Method and product for estimating density fluctuation characteristics of ice cover snow accumulation layer based on multi-band ice penetrating radar echoes

Abstract

The invention discloses a method and product for estimating density fluctuation characteristics of an ice cover accumulated snow layer based on multi-band ice-penetrating radar echoes, and the method comprises the steps: determining the frequency band of an ice-penetrating radar, and converting the observation value of the ice-penetrating radar echo intensity of the accumulated snow layer of a target region along with the time change into the depth distribution of the ice-penetrating radar echo intensity; establishing an accumulated snow layer density fluctuation characteristic empirical model containing to-be-estimated parameters; fitting depth distribution based on echo intensity to obtain a radar echo average change trend, and determining depth position parameters of the empirical model through least square regression; the method comprises the following steps of: calibrating system parameters in ice-penetrating radar echo forward simulation by combining actual measurement data of an ice core, adjusting undetermined density fluctuation parameters, performing forward simulation on depth distribution of echo intensity, and optimizing undetermined standard deviation parameters and related length parameters in an empirical model by fitting and actually measuring the depth distribution of the echo intensity of the ice-penetrating radar. And combining the depth position parameters to obtain accumulated snow layer density fluctuation characteristics of the target area.

Description

Technical Field

[0001] The present invention relates to the field of microwave remote sensing, and in particular to a method and product for estimating density fluctuation characteristics of ice cover snow layer based on multi-band ice-penetrating radar echoes. Background Art

[0002] In the polar ice sheet region, affected by snowfall events, insulation changes, monsoon events and suppression, there is a snow layer area from snow suppression to pure ice within a depth of 100 meters below the surface of the ice sheet, corresponding to the strong random density fluctuation characteristics, and also contains a large number of layered structures generated by density fluctuations. The density fluctuation characteristics of the ice sheet snow layer have a significant impact on the scattering and radiation characteristics of the ice sheet. In order to reduce the uncertainty introduced by the snow layer density fluctuation interference in the interpretation and inversion of active and passive remote sensing observations of the ice sheet, it is necessary to effectively estimate the density fluctuation characteristics of the ice sheet snow layer. At present, the random density fluctuation characteristics of the ice sheet snow layer can be measured in situ by high-resolution ice core technology, but due to the limitations of the environment and technical implementation costs, the in-situ measurement of the density fluctuation characteristics of the ice sheet snow layer is usually difficult to carry out. The existing ice core measurements are extremely sparse and cannot provide spatial coverage. Therefore, the actual observation data of the density fluctuation characteristics of the ice sheet snow layer is very scarce. This greatly affects the reliability of the interpretation and inversion of active and passive remote sensing observations of the ice sheet. Therefore, it is of great significance to develop a method to estimate the density fluctuation characteristics of the ice sheet snow layer by combining remote sensing observations.

[0003] Previously, a method for estimating the random fluctuation parameters of the density inside ice and snow using surface penetrating radar has been proposed. The simple empirical relationship between radar echo reflectivity and density contrast is used to calculate the density contrast size based on the reflectivity distribution derived from the radar echo, and then the statistical parameters of the density fluctuation standard deviation are estimated based on the density contrast size. However, the empirical relationship between radar echo reflectivity and density contrast in this method may have deviations under different density fluctuation correlation lengths, and this method cannot estimate the density fluctuation correlation length, and the density fluctuation correlation length parameters need to be pre-set; in addition, since the density contrast size cannot be directly corresponded to the density fluctuation standard deviation statistical parameters, and the estimation process of the density fluctuation standard deviation statistical parameters is also related to the correlation length parameters, there is coupling and ambiguity between the estimation results of the density contrast size and the density fluctuation standard deviation in this method and the correlation length. When the set density fluctuation correlation length deviates from the actual one, the estimation result will have a large error. Therefore, the density fluctuation characteristics obtained by this method are usually not able to well reflect the density fluctuation characteristics of the actual ice core measurement of the ice sheet snow layer.

[0004] In addition, a method for estimating the standard deviation of density fluctuation of the snow layer on the ice sheet using ice-penetrating radar echoes has been preliminarily proposed before, and an empirical model of density fluctuation characteristics of the snow layer has been established. However, this method does not consider the problem of radar echo calibration, and cannot simultaneously constrain the density fluctuation correlation length and density fluctuation standard deviation parameters. Therefore, the density fluctuation correlation length also needs to be pre-set before the density fluctuation standard deviation is estimated. The density fluctuation standard deviation estimation result is related to the set density fluctuation correlation length. There is coupling and ambiguity between the density fluctuation standard deviation estimation result and the correlation length. When the set density fluctuation correlation length deviates from the actual one, the estimation result will have a large error and cannot reflect the density fluctuation characteristics of the actual ice core measurement of the snow layer on the ice sheet. In addition, some depth position parameters in the density fluctuation empirical model in this method need to be jointly fitted and optimized with the density fluctuation standard deviation parameters. The spatial dimension of the parameters to be estimated is large, and the problem of multiple solutions of parameter fitting is easy to occur in the application. Therefore, this method cannot effectively estimate the density fluctuation characteristics of the snow layer on the ice sheet under general circumstances. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art, propose a method for estimating the density fluctuation characteristics of the ice cover snow layer based on multi-band ice-penetrating radar echoes, and publish a product realized based on this method.

[0006] In view of this, the present invention proposes a method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echoes, comprising:

[0007] Step 1) According to the target area, the frequency band of the ice-penetrating radar is determined, and the observed value of the ice-penetrating radar echo intensity of the snow layer in the target area changing with time is converted into the depth distribution of the ice-penetrating radar echo intensity;

[0008] Step 2) establishing an empirical model of snow layer density fluctuation characteristics including the parameters to be estimated;

[0009] Step 3) Based on the depth distribution fitting of the ice-penetrating radar echo intensity, the average change trend of the radar echo is obtained, and the depth position parameters of the empirical model of the snow layer density fluctuation characteristics are determined by least squares regression;

[0010] Step 4) Calibrate the system parameters in the forward simulation of the ice-penetrating radar echo in combination with the measured ice core data, adjust the unknown density fluctuation parameters, and perform forward simulation on the depth distribution of the ice-penetrating radar echo intensity. By fitting the measured ice-penetrating radar echo intensity depth distribution, optimize the unknown standard deviation parameters and related length parameters in the empirical model of the snow layer density fluctuation characteristics, and obtain the snow layer density fluctuation characteristics in the target area in combination with the depth position parameters.

[0011] Preferably, the step 1) determines the frequency band of the ice-penetrating radar according to the target area, including:

[0012] Based on the ice-penetrating radar detection data of the target area, at least two frequency bands with detection capability and suitable resolution for the ice cover snow layer are determined, and the ice-penetrating radar echoes in the two frequency bands have different interference response characteristics to the correlation length of the snow layer density fluctuation.

[0013] Preferably, the step 1) converts the observed value of the change in the echo intensity of the ice-penetrating radar of the snow layer in the target area over time into the depth distribution of the echo intensity of the ice-penetrating radar; comprising:

[0014] Determine the real part of the average relative dielectric constant ε′ of the snow layer according to the average density of the snow layer in the target area:

[0015]

[0016] in, is the average density of the snow layer, in g / cm 3 ;

[0017] The electromagnetic wave propagation speed v in the snow layer is determined according to the following formula:

[0018]

[0019] Where c is the speed of light;

[0020] According to the electromagnetic wave propagation velocity v in the snow layer, the ice-penetrating radar echo intensity time series is converted into the depth distribution of the ice-penetrating radar echo intensity.

[0021] Preferably, the empirical model of snow layer density fluctuation characteristics in step 2) is:

[0022]

[0023] Among them, ρ n (z) is the random fluctuation component of the snow layer density, which satisfies the Gaussian random process, z is the depth, z′ is the depth of the other point when calculating the correlation between the density fluctuations of two points; l is the correlation length of the density fluctuation, σ ρ (z) is the standard deviation of density fluctuation, z c1 and z c2 The corresponding density reaches the turning point density of the suppression effect ρ c1 and ρ c2 The position depth, ρ c1 =550kg / cm 3 , ρ c2 =820~840kg / cm 3 , δ 0 and δ 1 They are log 10 σ ρThe derivative of (z) at the surface and at depths exceeding z c2 The value after z m is the depth position of the second relative maximum of density fluctuation, z 1 and z 2 It is log 10 σ ρ The depth positions of the two turning points in the derivative trend of (z), σ 0 is the value of the standard deviation of the snow layer surface density fluctuation;

[0024] The parameters to be estimated in the empirical model of snow layer density fluctuation characteristics include l, z c1 , z c2 , δ 0 , δ 1 , z 1 , z 2 , z m and σ 0 ; Among them, z c1 , z c2 , z 1 , z 2 , z m is the depth position parameter, δ 0 , δ 1 , σ 0 is the density fluctuation standard deviation parameter, and l is the density fluctuation correlation length parameter.

[0025] Preferably, the step 3) comprises:

[0026] Based on the depth distribution of ice-penetrating radar echo intensity obtained in step 1), the least squares fitting is performed on the basis of the empirical form of density fluctuation standard deviation to obtain the average size and trend of ice-penetrating radar echo depth distribution. As the average result of the measured ice-penetrating radar echo intensity depth distribution, the depth position parameter z in the empirical model of snow layer density fluctuation characteristics in step 2) is determined by least squares regression. c1 , z c2 , z 1 , z 2 and z m .

[0027] Preferably, the step 4) calibrates the system parameters in the forward simulation of ice-penetrating radar echoes in combination with ice core measured data; comprising:

[0028] On the ice-penetrating radar route passing through the known ice core area, the forward simulation of the ice-penetrating radar echo intensity depth distribution in the ice core area is carried out based on the radar equation and the density distribution data measured by the ice core;

[0029] By adjusting the radar system parameters input into the radar equation, the simulation results of the ice-penetrating radar echo intensity depth distribution are made consistent with the measured results of the ice-penetrating radar echo in the ice core area, so as to realize the calibration of the ice-penetrating radar system parameters in the forward simulation.

[0030] Preferably, the step 4) adjusts the undetermined density fluctuation parameters, performs forward simulation on the depth distribution of the ice-penetrating radar echo intensity, and optimizes the undetermined standard deviation parameters and related length parameters in the empirical model of the snow layer density fluctuation characteristics by fitting the measured ice-penetrating radar echo intensity depth distribution, including:

[0031] Based on the depth position parameters obtained in step 3), within the reasonable value range of the density fluctuation of the ice cover snow layer, combined with the average density distribution, by adjusting the undetermined standard deviation parameter δ in the density fluctuation model 0 , δ 1 , σ 0 and the associated length parameter l, generating δ 0 , δ 1 , σ 0 and the density distribution data set corresponding to l;

[0032] Based on the density distribution data set and the calibration parameters of the ice-penetrating radar system, the radar equation is used to perform a forward simulation of the ice-penetrating radar echo intensity depth distribution. The ice-penetrating radar echo simulation results corresponding to the density samples contained in each group of undetermined density fluctuation parameters are averaged, and the averaged ice-penetrating radar echo simulation results are fitted with the least squares method to obtain the average size and trend of the forward simulated ice-penetrating radar echo corresponding to each group of undetermined density fluctuation parameters as the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation.

[0033] Calculate the mean square error between the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation and the average result of the measured ice-penetrating radar echo intensity depth distribution obtained in step 3) on the ice-penetrating radar frequency band, and find the undetermined density fluctuation parameter corresponding to the minimum mean square error of the selected frequency band. The corresponding parameter value is the density fluctuation standard deviation parameter δ obtained by fitting the ice-penetrating radar echo. 0 , δ 1 , σ 0 And the optimization results of the related length parameter l;

[0034] Combined with the depth position parameter z obtained in step 3) c1 , z c2 , z 1 , z 2 and z m , and the optimized density fluctuation standard deviation parameter δ 0 , δ 1 , σ 0and density fluctuation correlation length parameter l, and finally the density fluctuation characteristics of the ice cover snow layer in the target area are obtained.

[0035] On the other hand, the present invention provides a computer program product, comprising a computer program, characterized in that the computer program implements the steps of the above method when executed by a processor.

[0036] Compared with the prior art, the advantages of the present invention are:

[0037] 1. The present invention provides a method for estimating the density fluctuation characteristics of the ice cover snow layer based on multi-band ice-penetrating radar echoes, which changes the current situation where the density fluctuation characteristics of the ice cover snow layer can only be measured through on-site ice core technology.

[0038] 2. The present invention selects at least two ice-penetrating radar echo frequency bands with different interference response characteristics for the snow layer density fluctuation correlation length, and combines radar echo calibration to quantitatively optimize the snow layer density fluctuation characteristic parameters, including density fluctuation standard deviation and density fluctuation correlation length parameters, through multi-band ice-penetrating radar echo fitting, effectively reducing the coupling and ambiguity between density fluctuation standard deviation parameters and correlation length parameters during the optimization process; according to the depth distribution of ice-penetrating radar echoes, the depth position parameters in the density fluctuation model are determined by least squares regression, which can reduce the dimension of the parameter space to be estimated during the density fluctuation standard deviation and correlation length parameter fitting process, and reduce the influence of parameter fitting multi-solution. It overcomes the problems that the previous methods of estimating random fluctuation parameters of ice and snow internal density using surface penetrating radar and estimating the standard deviation of density fluctuation of ice cover snow layer density using ice-penetrating radar echo cannot estimate the density fluctuation correlation length parameters, there is coupling and ambiguity between the density fluctuation standard deviation estimation result and the correlation length, and there is parameter fitting multi-solution in the estimation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a simulation result diagram of the change of the equivalent reflectivity of a single range gate in a snow layer with different density fluctuation correlation lengths of the ice-penetrating radar frequency band selected by the embodiment of the present invention;

[0040] Figure 2 It is a result diagram of converting the ice-penetrating radar echo intensity time series observation value selected in the embodiment of the present invention into the echo intensity depth distribution;

[0041] Figure 3 It is a schematic diagram of position parameters of the snow layer density fluctuation empirical model provided by an embodiment of the present invention;

[0042] Figure 4 It is a simulation result diagram of the existing ice core measurement data of the Greenland ice sheet using the snow layer density fluctuation empirical model provided by the embodiment of the present invention;

[0043] Figure 5 is a comparison result diagram of the standard deviation distribution of density fluctuations measured in the ice core area of ​​the Greenland ice sheet selected by the embodiment of the present invention and the ice penetrating radar echo;

[0044] Figure 6 It is a comparison result diagram of the depth position parameter obtained by fitting the density fluctuation standard deviation distribution measured by the ice core in the Greenland ice sheet ice core area selected in the embodiment of the present invention and the depth position parameter obtained by least squares regression of ice penetrating radar echoes;

[0045] Figure 7 It is a forward simulation result diagram of ice penetrating radar echo in the ice core area using ice penetrating radar system simulation parameters obtained by calibration of the Greenland ice sheet ice core area and ice core measurement density distribution data in an embodiment of the present invention;

[0046] FIG8(a) is a comparison diagram of the result of estimating the snow layer density fluctuation characteristics based on the multi-band ice-penetrating radar echo provided by an embodiment of the present invention and the snow layer density fluctuation characteristics measured by ice cores; FIG8(b) is a comparison diagram of the result of estimating the snow layer density fluctuation characteristics based on the multi-band ice-penetrating radar echo provided by an embodiment of the present invention and the estimation result corresponding to the existing method of estimating the standard deviation of the ice cover snow layer density fluctuation using the ice-penetrating radar echo;

[0047] Fig. 9 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0048] In order to achieve the above object, the present invention provides a method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echoes, the method comprising:

[0049] Step 1) Select the target area, determine the frequency band of the ice-penetrating radar, and convert the observed value of the ice-penetrating radar echo intensity of the snow layer in the target area over time into the depth distribution of the ice-penetrating radar echo intensity;

[0050] Step 2) establishing an empirical model of snow layer density fluctuation characteristics including the parameters to be estimated;

[0051] Step 3) fitting the ice-penetrating radar echo depth distribution obtained in step 1) to obtain the average change trend of the radar echo, and determining the depth position parameters in the density fluctuation model established in step 2) by least squares regression;

[0052] Step 4) Calibrate the system parameters in the forward simulation of the ice-penetrating radar echo in combination with the measured ice core data, adjust the unknown density fluctuation parameters, and perform a forward simulation on the depth distribution of the ice-penetrating radar echo intensity. By fitting the measured depth distribution of the ice-penetrating radar echo intensity, optimize the unknown standard deviation parameters and related length parameters in the density fluctuation model established in step 2). Combined with the depth position parameters obtained in step 3), the density fluctuation characteristics of the snow layer in the target area are obtained.

[0053] The method steps are systematically described below.

[0054] In step 1), select the target area and determine the ice-penetrating radar frequency band, including:

[0055] Step 1-1) Select the target ice cover area where the snow layer density fluctuation characteristics are to be estimated;

[0056] Step 1-2) According to the ice-penetrating radar detection data of the target area, at least two frequency bands with detection capability and suitable resolution for the ice cover snow layer are determined, and the ice-penetrating radar echoes of different selected frequency bands are required to have different interference response characteristics to the snow layer density fluctuation correlation length, that is, with the change of the density fluctuation correlation length parameter, the equivalent reflectivity change trend of the snow layer in a single range gate of different frequency bands is different, so the change trend of the ice-penetrating radar echo intensity of the corresponding frequency band will also be different. In this way, when estimating the snow layer density fluctuation parameters according to the ice-penetrating radar echoes of the corresponding frequency bands, the coupling and ambiguity of the density fluctuation correlation length and standard deviation parameters in the optimization process can be effectively reduced.

[0057] In step 1), the observation value of the ice-penetrating radar echo intensity of the snow layer in the target area changing with time is converted into the depth distribution of the ice-penetrating radar echo intensity, which specifically includes:

[0058] Step 1-3) Convert the time series observations of the echo intensity of the ice-penetrating radar in the selected frequency band into observations of the echo intensity changing with the depth of the snow layer. The specific method is: determine the real part of the average relative dielectric constant of the snow layer according to the average density of the snow layer in the target area

[0059]

[0060] Where ε′ is the real part of the average relative permittivity of the snow layer, is the average density of the snow layer, in g / cm 3 .

[0061] Then the propagation speed of electromagnetic waves in the snow layer is determined to be

[0062]

[0063] Among them, c is the speed of light, v is the propagation speed of electromagnetic waves in the snow layer, and the unit is m / s.

[0064] According to the propagation speed of electromagnetic waves in the snow layer, the time series of ice-penetrating radar echo intensity can be converted into the depth distribution of ice-penetrating radar echo intensity.

[0065] In step 2), an empirical model of snow layer density fluctuation characteristics is established based on ice core measurement data of snow layer density fluctuation on the ice cover.

[0066]

[0067] Among them, ρ n (z) is the random fluctuation component of the snow layer density, which satisfies the Gaussian random process, z is the depth, and z′ is the depth of the other point when calculating the correlation between the density fluctuations of the two points;

[0068] l is the density fluctuation correlation length, σ ρ (z) is the standard deviation of density fluctuation, z c1 and z c2 The corresponding density reaches the turning point density of the suppression effect ρ c1 and ρ c2 The position depth, ρ c1 =550kg / cm 3 , ρ c2 =820~840kg / cm 3 , δ 0 and δ 1 They are log 10 σ ρ The derivative of (z) at the surface and at depths exceeding z c2 The value after z m is the depth position of the second relative maximum of density fluctuation, z 1 and z 2 It is log 10 σ ρ The depth positions of the two turning points in the derivative trend of (z), σ 0 is the value of the standard deviation of the snow layer surface density fluctuation. Figure 1 The location parameters in the empirical model of snow layer density fluctuation characteristics given by the standard deviation distribution of density fluctuations obtained from the B26 ice core measurement of the Greenland ice sheet are given.

[0069] The parameters to be estimated in the empirical model of snow layer density fluctuation characteristics include l, z c1 , z c2 , δ 0 , δ 1 , z 1 , z 2 , z m and σ 0 Among them, z c1 , z c2, z 1 , z 2 , z m is the depth position parameter, δ 0 , δ 1 , σ 0 is the density fluctuation standard deviation parameter, and l is the density fluctuation correlation length parameter.

[0070] In step 3), since density fluctuation is the main mechanism for generating dielectric contrast at the interface between layers in the snow layer area, the size of density fluctuation determines the size of dielectric contrast at the corresponding interface between layers, which directly affects the strength of the ice-penetrating radar reflection echo. Therefore, the ice-penetrating radar echo intensity depth variation trend is highly correlated with the density fluctuation variation trend. Based on the ice-penetrating radar echo depth distribution obtained in step 1), the average size and trend of the ice-penetrating radar echo depth distribution can be obtained by performing least squares fitting on the basis of the empirical form of the density fluctuation standard deviation. As the average result of the ice-penetrating radar echo intensity depth distribution, the depth position parameter z in the density fluctuation model established in step 2) is c1 , z c2 , z 1 , z 2 and z m can be determined in this process by least squares regression.

[0071] In step 4), the system parameters in the ice-penetrating radar echo simulation are calibrated in combination with the ice core measured data, so that the absolute size of the measured ice-penetrating radar echo intensity depth distribution can be quantitatively fitted during the optimization process, thereby realizing the simultaneous constraints on the density fluctuation correlation length and the density fluctuation standard deviation, and reducing the influence of the local optimal solution. Specifically including:

[0072] Step 4-1) on an ice-penetrating radar route passing through a known ice core area, a forward simulation of the ice-penetrating radar echo intensity depth distribution in the ice core area is performed based on the radar equation and the density distribution data measured by the ice core;

[0073] Step 4-2) adjusts the radar system parameters input into the radar equation so that the simulation results of the ice-penetrating radar echo intensity depth distribution are consistent with the measured results of the ice-penetrating radar echo in the ice core area, so as to realize the calibration of the ice-penetrating radar system parameters in the forward simulation. In this way, when the density fluctuation parameters are optimized at other locations on the similar ice-penetrating radar segment, the calibration parameter results of the ice-penetrating radar system in step 4-2) are used for the forward simulation of the ice-penetrating radar echo intensity depth distribution, and the measured ice-penetrating radar echo data are fitted in the optimization process.

[0074] In step 4), the undetermined density fluctuation parameters are adjusted, and the ice-penetrating radar echo intensity depth distribution is forward simulated using the ice-penetrating radar system calibration parameters in step 4-2). By fitting the measured ice-penetrating radar echo intensity depth distribution, the undetermined standard deviation parameters and related length parameters in the density fluctuation model established in step 2) are optimized. Since the interference effect of electromagnetic waves in the snow layer is very sensitive to the layer thickness and density, the undetermined standard deviation parameter δ 0 , δ 1 , σ 0 During the optimization of the correlation length parameter l, only the average size and trend of the depth distribution of the ice-penetrating radar echo intensity are considered to improve the robustness of the parameter optimization process and results. Specifically,

[0075] Step 4-3) Based on the depth position parameters obtained in step 3), within the reasonable value range of the density fluctuation of the ice cover snow layer, combined with the average density distribution, the standard deviation parameter δ in the density fluctuation model is adjusted. 0 , δ 1 , σ 0 and the associated length parameter l, generating δ 0 , δ 1 , σ 0 The density distribution data set corresponding to l. In order to avoid the influence of random density fluctuation on the optimization results, multiple density samples need to be generated for each set of unknown density fluctuation parameters;

[0076] Step 4-4) Based on the density distribution data set generated in step 4-3) and the ice-penetrating radar system calibration parameters obtained in step 4-2), the radar equation is used to perform a forward simulation of the ice-penetrating radar echo intensity depth distribution, and the ice-penetrating radar echo simulation results corresponding to the density samples contained in each group of undetermined density fluctuation parameters are averaged. Similar to step 3), the averaged ice-penetrating radar echo simulation results are fitted with the least squares method to obtain the average size and trend of the forward simulated ice-penetrating radar echo corresponding to each group of undetermined density fluctuation parameters as the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation;

[0077] Step 4-5) calculates the mean square error between the average result of the forward simulated ice-penetrating radar echo intensity depth distribution on the selected frequency band and the average result of the measured ice-penetrating radar echo intensity depth distribution obtained in step 3), and finds the undetermined density fluctuation parameter corresponding to the minimum mean square error of the selected frequency band (i.e., the best fit is achieved). The corresponding parameter value is the density fluctuation standard deviation parameter δ obtained by ice-penetrating radar echo fitting. 0 , δ 1 , δ 0 And the optimization results of the related length parameter l.

[0078] In step 4), the depth position parameter z obtained in step 3) is combinedc1 , z c2 , z 1 , z 2 and z m , and the density fluctuation standard deviation parameter δ optimized in step 4-5) 0 , δ 1 , σ 0 and the related length parameter l, and finally the density fluctuation characteristics of the snow layer on the ice cover in the target area are obtained.

[0079] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0080] Example 1

[0081] The embodiment of the present invention proposes a method for estimating the density fluctuation characteristics of the ice cover snow layer based on multi-band ice penetrating radar echoes, such as Fig. 9 As shown, this embodiment takes the area of ​​the Greenland ice sheet where ice cores have been used to measure the snow layer density fluctuation characteristics as an example, and includes the following steps:

[0082] Step 101: Select a target area, determine the frequency band of the ice-penetrating radar, and convert the observed value of the ice-penetrating radar echo intensity of the snow layer in the target area changing with time into the depth distribution of the ice-penetrating radar echo intensity.

[0083] (1) The areas of the Greenland Ice Sheet where ice cores have been used to measure the snow density fluctuation characteristics are selected as the target ice sheet areas to be estimated.

[0084] (2) Based on the existing ice-penetrating radar detection data in the target area of ​​the Greenland ice sheet, the accumulation rate radar and multi-channel coherent sounding radar echo data of the US IceBridge Project were selected as the ice-penetrating radar echoes used to estimate the density fluctuation characteristics. Among them, the accumulation rate radar frequency band is 600-900MHz, and the sub-ice resolution is better than 0.5m; the multi-channel coherent sounding radar frequency band is 180-210MHz, and the sub-ice resolution is better than 5m. Ice-penetrating radars in these two frequency bands have effective detection and resolution capabilities for the snow layer of the ice sheet.

[0085] In the attached figure Figure 1The simulation results of the equivalent reflectivity of a single range gate in the snow layer corresponding to the frequency bands of the accumulation rate radar and the multi-channel coherent sounding radar under different density fluctuation correlation lengths are given. It can be seen that with the change of the correlation length, the change trend of the equivalent reflectivity of a single range gate in the two frequency bands is opposite, which means that the change trend of the radar echo intensity in the corresponding frequency bands will also be opposite. This shows that in the process of optimizing the density fluctuation parameters of the snow layer, using the ice-penetrating radar echo data of the two frequency bands corresponding to the accumulation rate radar and the multi-channel coherent sounding radar can effectively reduce the coupling and ambiguity of the density fluctuation correlation length and the density fluctuation standard deviation parameters, and obtain more reliable optimization results of the snow layer density fluctuation characteristics.

[0086] (3) Determine the real part of the average relative dielectric constant of the snow layer based on the average density of the snow layer in the target area

[0087]

[0088] Where ε′ is the real part of the average relative permittivity of the snow layer, is the average density of the snow layer, in g / cm 3 .

[0089] Then the propagation speed of electromagnetic waves in the snow layer is determined to be

[0090]

[0091] Among them, c is the speed of light, v is the propagation speed of electromagnetic waves in the snow layer, and the unit is m / s.

[0092] According to the propagation speed of electromagnetic waves in the snow layer, the time series of ice-penetrating radar echo intensity is converted into the depth distribution of ice-penetrating radar echo intensity.

[0093] In the attached figure Figure 2 The results of converting the echo intensity time series observations of the accumulation rate radar and multi-channel coherent sounding radar in the B16 ice core area of ​​the Greenland ice sheet into echo intensity depth distribution maps are given.

[0094] Step 102: Establish an empirical model of snow layer density fluctuation characteristics including the parameters to be estimated.

[0095] Based on the ice core measurement data of snow layer density fluctuation on the ice sheet, an empirical model of snow layer density fluctuation characteristics is established.

[0096]

[0097] Among them, ρ n (z) is the random fluctuation component of the snow layer density, which satisfies the Gaussian random process, z is the depth, z′ is the depth of the other point when calculating the correlation between the density fluctuations of two points; l is the correlation length of the density fluctuation, σ ρ(z) is the standard deviation of density fluctuation, z c1 and z c2 The corresponding density reaches the turning point density of the suppression effect ρ c1 and ρ c2 The position depth, ρ c1 =550kg / cm 3 , ρ c2 =820~840kg / cm 3 , δ 0 and δ 1 They are log 10 σ ρ The derivative of (z) at the surface and at depths exceeding z c2 The value after z m is the depth position of the second relative maximum of density fluctuation, z 1 and z 2 It is log 10 σ ρ The depth positions of the two turning points in the derivative trend of (z), σ 0 is the value of the standard deviation of the snow layer surface density fluctuation. Figure 3 The position parameter z in the empirical model of snow layer density fluctuation characteristics is given by combining the standard deviation distribution of density fluctuations obtained from the B26 ice core measurement of the Greenland ice sheet. c1 , z c2 , z 1 , z 2 and z m 's hint.

[0098] The parameters to be estimated in the empirical model of snow layer density fluctuation characteristics include l, z c1 , z c2 , δ 0 , δ 1 , z 1 , z 2 , z m and σ 0 Among them, z c1 , z c2 , z 1 , z 2 , z m is the depth position parameter, δ 0 , δ 1 , σ 0 is the density fluctuation standard deviation parameter, and l is the density fluctuation correlation length parameter.

[0099] Figure 4 The simulation results of the snow layer density fluctuation empirical model established in the present invention on the standard deviation distribution data of snow layer density fluctuation measured by the existing B16, B17, B18, B21, B26 and B29 ice cores of the Greenland ice sheet are given.

[0100] Step 103: Based on the ice-penetrating radar echo depth distribution obtained in step 101, the average change trend of the radar echo is obtained by fitting, and the depth position parameters in the density fluctuation model established in step 102 are determined by least squares regression.

[0101] Since density fluctuation is the main mechanism for generating dielectric contrast at the interface between snow layers, the magnitude of density fluctuation determines the magnitude of dielectric contrast at the corresponding interface between layers, which directly affects the strength of the ice-penetrating radar reflection echo. Figure 5 The comparison results of the standard deviation distribution of snow density fluctuation measured by ice cores B16 and B26 of the Greenland Ice Sheet and the accumulation rate radar echo are given. It can be seen that the change trend of ice radar echo intensity depth is highly correlated with the change trend of density fluctuation.

[0102] Based on the ice-penetrating radar echo depth distribution obtained in step 101, the average size and trend of the ice-penetrating radar echo depth distribution are obtained by performing least square fitting on the basis of the empirical form of the density fluctuation standard deviation, which is used as the average result of the ice-penetrating radar echo intensity depth distribution. In this process, the depth position parameter z in the density fluctuation model established in step 102 is determined. c1 , z c2 , z 1 , z 2 and z m .

[0103] In the attached figure Figure 6 The comparison results of the depth position parameters obtained by fitting the density fluctuation standard deviation distribution measured by ice cores and the depth position parameters obtained by least squares regression of ice penetrating radar echoes in the B16 and B26 ice core areas of the Greenland ice sheet are given. It can be seen that the depth position parameters obtained by least squares regression of ice penetrating radar echoes can be used to well describe the characteristics of the measured density fluctuation standard deviation.

[0104] Step 104: Calibrate the system parameters in the forward simulation of the ice-penetrating radar echo in combination with the measured ice core data, adjust the unknown density fluctuation parameters, and perform a forward simulation on the ice-penetrating radar echo intensity depth distribution. By fitting the measured ice-penetrating radar echo intensity depth distribution, the unknown standard deviation parameters and related length parameters in the density fluctuation model established in step 102 are optimized. Combined with the depth position parameters obtained in step 103, the density fluctuation characteristics of the snow layer in the target area are obtained.

[0105] (1) In the embodiment of the present invention, the accumulation rate radar and multi-channel coherent sounding radar echo data and ice core density measurement data of the B17 ice core area of ​​the Greenland ice sheet are selected for calibration of the ice-penetrating radar system parameters in the forward simulation, and the forward simulation of the depth distribution of the ice-penetrating radar echo intensity in the ice core area is performed based on the radar equation and the density distribution data of the B17 ice core measurement.

[0106] (2) By adjusting the radar system parameters input into the radar equation, the simulation results of the depth distribution of the ice-penetrating radar echo intensity are consistent with the measured results of the ice-penetrating radar echo in the B17 ice core area, so as to realize the calibration of the ice-penetrating radar system parameters in the forward simulation. The calibrated ice-penetrating radar system simulation parameters are used to perform a forward simulation of the depth distribution of the ice-penetrating radar echo intensity on the flight segment close to the target area.

[0107] In the attached figure Figure 7 The simulation results of ice-penetrating radar echoes in the B18 and B29 ice core regions are given by using the simulation parameters of the ice-penetrating radar system obtained by calibration of the B17 ice core region of the Greenland ice sheet and the density distribution data measured by the B18 and B29 ice cores. It can be seen that the simulation parameters of the ice-penetrating radar system obtained by calibration of the B17 ice core and the density distribution data measured by the B18 and B29 ice cores can effectively simulate the depth distribution of ice-penetrating radar echo intensity in the corresponding region (because the depth of ice core measurement is limited, the maximum depth of the simulated echo is only up to the maximum depth of ice core density measurement). This means that the simulation parameters of the ice-penetrating radar system after calibration of the known ice core can realize the simulation of the absolute size of the ice-penetrating radar echo intensity in the process of optimizing the parameters of the snow layer density fluctuation characteristics, so that the absolute size of the ice-penetrating radar echo intensity can be considered for fitting in the optimization process, reducing the influence of the local optimal solution and improving the reliability of the optimization results of the snow layer density fluctuation characteristics.

[0108] (3) In the embodiment of the present invention, the B16 ice core area of ​​the Greenland ice sheet is taken as an example to fit the snow layer density fluctuation standard deviation parameter δ based on the multi-band ice penetrating radar echo. 0 , δ 1 , σ 0 The optimization process of the length parameter l is described in detail. Since the interference of electromagnetic waves in the snow layer is very sensitive to the layer thickness and density, the standard deviation parameter δ 0 , δ 1 , σ 0 In the process of optimizing the correlation length parameter l, only the average size and trend of the depth distribution of the ice-penetrating radar echo intensity are considered to improve the robustness of the parameter optimization process and results.

[0109] Based on the depth position parameters obtained in step 103, within the reasonable value range of the density fluctuation of the ice cover snow layer, combined with the average density distribution, by adjusting the undetermined standard deviation parameter δ in the density fluctuation model0 , δ 1 , σ 0 and the associated length parameter l, generating δ 0 , δ 1 , σ 0 The density distribution data set corresponding to l. In order to avoid the influence of random density fluctuation on the optimization results, multiple density samples need to be generated for each set of unknown density fluctuation parameters;

[0110] (4) Based on the generated density distribution data set and the simulation parameters of the ice-penetrating radar system after calibration with known ice cores, the radar equation is used to perform a forward simulation of the ice-penetrating radar echo intensity depth distribution, and the ice-penetrating radar echo simulation results corresponding to the density samples contained in each group of undetermined density fluctuation parameters are averaged. The averaged ice-penetrating radar echo simulation results are fitted with the least squares method to obtain the average size and trend of the forward simulated ice-penetrating radar echo corresponding to each group of undetermined density fluctuation parameters, which is used as the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation.

[0111] (5) Calculate the mean square error between the average result of the forward simulated ice-penetrating radar echo intensity depth distribution in the two frequency bands and the average result of the measured ice-penetrating radar echo intensity depth distribution obtained in step 103, and find the undetermined density fluctuation parameter corresponding to the minimum mean square error (i.e., the best fit is achieved). The corresponding parameter value is the density fluctuation standard deviation parameter δ obtained by ice-penetrating radar echo fitting. 0 , δ 1 , σ 0 And the optimization results of the related length parameter l.

[0112] (6) Combined with the depth position parameter z obtained in step 103 c1 , z c2 , z 1 , z 2 and z m , and the density fluctuation standard deviation parameter δ optimized in step 104 0 , δ 1 , σ 0 and the related length parameter l, and finally the density fluctuation characteristics of the snow layer on the ice cover in the target area are obtained.

[0113] Figure 8(a) in the attached drawings shows the comparison results of the density fluctuation standard deviation distribution corresponding to the density distribution generated under the optimized snow layer density fluctuation parameters and the measured data of the B16 ice core. It can be seen that the density fluctuation characteristics of the snow layer on the ice sheet obtained by the method for estimating the density fluctuation characteristics of the snow layer based on the multi-band ice penetrating radar echo provided by the present invention are well consistent with the measured ones.

[0114] Figure 8(b) in the attached drawings shows a comparison of the estimation results corresponding to the method of estimating the standard deviation of the density fluctuation of the ice cover snow layer using the ice penetrating radar echo. It can be seen that when the correlation length is unknown, the method of estimating the snow layer density fluctuation characteristics based on the multi-band ice penetrating radar echo provided by the present invention can better reflect the density fluctuation characteristics obtained by measuring the actual ice cover snow layer area, so that when the snow layer density fluctuation characteristics estimation results are used in the subsequent ice cover active and passive remote sensing interpretation and inversion problems, the interference introduced by the ice cover snow layer density fluctuation can be more effectively corrected.

[0115] In summary, this embodiment provides a method for estimating the density fluctuation characteristics of the snow layer on the ice sheet based on the multi-band ice-penetrating radar echo. Since density fluctuation is the main mechanism for generating dielectric contrast between interlayer interfaces in the snow layer area, the size of the density fluctuation determines the size of the dielectric contrast at the corresponding interlayer interface, which directly affects the strength of the ice-penetrating radar reflection echo. Therefore, there is a high correlation between the intensity of the ice-penetrating radar echo and the density fluctuation characteristics of the snow layer. According to the depth distribution of the multi-band ice-penetrating radar echo intensity in the snow layer area, the density fluctuation characteristic parameters of the snow layer area, including the density fluctuation standard deviation parameter and the density fluctuation correlation length parameter, can be quantitatively optimized. The estimation results can be used as prior information in the subsequent interpretation and inversion of active and passive remote sensing data of the ice sheet, to correct the interference caused by the density fluctuation of the snow layer, effectively reduce the dimensionality and uncertainty of the active and passive remote sensing interpretation and inversion problems of the ice sheet, and improve the reliability of the interpretation and inversion results.

[0116] Example 2

[0117] The embodiment of the present invention may also provide a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, each step in the above method embodiment can be implemented.

[0118] Summary:

[0119] The method of the present invention can obtain the characteristic information of density fluctuation of the snow layer on the ice sheet, estimate the characteristic parameters of density fluctuation of the snow layer by fitting the depth distribution of the echo intensity of the multi-band ice penetrating radar, change the current situation that the density fluctuation characteristics of the snow layer on the ice sheet can only be measured by the on-site ice core technology, overcome the defects of the previous method of estimating the random fluctuation change parameters of the internal density of ice and snow by surface penetrating radar and estimating the standard deviation of the density fluctuation of the snow layer on the ice sheet by using the ice penetrating radar echo, the inability to estimate the density fluctuation correlation length parameter, the coupling and fuzziness between the estimation result of the density fluctuation standard deviation and the correlation length, and the existence of multiple solutions of parameter fitting in the estimation process. In the method provided by the present invention, the density fluctuation characteristics of the snow layer on the ice sheet can be effectively characterized by establishing an empirical model of density fluctuation of the snow layer on the ice sheet, and the size and change trend of the echo intensity of the ice penetrating radar can be effectively simulated by combining the radar equation. In the case of selecting at least two ice penetrating radar echo frequency bands with different interference response characteristics for the correlation length of the density fluctuation of the snow layer, the characteristic parameters of the density fluctuation of the snow layer, including the density fluctuation standard deviation parameter and the density fluctuation correlation length parameter, can be quantitatively optimized by fitting the multi-band ice penetrating radar echo. The estimated results of the corresponding snow layer density fluctuation characteristics can better reflect the density fluctuation characteristics obtained by measuring the actual ice sheet snow layer area. Therefore, the ice sheet snow layer density fluctuation interference can be more effectively corrected in the active and passive remote sensing interpretation and inversion of the ice sheet, thereby effectively reducing the dimensionality and uncertainty of the active and passive remote sensing interpretation and inversion problems of the ice sheet, and improving the reliability of the interpretation and inversion results.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echoes, comprising: Step 1) According to the target area, the frequency band of the ice-penetrating radar is determined, and the observed value of the ice-penetrating radar echo intensity of the snow layer in the target area changing with time is converted into the depth distribution of the ice-penetrating radar echo intensity; Step 2) establishing an empirical model of snow layer density fluctuation characteristics including the parameters to be estimated; Step 3) Based on the depth distribution fitting of the ice-penetrating radar echo intensity, the average change trend of the radar echo is obtained, and the depth position parameters of the empirical model of the snow layer density fluctuation characteristics are determined by least squares regression; Step 4) Calibrate the system parameters in the forward simulation of the ice-penetrating radar echo in combination with the measured ice core data, adjust the unknown density fluctuation parameters, and perform forward simulation on the depth distribution of the ice-penetrating radar echo intensity. By fitting the measured ice-penetrating radar echo intensity depth distribution, optimize the unknown standard deviation parameters and related length parameters in the empirical model of the snow layer density fluctuation characteristics, and obtain the snow layer density fluctuation characteristics in the target area in combination with the depth position parameters.

2. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 1 is characterized in that: The step 1) determines the frequency band of the ice penetrating radar according to the target area, including: Based on the ice-penetrating radar detection data of the target area, at least two frequency bands with detection capability and suitable resolution for the ice cover snow layer are determined, and the ice-penetrating radar echoes in the two frequency bands have different interference response characteristics to the correlation length of the snow layer density fluctuation.

3. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 1 is characterized in that: The step 1) converts the observed value of the change of the ice penetrating radar echo intensity of the snow layer in the target area over time into the depth distribution of the ice penetrating radar echo intensity; comprising: Determine the real part of the average relative dielectric constant ε′ of the snow layer according to the average density of the snow layer in the target area: in, is the average density of the snow layer, in g / cm 3 ; The electromagnetic wave propagation speed v in the snow layer is determined according to the following formula: Where c is the speed of light; According to the electromagnetic wave propagation velocity v in the snow layer, the ice-penetrating radar echo intensity time series is converted into the depth distribution of the ice-penetrating radar echo intensity.

4. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 1 is characterized in that: The empirical model of snow layer density fluctuation characteristics in step 2) is: Among them, ρ n (z) is the random fluctuation component of the snow layer density, which satisfies the Gaussian random process, z is the depth, z′ is the depth of the other point when calculating the correlation between the density fluctuations of two points; l is the correlation length of the density fluctuation, σ ρ (z) is the standard deviation of density fluctuation, z c1 and z c2 The corresponding density reaches the turning point density of the suppression effect ρ c1 and ρ c2 The position depth, ρ c1 =550kg / cm 3 , ρ c2 =820~840kg / cm 3 , δ0 and δ1 are log 10 σ ρ The derivative of (z) at the surface and at depths exceeding z c2 The value after z m is the depth of the second relative maximum of the density fluctuation, z1 and z2 are log 10 σ ρ (z) is the depth position of the two turning points in the derivative variation trend, σ0 is the value of the standard deviation of the snow layer surface density fluctuation; The parameters to be estimated in the empirical model of snow layer density fluctuation characteristics include l, z c1 , z c2 ,δ0,δ1,z1,z2,z m and σ0; where z c1 , z c2 , z1, z2, z m is the depth position parameter, δ0, δ1, σ0 are the density fluctuation standard deviation parameters, and l is the density fluctuation correlation length parameter.

5. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 4 is characterized in that: The step 3) comprises: Based on the depth distribution of ice-penetrating radar echo intensity obtained in step 1), the least squares fitting is performed on the basis of the empirical form of density fluctuation standard deviation to obtain the average size and trend of ice-penetrating radar echo depth distribution. As the average result of the measured ice-penetrating radar echo intensity depth distribution, the depth position parameter z in the empirical model of snow layer density fluctuation characteristics in step 2) is determined by least squares regression. c1 , z c2 , z1, z2 and z m .

6. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 1 is characterized in that: The step 4) calibrates the system parameters in the forward simulation of the ice-penetrating radar echo in combination with the ice core measured data; comprising: On the ice-penetrating radar route passing through the known ice core area, the forward simulation of the ice-penetrating radar echo intensity depth distribution in the ice core area is carried out based on the radar equation and the density distribution data measured by the ice core; By adjusting the radar system parameters input into the radar equation, the simulation results of the ice-penetrating radar echo intensity depth distribution are made consistent with the measured results of the ice-penetrating radar echo in the ice core area, so as to realize the calibration of the ice-penetrating radar system parameters in the forward simulation.

7. The method for estimating the density fluctuation characteristics of ice cover snow layer based on multi-band ice penetrating radar echo according to claim 6 is characterized in that: The step 4) adjusts the undetermined density fluctuation parameters, performs forward simulation on the depth distribution of the ice-penetrating radar echo intensity, and optimizes the undetermined standard deviation parameters and related length parameters in the empirical model of the snow layer density fluctuation characteristics by fitting the measured ice-penetrating radar echo intensity depth distribution, including: Based on the depth position parameters obtained in step 3), within the reasonable value range of the density fluctuation of the ice cover snow layer, combined with the average density distribution, by adjusting the undetermined standard deviation parameters δ0, δ1, σ0 and the related length parameter l in the density fluctuation model, a density distribution data set corresponding to δ0, δ1, σ0 and l is generated; Based on the density distribution data set and the calibration parameters of the ice-penetrating radar system, the radar equation is used to perform a forward simulation of the ice-penetrating radar echo intensity depth distribution. The ice-penetrating radar echo simulation results corresponding to the density samples contained in each group of undetermined density fluctuation parameters are averaged, and the averaged ice-penetrating radar echo simulation results are fitted with the least squares method to obtain the average size and trend of the forward simulated ice-penetrating radar echo corresponding to each group of undetermined density fluctuation parameters as the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation. Calculate the mean square error between the average result of the ice-penetrating radar echo intensity depth distribution in the forward simulation and the average result of the measured ice-penetrating radar echo intensity depth distribution obtained in step 3) on the ice-penetrating radar frequency band, and find the undetermined density fluctuation parameter corresponding to the minimum mean square error of the selected frequency band. The corresponding parameter value is the optimization result of the density fluctuation standard deviation parameters δ0, δ1, σ0 and the correlation length parameter l obtained by fitting the ice-penetrating radar echo; Combined with the depth position parameter z obtained in step 3) c1 , z c2 , z1, z2 and z m , as well as the optimized density fluctuation standard deviation parameters δ0, δ1, σ0 and density fluctuation correlation length parameter l, and finally the density fluctuation characteristics of the ice cover snow layer in the target area are obtained.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

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