CN105005682A - Retrieval method for vertical exploration ionogram - Google Patents

Abstract

The invention discloses a retrieval method for a vertical exploration ionogram. The retrieval method comprises the following steps: S1: establishing a mathematical model of an ionized layer profile, wherein the model is a three-layer model which comprises an E layer, a grain layer and an F layer; S2) calculating the reflection echo virtual height of each layer, and deducing the calculation formulas of the echo virtual heights of the E layer and the F layer on the basis of an established ionized layer model; and S3) utilizing actual measurement ionogram data to combine with the calculation results of the echo virtual heights of the E layer and the F layer to carry out the retrieval of the ionized layer parameters of the E layer, the grain layer and the F layer. The retrieval method for the vertical exploration ionogram overcomes the defects in the prior art, and proposes a retrieval method, which carries out constrained optimization on the F layer parameters on the basis of a shifted chebyshev polynomial model, for the vertical exploration ionogram, the high-area echo tracing data of the F layer is selected after grain layer parameters are obtained, an F-layer profile multinomial coefficient is calculated under a constraint condition that the profile is guaranteed to be continuous and smooth, finally, the ionized layer profile is determined, and the precision and the stability of retrieval can be effectively improved.

Description

A kind of hanging down surveys ionogram inversion method

Technical field

The present invention relates to PROGRESS OF IONOSPHERIC RESEARCH IN and application, particularly relate to a kind of method utilizing the survey ionogram inverting Ionospheric Parameters that hangs down.

Background technology

Utilize survey ionogram inverting Ionospheric Profile (corresponding relation of layer height and plasma frequency or electron concentration) of hanging down to attract widespread attention always, at present, the survey ionogram inversion method that hangs down can be summarized as following two kinds: 1. direct computing method, the method directly utilizes actual measurement virtual height to calculate the true reflection height (being called for short very high) of respective frequencies, mainly contain burst method, single polynomial method, overlapping polynomial method etc., the Simultaneous Equations by setting up very high and virtual height is had plenty of in these methods, directly solve very high according to actual measurement virtual height, as burst method and single polynomial method, have plenty of from lower frequency to higher frequency, corresponding very high of each frequency is progressively determined by calculating, as burst method and overlapping polynomial method, 2. type method, the method hypothesis Ionospheric Profile can characterize with certain model, determines Ionospheric Profile by finding the vertical survey trace making to synthesize based on this model with the actual measurement trace model parameter that the best is coincide in some sense.Wherein, compared to first two method, type method is so not harsh for ionogram quality requirements, and can obtain good inversion result, application is comparatively general, the Chinese scholars multiple Ionospheric Parameters inversion method based on type method that utilized different detection datas to develop.

Based on type method thought, Huang Xue to admire etc. and discloses a kind of method based on displacement Chebyshev polynomials model inversion Ionospheric Profile, in the method, F layer is modeled as displacement Chebyshev polynomials, solve to meet and calculate virtual height and actual measurement virtual height best multinomial coefficient coincide in least square meaning, thus determine Ionospheric Profile.The weak point of the method is, the data for inverting paddy layer parameter that direct utilization is chosen determine paddy layer parameter and F layer section multinomial coefficient in the lump, make the vertical survey ionogram based on inversion result synthesis larger with actual measurement ionogram F layer upper zone echo trace deviation like this.

Summary of the invention

Technical matters to be solved by this invention is just to provide a kind of method utilizing the survey ionogram inverting Ionospheric Parameters that hangs down.

The present invention adopts following technical scheme:

A kind of hanging down surveys ionogram inversion method, and its improvements are, said method comprising the steps of:

Step 1: set up Ionospheric Profile mathematical model, described model is the three layer model comprising E layer, paddy layer and F layer, wherein, E layer and paddy layer section parabolic model representation, F layer section displacement Chebyshev polynomials model representation;

Step 2: the calculating of each layer reflection echo virtual height, based on the ionospheric model set up, the computing formula of derivation E layer, F layer echo virtual height;

Step 3: utilize actual measurement ionogram data, in conjunction with E layer, F layer echo virtual height result of calculation, carry out the inverting of E layer, paddy layer, F layer Ionospheric Parameters.

Further, described step 1 specifically comprises:

Step 11: Ionospheric electron density profile concrete form is shown below:

$\left\{\begin{array}{c}{f}_{NE}^2=f_{CE}^2\[1-{\left(\frac{h-h_{mE}}{y_{mE}}\right)}^2\]h_{bE}\≤h\≤h_{mE},h_{mE}\≤h\≤h_1\\ f_{NV}^2=f_{CV}^2\[1+{\left(\frac{h-h_{mV}}{y_{mV}}\right)}^2\]h_1\≤h\≤h_2\\ h=A_{I+1}+g^{1/2}\underset{i=0}{\overset{I}{\Σ}}{A}_i{T}_i\left(g\right)h_2\≤h\≤h_{mF}\end{array}\right.$ In formula, the concrete meaning of each symbol is as follows:

E layer: f _nErepresent E layer plasma frequency; f _cErepresent that E layer faces frequently; h _mErepresent that E range upon range of mountains is high; y _mErepresent that E layer half is thick; h _bE=h _mE-y _mErepresent high at the bottom of E layer; Paddy layer: f _nVrepresent paddy layer plasma frequency; f _cVrepresent the minimum plasma frequency of paddy layer; h _mVrepresent that paddy layer plasma frequency is f _cVtime corresponding layer height; y _mVrepresent that paddy layer half is thick; h ₂=h _mE+ W, W are defined as paddy layer width; F layer: T _ig () is displacement Chebyshev polynomials, have form shown in following formula:

F _nFrepresent F layer plasma frequency; f _cFrepresent that F layer faces frequently; A _i(i=0 ~ I+1) is displacement Chebyshev polynomials coefficient, and: h _mFrepresent that F range upon range of mountains is high, and: h _mF=A _i+1,

The tie point of E layer and paddy layer is positioned at E range upon range of mountains height h _mE, the tie point of paddy layer and F layer is positioned at height h ₂place, and at height h ₂the plasma frequency at place equals E layer and faces f frequently _cE, paddy layer comprises two parts: with the coupling part of E layer and the coupling part with F layer, and this two-part tie point is positioned at height h ₁place;

Step 12: in order to ensure the entire profile continuous and derivable, then at the tie point place of layer and layer, based on more than tie point and the square value of plasma frequency that calculates respectively of following ionospheric model and section gradient should be equal, according to this condition, limit the internal relation between correlation parameter.

Further, described step (2) specifically comprises:

Step 21: f is less than or equal to for frequency _cEelectric wave will reflect at E layer, carry out the derivation of E layer echo virtual height computing formula;

Step 22: f is greater than for frequency _cE, be less than or equal to f _cFelectric wave will reflect at F layer, carry out the derivation of F layer echo virtual height computing formula, be mainly included in the group distance, delta h ' of E Es-region propagations _e(f), the group distance, delta h ' propagated with E layer coupling part in paddy layer _j(f), the group distance, delta h ' propagated with F layer coupling part in paddy layer _v(f) and the group distance, delta h ' in F-layer propagation _fthe computing formula of (f).

Further, described step (3) specifically comprises:

Step 31: choose actual measurement E layer trace data, adopt the method for range searching to realize E layer f _cE, h _mEor h _bE, y _mEthe inverting of three parameters;

Step 32: choose in F layer trace the data be greater than between E layer faces frequently and the minimum virtual height of F layer trace is corresponding frequency, realizes the inverting of paddy layer parameter based on search, alternative manner;

Step 33, choose in F layer trace, frequency corresponding to the minimum virtual height of F layer trace is to f _cFbetween data, utilize contained optimization method to realize the inverting of F layer parameter.

Beneficial effect of the present invention is:

Vertical survey ionogram inversion method disclosed in this invention, overcome shortcoming of the prior art, propose the vertical survey ionogram inversion method of the constrained optimization F layer parameter based on displacement Chebyshev polynomials model, namely after obtaining paddy layer parameter, choose F layer upper zone echo trace data, under the constraint condition ensureing section continuous and derivable, calculate F layer section multinomial coefficient, finally determine Ionospheric Profile, can effectively improve inversion accuracy and stability.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of vertical survey ionogram inversion method disclosed in this invention;

Fig. 2 is two-layer ionospheric inversion example.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

Embodiment 1, as shown in Figure 1, present embodiment discloses a kind of hanging down and surveys ionogram inversion method, comprise the following steps:

(1) Ionospheric Profile mathematical model is set up:

The present invention is based on the thought of type method, it is the three layer model comprising E layer, paddy layer and F layer by ionosphere modeling, E layer and paddy layer section parabolic model representation, F layer section displacement Chebyshev polynomials model representation, Ionospheric electron density profile has form shown in formula (1):

$\left\{\begin{array}{c}{f}_{NE}^2=f_{CE}^2\[1-{\left(\frac{h-h_{mE}}{y_{mE}}\right)}^2\]h_{bE}\≤h\≤h_{mE},h_{mE}\≤h\≤h_1\\ f_{NV}^2=f_{CV}^2\[1+{\left(\frac{h-h_{mV}}{y_{mV}}\right)}^2\]h_1\≤h\≤h_2\\ h=A_{I+1}+g^{1/2}\underset{i=0}{\overset{I}{\Σ}}{A}_i{T}_i\left(g\right)h_2\≤h\≤h_{mF}\end{array}\right.---\left(1\right)$

The tie point of E layer and paddy layer is positioned at E range upon range of mountains height h _mE, the tie point of paddy layer and F layer is positioned at height h ₂place, and at height h ₂the plasma frequency at place equals E layer and faces f frequently _cE, paddy layer comprises two parts: with the coupling part of E layer and the coupling part with F layer, and this two-part tie point is positioned at height h ₁place, in formula (1), the concrete meaning of each symbol is as follows:

E layer:

F _nErepresent E layer plasma frequency; f _cErepresent that E layer faces frequently; h _mErepresent that E range upon range of mountains is high; y _mErepresent that E layer half is thick; h _bE=h _mE-y _mErepresent high at the bottom of E layer;

Paddy layer:

F _nVrepresent paddy layer plasma frequency; f _cVrepresent the minimum plasma frequency of paddy layer; h _mVrepresent that paddy layer plasma frequency is f _cVtime corresponding layer height; y _mVrepresent that paddy layer half is thick; h ₂=h _mE+ W, W are defined as paddy layer width;

F layer:

T _ig () is displacement Chebyshev polynomials, have form shown in formula (2):

$\left\{\begin{array}{c}{T}_i\left(g\right)=2(2g-1)T_{i-1}\left(g\right)-T_{i-2}\left(g\right)\\ T_0\left(g\right)=1,T_1\left(g\right)=2g-1\end{array}\right.---\left(2\right)$

$g=\frac{\ln (f_{NF}/f_{CF})}{\ln (f_{CE}/f_{CF})}0\≤g\≤1---\left(3\right)$

F _nFrepresent F layer plasma frequency; f _cFrepresent that F layer faces frequently; A _i(i=0 ~ I+1) is displacement Chebyshev polynomials coefficient, and:

$A_{i+1}=h_2-\underset{i=0}{\overset{I}{\Σ}}{A}_i---\left(4\right)$

H _mFrepresent that F range upon range of mountains is high, and:

h _mF＝A _I+1

(5)

In order to ensure the entire profile continuous and derivable, then at the tie point place of layer and layer, based on more than tie point and the square value of plasma frequency that calculates respectively of following ionospheric model and section gradient should be equal, according to this condition, limit the internal relation between correlation parameter, that is:

At h=h ₂place, has:

$\left\{\begin{array}{c}{f}_{NF}^2{|}_{h=h_2}=f_{NV}^2{|}_{h=h_2}\\ \frac{\∂f_{NF}^2}{\∂h}{|}_{h=h_2}=\frac{\∂f_{NV}^2}{\∂h}{|}_{h=h_2}\end{array}\right.---\left(6\right)$

Consider $f_{NF}^2{|}_{h=h_2}=f_{CE}^2,$ And make $D\stackrel{\mathrm{\Δ}}{=}{f}_{CE}^2-f_{CV}^2$ And $\frac{\∂f_{NF}^2}{\∂h}{|}_{h=h_2}\stackrel{\mathrm{\Δ}}{=}\frac{1}{B},$ That is:

$B\stackrel{\mathrm{\Δ}}{=}\frac{1}{4f_{CE}^2\ln (f_{CE}/f_{CF})}\underset{i=0}{\overset{I}{\Σ}}{A}_i(1+2\frac{{\mathrm{dT}}_i\left(g\right)}{dg}{/}_{g=1})---\left(7\right)$

Then obtained by formula (6):

$\{\begin{array}{c}{h}_{mV}=h_2-2BD\\ y_{mV}=2{\mathrm{Bf}}_{CV}{D}^{1/2}\end{array}---\left(8\right)$

At h=h ₁place, has:

$\left\{\begin{array}{c}{f}_{\mathrm{NE}}^2{|}_{h=h_1}=f_{NV}^2{|}_{h=h_1}\\ \frac{\∂f_{\mathrm{NE}}^2}{\∂h}{|}_{h=h_1}=\frac{\∂f_{NV}^2}{\∂h}{|}_{h=h_1}\end{array}\right.---\left(9\right)$

Can be obtained by the above formula in formula (9):

h _mV＝h _mE+[(4B ²D+Q)D] ^1/2(10)

Wherein, above formula in formula (10) convolution (8) and W can obtain further:

$D=\frac{W^2}{Q+4BW}---\left(11\right)$

H can be provided by the following formula in formula (9) ₁result of calculation be:

$h_1=\frac{4B^2{\mathrm{Dh}}_{mE}+h_{mV}Q}{Q+4B^{2}D}---\left(12\right)$

Derived as can be seen from above, after obtaining E layer parameter, as long as paddy layer determines B and W two parameters, then paddy layer section just can be determined, therefore, in the inverting of follow-up paddy layer parameter, we only need determine B and W.

(2) calculating of each layer reflection echo virtual height:

Survey ionogram based on relating in the Ionospheric Parameters inversion method of type method according to the Ionospheric Profile model synthesis of setting up is vertical, its essence carries out the calculating of different operating frequency hop echo virtual height.In order to simplify computation process, very large error can not be introduced again simultaneously, the impact of terrestrial magnetic field is not considered when calculating group's distance of electric wave at E layer and paddy Es-region propagations, when calculating the group distance of electric wave in F-layer propagation, magnetic field is certain value hypothetically, and namely the terrestrial magnetic field of any position is consistent with the terrestrial magnetic field of vertical survey station overhead 300km At The Height.

The calculating of E layer echo virtual height:

F is less than or equal to for frequency _cEelectric wave will reflect at E layer, echo virtual height computing formula is:

$h^{\′}\left(f\right)=h_{bE}+{\∫}_{h_{bE}}^{h_r}{\mathrm{\μ}}^{\′}dh---\left(13\right)$

Wherein, f is wave frequency, h _rfor radio wave attenuation point place height, μ ' is group refractive index, when not considering terrestrial magnetic field, has following form:

${\mathrm{\μ}}^{\′}={(1-f_N^2/f^2)}^{-1/2}---\left(14\right)$

F in formula _nrepresent corresponding position plasma frequency.

Based on the E layer ionospheric model set up, then formula (13) can calculate further:

$h^{\′}\left(f\right)=h_{bE}+\frac{1}{2}{y}_{mE}\frac{f}{f_{CE}}\ln \frac{f_{CE}+f}{f_{CE}-f}---\left(15\right)$

The calculating of F layer echo virtual height:

F is greater than for frequency _cE, be less than or equal to f _cFelectric wave will reflect at F layer, echo virtual height computing formula is:

$h^{\′}\left(f\right)=h_{bE}+{\∫}_{h_{bE}}^{h_{mE}}{\mathrm{\μ}}^{\′}dh+{\∫}_{h_{mE}}^{h_1}{\mathrm{\μ}}^{\′}dh+{\∫}_{h_1}^{h_2}{\mathrm{\μ}}^{\′}dh+{\∫}_{h_2}^{h_r}{\mathrm{\μ}}^{\′}dh---\left(16\right)$

Wherein, in formula (16), Section 2 is the group distance of electric wave at E Es-region propagations, is designated as Δ h ' _ef (), Section 3 is group's distance that electric wave is propagated with E layer coupling part in paddy layer, is designated as Δ h ' _jf (), Section 4 is group's distance that electric wave is propagated with F layer coupling part in paddy layer, is designated as Δ h ' _vf (), Section 5 is the group distance of electric wave in F-layer propagation, is designated as Δ h ' _f(f).

Calculate Δ h ' _e(f), Δ h ' _j(f), Δ h ' _vf the μ ' used time () still has the form of formula (14), result of calculation is respectively:

${\mathrm{\Δh}}_E^{\′}\left(f\right)=\frac{1}{2}{y}_{mE}\frac{f}{f_{CE}}\ln \frac{f+f_{CE}}{f-f_{CE}}---\left(17\right)$

${\mathrm{\Δh}}_J^{\′}\left(f\right)={\mathrm{fQ}}^{1/2}\ln \{\[\sqrt{\frac{QD}{Q+4B^{2}D}}+\sqrt{f^2-f_{CE}^2+\frac{QD}{Q+4B^{2}D}}\]{(f^2-f_{CE}^2)}^{-1/2}\}---\left(18\right)$

${\mathrm{\Δh}}_V^{\′}\left(f\right)=2fB\sqrt{D}\[\arcsin \left(\sqrt{\frac{D}{f^2-f_{CE}^2+D}}\right)+\arcsin \left(\frac{2BD}{\sqrt{(Q+4B^{2}D)(f^2-f_{CE}^2+D)}}\right)\]---\left(19\right)$

Calculate Δ h ' _ff the μ ' used time () has following form:

${\mathrm{\μ}}^{\′}=\frac{G_o}{{\mathrm{\μ}}_o}---\left(20\right)$ Wherein, ${\mathrm{\μ}}_o=\sqrt{1-X_o}---\left(21\right)$

$X_o=f_N^2/f^2---\left(22\right)$

$G_o=\frac{{\mathrm{\μ}}_o}{n_o}\{1+\frac{x_o{\tan }^2\mathrm{\θ}}{M^2}\[\frac{1+x_o}{{(1+{\mathrm{\γ\μ}}_o^4)}^{1/2}}-\frac{2}{1+{(1+{\mathrm{\γ\μ}}_o^4)}^{1/2}}\]\}---\left(23\right)$

$\mathrm{\γ}=\frac{4{\tan }^2\mathrm{\θ}}{Y_o^2{\cos }^2\mathrm{\θ}}---\left(24\right)$

Y _o＝f _H/f (25)

$M=1+{\mathrm{\μ}}_o^2\frac{2{\tan }^2\mathrm{\θ}}{1+{(1+{\mathrm{\γ\μ}}_o^4)}^{1/2}}---\left(26\right)$

${\left(\frac{{\mathrm{\μ}}_o}{n_o}\right)}^2=\frac{M}{1+2{\tan }^2\mathrm{\θ}/\[1+{(1+{\mathrm{\γ\μ}}_o^4)}^{1/2}\]}---\left(27\right)$

In formula, f _hfor 300km place, vertical survey station overhead gyro-frequency, θ is 300km place, the survey station overhead magnetic dip that hangs down.Now, Δ h ' cannot directly be provided _ff the analytical expression of (), can only adopt numerical integration method to calculate Δ h ' _ff (), considers at reflection spot place, μ ' is infinitely great, in order to carry out numerical evaluation, makes following variable and replaces, that is:

$f_{NF}^2=f^2-t^2(f^2-f_{CE}^2)0\≤t\≤1---\left(28\right)$

Then Δ h ' _ff () can be written as:

${\mathrm{\Δh}}_F^{\′}\left(f\right)={\∫}_{h_2}^{h_r}{\mathrm{\μ}}^{\′}dh={\∫}_{f_{CE}^2}^{f^2}{\mathrm{\μ}}^{\′}\frac{dh}{{\mathrm{df}}_{NF}^2}{\mathrm{df}}_{NF}^2={\∫}_0^{1}2{\mathrm{\μ}}^{\′}t(f^2-f_{CE}^2)\frac{dh}{{\mathrm{df}}_{NF}^2}dt---\left(29\right)$

According to the F layer ionospheric model (following formula in formula (1)) set up, can obtain:

$\frac{dh}{{\mathrm{df}}_{NF}^2}=\frac{1}{21n(f_{CE}/f_{CF})f_{NF}^2}\{\frac{1}{2}{g}^{-1/2}\[\underset{i=0}{\overset{I}{\Σ}}{A}_i{T}_i\left(g\right)+2g\underset{i=0}{\overset{I}{\Σ}}{A}_i\frac{{\mathrm{dT}}_i\left(g\right)}{dg}\]\}---\left(30\right)$

Formula (30) is updated to formula (29), then Δ h ' _ff () can be written as further:

${\mathrm{\Δh}}_F^{\′}\left(f\right)=\underset{i=0}{\overset{I}{\Σ}}{A}_i{S}_i\left(f\right)---\left(31\right)$

In formula,

$S_i\left(f\right)=\frac{f^2-f_{CE}^2}{2ln(f_{CE}/f_{CF})}{\∫}_0^1\frac{{\mathrm{\μ}}^{\′}t}{f_{NF}^2{g}^{1/2}}\[T_i\left(g\right)+2g\frac{{\mathrm{dT}}_i\left(g\right)}{dg}\]dt---\left(32\right)$

Now, closing on reflection spot (t → 0) place, by formula (21) ~ formula (27), can μ obtained _o→ 0, M → 1, thus obtained by formula (20) so, as long as magnetic dip s _if () just can be calculated by formula (32), wherein f _cFautomatically can be provided by vertical survey ionogram intelligent interpretation software, thus Δ h ' can be obtained according to formula (31) _f(f).

(3) inverting of each layer parameter:

The inverting of ionosphere model parameters in type method thought, mainly finds such parameter, and the difference of the virtual height namely calculated by these parameters and actual measurement virtual height is minimum in some sense.

1) inverting of E layer parameter

From above formula in formula (1), determine three parameter mainly f of E layer section _cE, h _mE(or h _bE), y _mE, wherein f _cEautomatically can be provided by vertical survey ionogram intelligent interpretation software, error is less than 0.2MHz, adopts a kind of method of range searching to realize the inverting of E layer parameter, be specially in the present invention:

Suppose that the E layer trace that vertical survey ionogram intelligent interpretation obtains has K point, frequency of operation and the virtual height of its correspondence are respectively f _kwith h " (f _k), the E layer of reading faces frequently and minimum virtual height be designated as respectively into with h " _minE, then to parameter f _cE, h _bE, y _mEexist respectively [h " _minE-δ ₁, h " _minE+ δ ₂], [0, δ ₃] (wherein δ ₁, δ ₂and δ ₃hunting zone controlled quentity controlled variable) obtain different group parameter with certain stepping value, each group parameter calculates the h ' (f of K point according to formula (15) _k), then calculate the error sum of squares of actual measurement virtual height and calculating virtual height:

make ε reach that minimum group parameter and be namely defined as E layer parameter.

2) inverting of paddy layer parameter

From analysis above, as long as determine B and W two parameters, paddy layer section just can be determined.Based on the inverting of searching for, alternative manner realizes paddy layer parameter in the present invention.

In F layer trace, be greater than E layer face frequently and the minimum virtual height of F layer trace (be designated as 0.7h " _minF) data between corresponding frequency are more responsive to paddy layer parameter, therefore, in the refutation process of paddy layer parameter, select this part tracing point to be used for determining paddy layer parameter, suppose to have K point, frequency of operation and the virtual height of its correspondence are respectively f _kwith h " (f _k).

The basic step of paddy layer parameter inverting is:

1. W=0 is set;

2. B=0 is set, I=7;

3. F layer section coefficient A is calculated based on least square method _i(i=0 ~ I+1);

4. the coefficient A of calculating is checked _iwhether (i=0 ~ I) meets F layer section monotone increasing characteristic, if (a) does not meet, then 5. I=I+1, if I < 0, then perform, otherwise, perform 3.; If b () meets, to A _i+1compare with the value of a front iteration record, if the difference of the two is less than a certain smaller value (such as 0.5km), the then error sum of squares of a calculating K point actual measurement virtual height and calculating virtual height, record the value of the error sum of squares of current B, W and calculating, otherwise, in the maximum iteration time situation not exceeding restriction, according to A _i(i=0 ~ I) adjusts I automatically, upgrades the value of B according to formula (7), performs 3., if exceed the maximum iteration time of restriction, then performs 5.;

5. W=W+1 (unit is km), if W is less than the hunting zone (such as 0.7h " of setting _minF-h _mE), then perform 2., otherwise, perform 6.;

6. find out the minimum value of the error sum of squares of record, namely corresponding B, the W of this minimum value be defined as paddy layer parameter, if do not record effective B and W, then and W=0, B=0.

Wherein, above-mentioned steps concrete grammar is 3.:

K some actual measurement virtual height h " (f is provided according to formula (16) _k) and calculate virtual height h ' (f _k) error sum of squares:

$\begin{array}{c}\mathrm{\&epsiv;}=\underset{k=1}{\overset{K}{\&Sigma;}}{\left(h^{\&prime;\&prime;}\right(f_k)-h^{\&prime;}(f_k\left)\right)}^2=\underset{k=1}{\overset{K}{\&Sigma;}}{\left(h^{\&prime;\&prime;}\right(f_k)-h_{bE}-{\mathrm{\&Delta;h}}_E^{\&prime;}(f_k)-{\mathrm{\&Delta;h}}_J^{\&prime;}(f_k)-{\mathrm{\&Delta;h}}_V^{\&prime;}(f_k)-{\mathrm{\&Delta;h}}_F^{\&prime;}(f_k\left)\right)}^2\\ =\underset{k=1}{\overset{K}{\&Sigma;}}{\left({\mathrm{\&Delta;h}}^{\&prime;}\right(f_k)-\underset{i=0}{\overset{I}{\&Sigma;}}{A}_i{S}_i(f_k\left)\right)}^2\end{array}---\left(34\right)$

Wherein, ${\mathrm{\&Delta;h}}^{\&prime;}\left(f_k\right)\stackrel{\mathrm{\&Delta;}}{=}{h}^{\&prime;\&prime;}\left(f_k\right)-h_{bE}-{\mathrm{\&Delta;h}}_E^{\&prime;}\left(f_k\right)-{\mathrm{\&Delta;h}}_J^{\&prime;}\left(f_k\right)-{\mathrm{\&Delta;h}}_V^{\&prime;}\left(f_k\right).$ Make ε reach minimum, namely solve the coefficient A meeting formula (35) _i(i=0 ~ I):

$\frac{\&part;\mathrm{\&epsiv;}}{\&part;A_j}=\underset{k=1}{\overset{K}{\&Sigma;}}2\left({\mathrm{\&Delta;h}}^{\&prime;}\right(f_k)s_j\left(f_k\right)-\underset{i=0}{\overset{I}{\&Sigma;}}{A}_i{S}_i\left(f_k\right)s_j\left(f_k\right))=0(j=0~I)---\left(35\right)$

Formula (35) further abbreviation is:

$\underset{i=0}{\overset{I}{\&Sigma;}}{A}_i\left(\underset{k=1}{\overset{K}{\&Sigma;}}{S}_i\left(f_k\right)S_j\left(f_k\right)\right)=\underset{k=1}{\overset{K}{\&Sigma;}}{\mathrm{\&Delta;h}}^{\&prime;}\left(f_k\right)S_j\left(f_k\right)(j=0~I)---\left(36\right)$

Solve above-mentioned system of equations and can obtain coefficient A _i(i=0 ~ I), then can calculate A according to formula (4) _i+1.

3) inverting of F layer parameter:

Choose in F layer trace, frequency corresponding to the minimum virtual height of F layer trace is to f _cFbetween data be used for determining F layer parameter, suppose total K data point, frequency of operation and the virtual height of its correspondence are respectively f _kwith h " (f _k).Have read f _cFwhen, F layer section is by coefficient A _i(i=0 ~ I+1) determines completely, and the method used during similar inverting paddy layer parameter can be adopted to calculate these coefficients, it is noted herein that, after paddy layer parameter is determined, the section gradient of paddy layer and F layer point of intersection is also determined, so, according to the coefficient A that current data calculates _i(i=0 ~ I) must meet formula (7), and therefore, the inverting of F layer parameter is actually a constrained optimization problem, that is:

$\underset{A_i}{\min }\mathrm{\&epsiv;}=\underset{A_i}{\min }\underset{k=1}{\overset{K}{\&Sigma;}}{({\mathrm{\&Delta;h}}^{\&prime;}\left(f_k\right)-\underset{i=0}{\overset{I}{\&Sigma;}}{A}_i{S}_i\left(f_k\right))}^2$

$s.t.\frac{1}{4f_{CE}^2\ln (f_{CE}/f_{CF})}\underset{i=0}{\overset{I}{\&Sigma;}}{A}_i(1+2\frac{{\mathrm{dT}}_i\left(g\right)}{dg}{|}_{g=1})=B---\left(37\right)$

Lagrangian method can be adopted to solve inverting that the problems referred to above carry out F layer parameter, concrete is:

1. a new function is set up according to formula (37):

2. partial derivative is asked to each independent variable in formula (38), sets up system of equations:

3. solve above-mentioned system of equations, obtain coefficient A _i(i=0 ~ I), checks the coefficient A calculated _iwhether (i=0 ~ I) meets F layer section monotone increasing characteristic, if (a) does not meet, then 4. I=I-1, if I < 0, perform, otherwise, perform 1.; If b () meets, perform 4..

According to the method described above to the result after two-layer ionospheric inversion as shown in Figure 2.

Claims (4)

1. hang down and survey an ionogram inversion method, it is characterized in that, said method comprising the steps of:

Step 1: set up Ionospheric Profile mathematical model, described model is the three layer model comprising E layer, paddy layer and F layer, wherein, E layer and paddy layer section parabolic model representation, F layer section displacement Chebyshev polynomials model representation;

Step 2: the calculating of each layer reflection echo virtual height, based on the ionospheric model set up, the computing formula of derivation E layer, F layer echo virtual height;

Step 3: utilize actual measurement ionogram data, in conjunction with E layer, F layer echo virtual height result of calculation, carry out the inverting of E layer, paddy layer, F layer Ionospheric Parameters.

2. vertical survey ionogram inversion method according to claim 1, it is characterized in that, described step 1 specifically comprises:

Step 11: Ionospheric electron density profile concrete form is shown below:

in formula, the concrete meaning of each symbol is as follows:

E layer: f _nErepresent E layer plasma frequency; f _cErepresent that E layer faces frequently; h _mErepresent that E range upon range of mountains is high; y _mErepresent that E layer half is thick; h _bE=h _mE-y _mErepresent high at the bottom of E layer; Paddy layer: f _nVrepresent paddy layer plasma frequency; f _cVrepresent the minimum plasma frequency of paddy layer; h _mVrepresent that paddy layer plasma frequency is f _cVtime corresponding layer height; y _mVrepresent that paddy layer half is thick; h ₂=h _mE+ W, W are defined as paddy layer width; F layer: T _ig () is displacement Chebyshev polynomials, have form shown in following formula:

F _nFrepresent F layer plasma frequency; f _cFrepresent that F layer faces frequently; A _i(i=0 ~ I+1) is displacement Chebyshev polynomials coefficient, and: h _mFrepresent that F range upon range of mountains is high, and: h _mF=A _i+1,

The tie point of E layer and paddy layer is positioned at E range upon range of mountains height h _mE, the tie point of paddy layer and F layer is positioned at height h ₂place, and at height h ₂the plasma frequency at place equals E layer and faces f frequently _cE, paddy layer comprises two parts: with the coupling part of E layer and the coupling part with F layer, and this two-part tie point is positioned at height h ₁place;

Step 12: in order to ensure the entire profile continuous and derivable, then at the tie point place of layer and layer, based on more than tie point and the square value of plasma frequency that calculates respectively of following ionospheric model and section gradient should be equal, according to this condition, limit the internal relation between correlation parameter.

3. vertical survey ionogram inversion method according to claim 1, it is characterized in that, described step 2 specifically comprises:

Step 21: f is less than or equal to for frequency _cEelectric wave will reflect at E layer, carry out the derivation of E layer echo virtual height computing formula;

Step 22: f is greater than for frequency _cE, be less than or equal to f _cFelectric wave will reflect at F layer, carry out the derivation of F layer echo virtual height computing formula, be mainly included in the group distance, delta h ' of E Es-region propagations _e(f), the group distance, delta h ' propagated with E layer coupling part in paddy layer _j(f), the group distance, delta h ' propagated with F layer coupling part in paddy layer _v(f) and the group distance, delta h ' in F-layer propagation _fthe computing formula of (f).

4. vertical survey ionogram inversion method according to claim 1, it is characterized in that, described step 3 specifically comprises:

Step 31: choose actual measurement E layer trace data, adopt the method for range searching to realize E layer f _cE, h _mEor h _bE, y _mEthe inverting of three parameters;

Step 32: choose in F layer trace the data be greater than between E layer faces frequently and the minimum virtual height of F layer trace is corresponding frequency, realizes the inverting of paddy layer parameter based on search, alternative manner;

Step 33, choose in F layer trace, frequency corresponding to the minimum virtual height of F layer trace is to f _cFbetween data, utilize contained optimization method to realize the inverting of F layer parameter.