CN113960690A - Method and device for calculating influence of sea surface gravity data measurement precision on submarine topography inversion result - Google Patents

Method and device for calculating influence of sea surface gravity data measurement precision on submarine topography inversion result Download PDF

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CN113960690A
CN113960690A CN202111033017.3A CN202111033017A CN113960690A CN 113960690 A CN113960690 A CN 113960690A CN 202111033017 A CN202111033017 A CN 202111033017A CN 113960690 A CN113960690 A CN 113960690A
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范雕
李姗姗
赵东明
李新星
张金辉
范昊鹏
冯进凯
单建晨
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Information Engineering University of PLA Strategic Support Force
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Abstract

The invention discloses a method and a device for calculating the influence of sea surface gravity data measurement precision on a submarine topography inversion result, wherein the method comprises the following steps: taking the sea depth as input data, resolving gravity field element information generated by the sea depth by using a strict prism volume division method, and obtaining an effective integral radius; adding sea depth Gaussian white noises corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies; based on the obtained effective integral radius, respectively taking the error-free sea depth and the obtained sea depth data with different relative precisions as input, and forward calculating to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions; the forward gravity field element result of the sea depth data with different relative precisions is subtracted from the error-free forward gravity field element result of the sea depth to obtain a forward gravity field element difference value; and taking the difference value as input, and counting the difference result index. The invention discloses an internal correlation between gravity data and seafloor topography data.

Description

Method and device for calculating influence of sea surface gravity data measurement precision on submarine topography inversion result
Technical Field
The invention belongs to the technical field of submarine topography inversion, and particularly relates to a method and a device for calculating influence of sea surface gravity data measurement precision on a submarine topography inversion result.
Background
The measurement of the submarine topography (sea depth) is used as a basic means and a system engineering for observing the sea and recognizing the sea, and can play an irreplaceable role in the aspects of sea resource development, sea ecological environment protection, sea technological innovation, sea equity maintenance and the like. Currently, the submarine topography measuring technology mainly includes a ship-based submarine topography measuring technology, a submarine topography measuring technology, an Airborne laser radar depth measurement (ALB) technology, a satellite-based submarine topography measuring technology, and the like. The space grid size of the firstly issued grid is a 15 'global submarine topography model (GEBCO _2019), and the space grid size recovered by organizations such as SIO, NOAA, NGA and the like based on the SRTM15+ V1.0 and other terrain models is a 15' global topography model (SRTM15+ V2.0), wherein most submarine topography data of the ocean area are recovered by means of satellite altimetry gravity data inversion.
Generally, the accuracy of inverting a submarine topography model by using a satellite height measurement technology is to be improved. The inversion of the nature of the submarine topography by the multi-source sea surface gravity data (satellite altimetry gravity data, ship survey gravity data, aviation gravity data and the like) is the inverse solution of the problem of the forward disturbance field element of the submarine topography, so that the accuracy of constructing a submarine topography model by the gravity data is mainly influenced by two factors, namely the calculation model error of the submarine topography by gravity inversion; secondly, gravity input data error. The sea surface gravity input data quality will directly affect the sea surface gravity data based seafloor terrain modeling effect.
Disclosure of Invention
The invention provides a method and a device for calculating the influence of sea surface gravity data measurement precision on a sea surface topography inversion result, aiming at the problem that the sea surface gravity data inversion precision is influenced by sea surface input gravity field metadata quality by utilizing satellite height measurement gravity data.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for calculating the influence of sea surface gravity data measurement precision on a submarine topography inversion result, which comprises the following steps:
step 1: taking the sea depth as input data, resolving gravity field element information generated by the sea depth by using a strict prism volume division method, and obtaining an effective integral radius;
step 2: adding sea depth Gaussian white noises corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
and step 3: taking the effective integral radius obtained in the step 1 as a basis, respectively taking the error-free sea depth and the sea depth data with different relative precisions obtained in the step 2 as input, and forward-calculating to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions;
and 4, step 4: 3, the gravity field element result obtained by forward modeling of the sea depth data with different relative precisions in the step 3 is subtracted from the gravity field element result obtained by forward modeling of the sea depth without errors to obtain a forward gravity field element difference value;
and 5: and 4, taking the difference obtained in the step 4 as input, and counting the difference result indexes.
Further, the step 1 comprises:
resolving gravity field element information generated by sea depth by using a strict prism volume division method, wherein the gravity field elements comprise sea surface gravity anomaly and gravity anomaly vertical gradient:
Figure BDA0003245886070000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003245886070000022
wherein G is the earth gravitational potential constant and takes the value of 6.672 multiplied by 10-8cm3/(g·s2)；ρcAnd ρwRespectively representing the density of the crust of the earth and the density of the seawater; (i)p,jp) To study the site location; (i, j) is the flow point position; h (i, j) is the corresponding sea depth of the (i, j) point; l is the distance between the point of interest and the flow point; (x, y, z) are flow point coordinates; sLAnd SBRespectively representing the points of the integral radius of the central area in the longitude and latitude directions; Δ x and Δ y represent grid sizes in the longitude and latitude directions, respectively; t iszFor disturbance gravity, the disturbance gravity is used to represent sea surface gravity anomaly; t iszzIs a gravity abnormal vertical gradient.
Further, the step 2 comprises:
sea depth data of different relative precisions are generated by formula (3):
herr＝h0+hno (3)
in the formula, herrDifferent relative precision depths; h is0The sea depth is error-free; h isnoThe sea depth Gaussian white noise standard deviation is equal to the product of the error-free sea depth average value and the relative precision.
Further, in step 4, the forward gravitational field component difference value is obtained according to the formula (4):
Figure BDA0003245886070000031
in the formula, gammaiGravity representing the ith forward performanceA field element difference value;
Figure BDA0003245886070000032
and
Figure BDA0003245886070000033
respectively representing the ith gravity field element values obtained by forward modeling of different relative precision sea depths and error-free sea depths; and N is the number of the statistical gravity difference values.
Further, in step 5, the difference result indicator includes:
Figure BDA0003245886070000034
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element; delta gammamax、△γmin、△γmeanAnd Δ γstdThe maximum, minimum, mean and standard deviation of the difference are indicated, respectively.
The invention also provides a device for calculating the influence of the sea surface gravity data measurement precision on the inversion result of the submarine topography, which comprises:
the resolving module is used for resolving gravity field element information generated by the sea depth by using a strict prism volume division method by taking the sea depth as input data to obtain an effective integral radius;
the noise adding module is used for adding sea depth Gaussian white noise corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
the forward modeling module is used for forward modeling to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions, which are obtained by the noise adding module, by taking the effective integral radius obtained by the resolving module as a basis and respectively taking the error-free sea depth and the sea depth data with different relative precisions obtained by the noise adding module as input;
the error making module is used for making an error between a gravity field element result obtained by forward modeling of the sea depth data with different relative precisions of the forward modeling module and a gravity field element result obtained by forward modeling of the error-free sea depth to obtain a forward gravity field element difference value;
and the statistical module is used for taking the difference value of the difference making module as input and counting the difference result index.
Further, the gravity field element comprises a sea surface gravity anomaly and a gravity anomaly vertical gradient.
Further, the difference result indicator includes a maximum value, a minimum value, an average value, and a standard deviation of the difference.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a method for calculating theoretical precision requirements of sea surface gravity anomaly and gravity anomaly vertical gradient measurement data under different inversion precision index requirements of submarine topography. The invention removes the entanglement influence of algorithm errors and data errors, completely realizes the requirement of calculating the inversion result quality of the submarine topography on the accuracy of the gravity input data from the input and output data level, and reveals the internal association between the gravity data (input data) and the submarine topography data (output data).
The method has beneficial reference values for researching the measurement precision requirements of different construction precision requirements of the submarine topography on the sea surface gravity data and utilizing the result to design a height measurement satellite constellation scheme for inverting the submarine topography by utilizing the satellite height measurement gravity data and recovering, analyzing and processing the marine gravity field data based on the satellite height measurement technology.
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FIG. 1 is a basic flow chart of a method for calculating the influence of sea surface gravity data measurement accuracy on a submarine topography inversion result according to an embodiment of the present invention;
FIG. 2 is an exemplary diagram of a noise-free sea depth model;
FIG. 3 is an exemplary diagram of the calculation results of different gravitational field components at an exemplary point;
FIG. 4 is an exemplary diagram of a model of different relative precisions of the sea depth of the target sea area;
fig. 5 is a schematic structural diagram of a device for calculating an influence of sea surface gravity data measurement accuracy on a submarine topography inversion result according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, a method for calculating the influence of the measurement accuracy of the sea surface gravity data on the inversion result of the submarine topography includes:
step S101: taking the sea depth as input data, resolving gravity field element information generated by the sea depth by using a strict prism volume division method, and obtaining an effective integral radius;
step S102: adding sea depth Gaussian white noises corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
step S103: taking the effective integral radius obtained in the step S101 as a basis, respectively taking the error-free sea depth and the sea depth data with different relative precisions obtained in the step S102 as input, and forward-calculating to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions;
step S104: the gravity field element result obtained by forward modeling of the sea depth data with different relative precisions in the step S103 is subtracted from the gravity field element result obtained by forward modeling of the sea depth without error to obtain a forward gravity field element difference value; specifically, the forward gravity field element difference includes a forward gravity abnormal difference and a forward gravity abnormal vertical gradient difference;
step S105: and taking the difference obtained in the step S104 as an input, and counting the difference result index.
Further, the step S101 includes:
resolving gravity field element information generated by sea depth by using a strict prism volume division method, wherein the gravity field elements comprise sea surface gravity anomaly and gravity anomaly vertical gradient:
Figure BDA0003245886070000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003245886070000052
wherein G is the earth gravitational potential constant, and takes the valueIs 6.672 x 10-8cm3/(g·s2)；ρcAnd ρwRespectively representing the density of the crust of the earth and the density of the seawater; (i)p,jp) To study the site location; (i, j) is the flow point position; h (i, j) is the corresponding sea depth of the (i, j) point; l is the distance between the point of interest and the flow point; (x, y, z) are flow point coordinates; sLAnd SBRespectively representing the points of the integral radius of the central area in the longitude and latitude directions; Δ x and Δ y represent grid sizes in the longitude and latitude directions, respectively; t iszFor disturbance gravity, the disturbance gravity is used to represent sea surface gravity anomaly; t iszzIs a gravity abnormal vertical gradient.
Further, the step S102 includes:
sea depth data of different relative precisions are generated by formula (3):
herr＝ho+hno (3)
in the formula, herrDifferent relative precision depths; h is0The sea depth is error-free; h isnoThe sea depth Gaussian white noise standard deviation is equal to the product of the error-free sea depth average value and the relative precision.
Further, in step S104, a forward gravitational field component difference value is obtained according to the formula (4):
Figure BDA0003245886070000061
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element;
Figure BDA0003245886070000062
and
Figure BDA0003245886070000063
respectively representing the ith gravity field element values obtained by forward modeling of different relative precision sea depths and error-free sea depths; and N is the number of the statistical gravity difference values.
Further, in step S105, the difference result index includes:
Figure BDA0003245886070000064
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element; delta gammamax、△γmin、△γmeanAnd Δ γstdThe maximum, minimum, mean and standard deviation of the difference are indicated, respectively.
Specifically, taking a 3 ° × 3 ° (111 ° E-114 ° E, 12 ° N-15 ° N) sea area in south china as an example, an S & S V19.1.1 error-free sea depth model is used as an error-free sea depth reference, and corresponding sea surface gravity anomaly and gravity anomaly vertical gradient accuracy requirements are respectively calculated under the conditions that the relative accuracies of the sea floor terrain are respectively 6%, 8% and 10%.
The method comprises the following steps: the calculation uses the central point (13 degrees 29 '30' N, 112 degrees 29 '30' E) of the south sea test sea area as an analysis sample point, and adopts the formula (1) to calculate the variation trend results of Tz and Tzz along with the integral radius under the noise-free south sea depth model (figure 2) (see figure 3). The effective integration radius is set to be about 61km, taking the figure 3 trend into account.
Step two: based on the S & S V19.1.1 error-free sea depth model, sea depth models with relative accuracies of 6%, 8%, and 10% were obtained using equation (3), and the results are shown in fig. 4.
Step three: and (3) calculating gravity field elements obtained by forward modeling of the sea depths with relative accuracies of 6%, 8% and 10% and gravity field element results obtained by forward modeling of the error-free sea depths respectively by adopting a formula (1) based on the effective integration radius of 61km obtained in the step one.
Step four: the gravity field elements obtained by forward performance of the sea depths with the relative precision of 6%, 8% and 10% obtained in the third step are subjected to error correction with the gravity field element result obtained by forward performance of the sea depths without errors through a formula (4), so that a forward gravity field element difference value is obtained;
step five: taking the difference obtained in the step four as input, and counting difference result indexes according to the formula (5); the difference statistics are shown in table 1.
TABLE 1 statistics of sea surface disturbance field element difference results corresponding to different relative precision sea depths
Figure BDA0003245886070000071
According to table 1, it can be known that the higher the sea depth relative accuracy is, the greater the corresponding sea surface gravity data accuracy requirement is, for example, when the sea depth relative accuracy in the south sea area is 6%, the corresponding sea surface Tz theoretical accuracy is 1.99 mGal; and when the relative precision of the sea depth of the sea area of the south sea is reduced to 8%, the theoretical precision of the corresponding sea surface Tz is reduced to 2.47 mGal. When the relative accuracy requirement of the sea depth of the south sea is within 10%, the corresponding sea surface Tz and Tzz accuracy at least reaches 3.23mGal and 18.25E theoretically.
On the basis of the foregoing embodiment, as shown in fig. 5, another aspect of the present invention provides an apparatus for calculating an influence of sea surface gravity data measurement accuracy on a submarine topography inversion result, including:
the calculating module 201 is used for calculating gravity field element information generated by the sea depth by using a strict prism volume division method by taking the sea depth as input data to obtain an effective integral radius;
the noise adding module 202 is used for adding sea depth Gaussian white noise corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
the forward modeling module 203 is used for forward modeling to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative accuracies, which are obtained by the noise adding module, by taking the effective integral radius obtained by the resolving module as a basis and respectively taking the error-free sea depth and the sea depth data with different relative accuracies obtained by the noise adding module as input;
the difference making module 204 is configured to make a difference between a gravity field element result obtained by forward modeling of the sea depth data with different relative accuracies of the forward modeling module and a gravity field element result obtained by forward modeling of the error-free sea depth, so as to obtain a forward-modeled gravity field element difference value;
and the statistical module 205 is configured to take the difference value of the difference module as an input, and count a difference result index.
Further, the resolving module 201 includes:
resolving gravity field element information generated by sea depth by using a strict prism volume division method, wherein the gravity field elements comprise sea surface gravity anomaly and gravity anomaly vertical gradient:
Figure BDA0003245886070000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003245886070000082
wherein G is the earth gravitational potential constant and takes the value of 6.672 multiplied by 10-8cm3/(g·s2)；ρcAnd ρwRespectively representing the density of the crust of the earth and the density of the seawater; (i)p,jp) To study the site location; (i, j) is the flow point position; h (i, j) is the corresponding sea depth of the (i, j) point; l is the distance between the point of interest and the flow point; (x, y, z) is the flow point coordinate SLAnd SBRespectively representing the points of the integral radius of the central area in the longitude and latitude directions; Δ x and Δ y represent grid sizes in the longitude and latitude directions, respectively; t iszFor disturbance gravity, the disturbance gravity is used to represent sea surface gravity anomaly; t iszzIs a gravity abnormal vertical gradient.
Further, the noise adding module 202 includes:
sea depth data of different relative precisions are generated by formula (3):
herr＝ho+hno (3)
in the formula, herrDifferent relative precision depths; h is0The sea depth is error-free; h isnoThe sea depth Gaussian white noise standard deviation is equal to the product of the error-free sea depth average value and the relative precision.
Further, in the difference module 204, the forward gravitational field component difference value is obtained according to the formula (4):
Figure BDA0003245886070000083
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element;
Figure BDA0003245886070000084
and
Figure BDA0003245886070000085
respectively representing the ith gravity field element values obtained by forward modeling of different relative precision sea depths and error-free sea depths; and N is the number of the statistical gravity difference values.
Further, in the statistical module 205, the difference result indicator includes:
Figure BDA0003245886070000091
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element; delta gammamax、△γmin、△γmeanAnd Δ γstdThe maximum, minimum, mean and standard deviation of the difference are indicated, respectively.
In conclusion, the invention provides a calculation method for theoretical precision requirements of sea surface gravity anomaly and gravity anomaly vertical gradient measurement data under different inversion precision index requirements of submarine topography. The invention removes the entanglement influence of algorithm errors and data errors, completely realizes the requirement of calculating the inversion result quality of the submarine topography on the accuracy of the gravity input data from the input and output data level, and reveals the internal association between the gravity data (input data) and the submarine topography data (output data).
The method has beneficial values for exploring the measurement precision requirements of different construction precision requirements of the submarine topography on the sea surface gravity data, reflecting the underwater topography and topography as truly, completely, globally and accurately as possible according to the result, improving the global marine information acquisition, analysis and forecast capability, enhancing the marine cognition, marine forecast and marine information service capability, and realizing the forecast capability of hundreds of meters in the global marine mesoscale and key sea areas.
The above shows only the preferred embodiments of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.

Claims (8)

1. A method for calculating the influence of sea surface gravity data measurement precision on a submarine topography inversion result is characterized by comprising the following steps:
step 1: taking the sea depth as input data, resolving gravity field element information generated by the sea depth by using a strict prism volume division method, and obtaining an effective integral radius;
step 2: adding sea depth Gaussian white noises corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
and step 3: taking the effective integral radius obtained in the step 1 as a basis, respectively taking the error-free sea depth and the sea depth data with different relative precisions obtained in the step 2 as input, and forward-calculating to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions;
and 4, step 4: 3, the gravity field element result obtained by forward modeling of the sea depth data with different relative precisions in the step 3 is subtracted from the gravity field element result obtained by forward modeling of the sea depth without errors to obtain a forward gravity field element difference value;
and 5: and 4, taking the difference obtained in the step 4 as input, and counting the difference result indexes.
2. The method for calculating the influence of the sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 1, wherein the step 1 comprises:
resolving gravity field element information generated by sea depth by using a strict prism volume division method, wherein the gravity field elements comprise sea surface gravity anomaly and gravity anomaly vertical gradient:
Figure FDA0003245886060000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003245886060000012
wherein G is the earth gravitational potential constant and takes the value of 6.672 multiplied by 10-8cm3/(g·s2)；ρcAnd ρwRespectively representing the density of the crust of the earth and the density of the seawater; (i)p,jp) To study the site location; (i, j) is the flow point position; h (i, j) is the corresponding sea depth of the (i, j) point; l is the distance between the point of interest and the flow point; (x, y, z) are flow point coordinates; sLAnd SBRespectively representing the points of the integral radius of the central area in the longitude and latitude directions; Δ x and Δ y represent grid sizes in the longitude and latitude directions, respectively; t iszFor disturbance gravity, the disturbance gravity is used to represent sea surface gravity anomaly; t iszzIs a gravity abnormal vertical gradient.
3. The method for calculating the influence of the sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 1, wherein the step 2 comprises:
sea depth data of different relative precisions are generated by formula (3):
herr＝h0+hno (3)
in the formula, herrDifferent relative precision depths; h is0The sea depth is error-free; h isnoThe sea depth Gaussian white noise standard deviation is equal to the product of the error-free sea depth average value and the relative precision.
4. The method for calculating the influence of the sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 1, wherein in the step 4, a forward gravity field element difference value is obtained according to the formula (4):
Figure FDA0003245886060000021
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element;
Figure FDA0003245886060000022
and
Figure FDA0003245886060000023
respectively representing the ith gravity field element values obtained by forward modeling of different relative precision sea depths and error-free sea depths; and N is the number of the statistical gravity difference values.
5. The method for calculating the influence of the sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 4, wherein in the step 5, the difference result index comprises:
Figure FDA0003245886060000024
in the formula, gammaiRepresenting the difference value of the ith forward acting gravity field element; delta gammamax、△γmin、△γmeanAnd Δ γstdThe maximum, minimum, mean and standard deviation of the difference are indicated, respectively.
6. A device for calculating influence of sea surface gravity data measurement precision on a submarine topography inversion result is characterized by comprising:
the resolving module is used for resolving gravity field element information generated by the sea depth by using a strict prism volume division method by taking the sea depth as input data to obtain an effective integral radius;
the noise adding module is used for adding sea depth Gaussian white noise corresponding to sea depths with different relative accuracies on the basis of the error-free sea depth, and further generating sea depth data with different relative accuracies;
the forward modeling module is used for forward modeling to obtain gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precisions, which are obtained by the noise adding module, by taking the effective integral radius obtained by the resolving module as a basis and respectively taking the error-free sea depth and the sea depth data with different relative precisions obtained by the noise adding module as input;
the error making module is used for making an error between a gravity field element result obtained by forward modeling of the sea depth data with different relative precisions of the forward modeling module and a gravity field element result obtained by forward modeling of the error-free sea depth to obtain a forward gravity field element difference value;
and the statistical module is used for taking the difference value of the difference making module as input and counting the difference result index.
7. The device for calculating the influence of the measurement accuracy of the sea surface gravity data on the inversion result of the submarine topography according to claim 6, wherein the gravity field elements comprise sea surface gravity anomaly and gravity anomaly vertical gradient.
8. The device for calculating the influence of the measurement accuracy of the sea surface gravity data on the inversion result of the submarine topography as claimed in claim 6, wherein the difference result index comprises a maximum value, a minimum value, an average value and a standard deviation of the difference.
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