paddy layer section, F layers of section are calculated using overlapping multinomial model, it is described Step D is specially：

Based on actual measurement virtual height and calculating virtual height error ε is made to reach minimum F layers of cross-sectional data of that group of inverting in step C, it is determined as Final F layer sections.