CN113960690B - Method and device for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion result - Google Patents
Method and device for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion result Download PDFInfo
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Abstract
The invention discloses a method and a device for calculating influence of sea surface gravity data measurement accuracy on a submarine topography inversion result, wherein the method comprises the following steps: the sea depth is used as input data, and the gravity field meta-information generated by the sea depth is calculated by using a strict prism integration method, so that an effective integration radius is obtained; adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depth, so as to generate sea depth data with different relative precision; respectively taking the obtained effective integral radius as a basis, taking the sea depth without errors and the obtained sea depth data with different relative precision as input, and forward modeling to obtain gravitational field element results corresponding to the sea depth data without errors and different relative precision; the method comprises the steps of performing difference between a forward gravity field element result of sea depth data with different relative precision and an error-free forward gravity field element result to obtain a forward gravity field element difference value; taking the difference as input, and counting a difference result index. The present invention discloses an inherent correlation between gravity data and seafloor topography data.
Description
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 accuracy on submarine topography inversion results.
Background
The submarine topography (sea depth) measurement is used as a basic means and system engineering for observing the ocean and cognizing the ocean, and can play an irreplaceable role in the aspects of ocean resource development, ocean ecological environment protection, ocean technological innovation, ocean equity maintenance and the like. Current seafloor topography techniques mainly include ship-based seafloor topography techniques, submarine seafloor topography techniques, airborne lidar sounding (Airborne Lidar bathymetry, ALB) techniques, star-based seafloor topography techniques, and the like. The satellite-based submarine topography measurement technology (such as satellite height measurement and gravity inversion submarine topography) is a method means for quickly constructing global submarine topography mainly relied on at present, for example, in 2019, GEBCO depends on the Nippon Foundation-GEBCO set 2030 project, a first-published submarine topography model (GEBCO_2019) with a grid size of 15 'global, and a space grid model (SRTM 15+V2.0) with a grid size of 15' global, which is restored by organizations such as SIO, NOAA and NGA based on topography models such as SRTM15+V1.0, wherein most submarine topography data in a sea area are restored by satellite height measurement and gravity data inversion.
In general, the accuracy of inversion of submarine topography models by satellite altimetry technology is currently in need of improvement. Inversion of the nature of the submarine topography is the inverse solution of the problem of the forward disturbance field 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 gravity inversion of the submarine topography; and secondly, inputting data errors by gravity. Sea surface gravity input data quality will directly affect the modeling effect of the seafloor topography based on sea surface gravity data.
Disclosure of Invention
The invention provides a method and a device for calculating the influence of sea surface gravity data measurement accuracy on sea surface topography inversion results, aiming at the current problem that sea surface topography accuracy is influenced by sea surface input gravity field metadata quality by utilizing satellite height measurement gravity data.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the invention provides a method for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion results, which comprises the following steps:
step 1: the sea depth is used as input data, and the gravity field meta-information generated by the sea depth is calculated by using a strict prism integration method, so that an effective integration radius is obtained;
step 2: adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depth, so as to generate sea depth data with different relative precision;
step 3: taking the effective integral radius obtained in the step 1 as a basis, respectively taking the sea depth data without errors and with different relative precision obtained in the step 2 as input, and forward modeling to obtain gravity field element results corresponding to the sea depth data without errors and with different relative precision;
step 4: the gravity field element result obtained by forward modeling of the sea depth data with different relative precision in the step 3 is differenced with the gravity field element result obtained by forward modeling of the sea depth without error, so as to obtain a forward modeling gravity field element difference value;
step 5: and (3) taking the difference value obtained in the step (4) as input, and counting a difference value result index.
Further, the step 1 includes:
solving gravitational field element information generated by sea depths by using a strict prism integration method, wherein the gravitational field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient:
in the method, in the process of the invention,
wherein G is the gravitational constant and takes the value of 6.672 multiplied by 10 -8 cm 3 /(g·s 2 )；ρ c And ρ w Respectively representing the crust density and the sea water density; (i) p ,j p ) To study the point location; (i, j) is the flow point position; h (i, j) is the sea depth corresponding to the point (i, j); l is the study point to pour point distance; (x, y, z) is the flow point coordinates; s is S L And S is B Points of integration radius of the central area in the longitude and latitude directions are respectively represented; Δx and Δy represent grid sizes in the longitudinal and latitudinal directions, respectively; t (T) z For disturbance gravity, here, disturbance gravity is used to represent sea surface gravity anomaly; t (T) zz Is a gravity anomaly vertical gradient.
Further, the step 2 includes:
sea depth data of different relative accuracies are generated by the formula (3):
h err ＝h 0 +h no (3)
in the formula, h err Sea depths for different relative accuracies; h is a 0 Is the sea depth without error; h is a no Is sea depth Gaussian white noise corresponding to different relative precision sea depths, and the standard deviation of the sea depth Gaussian white noise is equal to the product of the error-free sea depth average value and the relative precision.
Further, in the step 4, the forward gravity field element difference value is obtained according to the formula (4):
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling;
and->
Respectively representing ith gravity field element values obtained by forward modeling of sea depths with different relative precision and sea depths without errors; n is the number of the counted gravity difference values.
Further, in the step 5, the difference result index includes:
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling; Δγ max 、△γ min 、△γ mean And Deltay std The maximum value, minimum value, average value and standard deviation of the difference values are represented, respectively.
The invention also provides a device for calculating the influence of sea surface gravity data measurement accuracy on the submarine topography inversion result, which comprises the following steps:
the resolving module is used for resolving gravitational field meta-information generated by sea depth by using a strict prism integration method by taking sea depth as input data to acquire an effective integration radius;
the noise adding module is used for adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depths so as to generate sea depth data with different relative precision;
the forward modeling module is used for taking the effective integral radius obtained by the resolving module as a basis, respectively taking sea depth data with different relative precision obtained by the error-free sea depth and noise adding module as input, and obtaining the gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precision through forward modeling;
the forward modeling module is used for modeling the sea depth data of different relative precision according to the sea depth data of the forward modeling module, and obtaining a forward modeling gravity field element difference value;
and the statistics module is used for taking the difference value of the difference making module as input and counting a difference value result index.
Further, the gravitational field elements include sea surface gravity anomalies and gravity anomaly vertical gradients.
Further, the difference result index 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 beneficial effects that:
the invention provides a calculation method for theoretical accuracy requirements of sea surface gravity anomaly and gravity anomaly vertical gradient measurement data under different inversion accuracy index requirements of submarine topography. The invention peels off the entanglement effect of algorithm errors and data errors, completely realizes the calculation of the accuracy requirement of the quality of the submarine topography inversion result on gravity input data from the input and output data layers, and reveals the internal correlation between gravity data (input data) and submarine topography data (output data).
The invention has beneficial reference value for exploring the requirements of different construction precision of submarine topography on the measurement precision of sea surface gravity data, and inverting the design of a height measurement satellite constellation scheme of the submarine topography by utilizing satellite height measurement gravity data and the recovery, analysis and processing of the sea gravity field data based on satellite height measurement technology according to the requirements.
Drawings
FIG. 1 is a basic flow chart of a method for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion results according to an embodiment of the invention;
FIG. 2 is an exemplary diagram of a noiseless sea depth model;
FIG. 3 is an exemplary graph of the results of different gravity primitive calculations at an exemplary point;
FIG. 4 is an exemplary diagram of different relative accuracy sea depth models for a target sea area;
fig. 5 is a schematic structural diagram of a device for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion results according to an embodiment of the invention.
Detailed Description
The invention is further illustrated by the following description of specific embodiments in conjunction with the accompanying drawings:
as shown in fig. 1, a method for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion results includes:
step S101: the sea depth is used as input data, and the gravity field meta-information generated by the sea depth is calculated by using a strict prism integration method, so that an effective integration radius is obtained;
step S102: adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depth, so as to generate sea depth data with different relative precision;
step S103: taking the effective integral radius obtained in the step S101 as a basis, respectively taking the sea depth data without errors and with different relative precision obtained in the step S102 as input, and forward modeling to obtain gravity field element results corresponding to the sea depth data without errors and with different relative precision;
step S104: the gravity field element result obtained by forward modeling of sea depth data with different relative precision in the step S103 is differenced from the gravity field element result obtained by forward modeling of the sea depth without error, so as to obtain a forward modeling gravity field element difference value; specifically, the forward gravity primitive difference value comprises a forward gravity anomaly difference value and a forward gravity anomaly vertical gradient difference value;
step S105: taking the difference value obtained in the step S104 as input, and counting a difference value result index.
Further, the step S101 includes:
solving gravitational field element information generated by sea depths by using a strict prism integration method, wherein the gravitational field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient:
in the method, in the process of the invention,
wherein G is the gravitational constant and takes the value of 6.672 multiplied by 10 -8 cm 3 /(g·s 2 )；ρ c And ρ w Respectively representing the crust density and the sea water density; (i) p ,j p ) To study the point location; (i, j) is the flow point position; h (i, j) is the sea depth corresponding to the point (i, j); l is the study point to pour point distance; (x, y, z) is the flow point coordinates; s is S L And S is B Points of integration radius of the central area in the longitude and latitude directions are respectively represented; Δx and Δy represent grid sizes in the longitudinal and latitudinal directions, respectively; t (T) z For disturbance gravity, here, disturbance gravity is used to represent sea surface gravity anomaly; t (T) zz Is a gravity anomaly vertical gradient.
Further, the step S102 includes:
sea depth data of different relative accuracies are generated by the formula (3):
h err ＝h o +h no (3)
in the formula, h err Sea depths for different relative accuracies; h is a 0 Is the sea depth without error; h is a no Is of different relative essenceThe standard deviation of the sea depth Gaussian white noise corresponding to the sea depth is equal to the product of the error-free sea depth average value and the relative precision.
Further, in the step S104, a forward gravity field element difference value is obtained according to the formula (4):
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling;
and->
Respectively representing ith gravity field element values obtained by forward modeling of sea depths with different relative precision and sea depths without errors; n is the number of the counted gravity difference values.
Further, in the step S105, the difference result index includes:
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling; Δγ max 、△γ min 、△γ mean And Deltay std The maximum value, minimum value, average value and standard deviation of the difference values are represented, respectively.
Specifically, taking a south China sea 3 degree multiplied by 3 degree (111 degree E-114 degree E,12 degree N-15 degree N) sea area as an example, using an S & S V19.1.1 error-free sea depth model as an error-free sea depth reference, and respectively calculating corresponding sea surface gravity anomaly and gravity anomaly vertical gradient precision requirements under the conditions that the relative precision of submarine topography is 6%, 8% and 10% respectively.
Step one: calculating the trend of Tz and Tzz along with the integral radius under a noise-free south sea depth model (figure 2) by using a south sea test sea area central point (13 DEG 29 '30' N,112 DEG 29 '30' E) as an analysis example point and adopting (1) (see figure 3). With the trend of fig. 3 taken together, the effective integration radius is set to about 61km.
Step two: based on the S & S V19.1 error-free sea depth model, sea depth models with relative accuracy of 6%, 8% and 10% were obtained by using the formula (3), and the results are shown in fig. 4.
Step three: based on the 61km effective integral radius obtained in the first step, respectively calculating the gravity field element obtained by sea depth forward modeling and the gravity field element result obtained by error-free sea depth forward modeling with relative accuracy of 6%, 8% and 10% by adopting the formula (1).
Step four: the gravity field element obtained by forward modeling of sea depth with relative accuracy of 6%, 8% and 10% obtained in the step three is differenced with the gravity field element obtained by forward modeling of sea depth without error in the formula (4), so as to obtain the difference value of the gravity field elements of the forward modeling;
step five: taking the difference value obtained in the step four as input, and counting a difference value result index according to the step (5); the difference statistics are shown in Table 1.
TABLE 1 sea surface disturbance field element difference result statistics corresponding to sea depths of different relative accuracies
According to table 1, the higher the relative accuracy of sea depth, the higher the accuracy requirement of the corresponding sea surface gravity data, for example, when the relative accuracy of sea depth in the south sea area is 6%, the theoretical accuracy of the corresponding sea surface Tz is 1.99mGal; and when the relative sea depth precision of the south sea area is reduced to 8%, the theoretical precision of the corresponding sea surface Tz is reduced to 2.47mGAL. When the relative sea depth of the south sea area is required to be within 10%, the respective sea surface Tz and Tz precision should theoretically reach at least 3.23mGAL and 18.25E.
On the basis of the above embodiment, as shown in fig. 5, another aspect of the present invention provides a device for calculating the influence of sea surface gravity data measurement accuracy on the submarine topography inversion result, including:
the resolving module 201 is configured to use sea depth as input data, and utilize a strict prism integration method to resolve gravitational field meta information generated by sea depth, so as to obtain an effective integration radius;
the noise adding module 202 is configured to add sea depth gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depths, so as to generate sea depth data with different relative precision;
the forward modeling module 203 is configured to forward model to obtain gravity field element results corresponding to the sea depth data with no error and different relative precision, based on the effective integral radius obtained by the resolving module and respectively based on the sea depth data with different relative precision obtained by the error-free sea depth and noise adding module;
the difference making module 204 is configured to make a difference between a gravity field element result obtained by forward modeling of sea depth data with different relative accuracy of the forward modeling module and a gravity field element result obtained by error-free sea depth forward modeling, so as to obtain a forward modeling gravity field element difference value;
the statistics module 205 is configured to take the difference value of the difference making module as an input, and count a difference result index.
Further, the resolving module 201 includes:
solving gravitational field element information generated by sea depths by using a strict prism integration method, wherein the gravitational field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient:
in the method, in the process of the invention,
wherein G is the gravitational constant and takes the value of 6.672 multiplied by 10 -8 cm 3 /(g·s 2 )；ρ c And ρ w Respectively representing the crust density and the sea water density; (i) p ,j p ) To study the point location; (i, j) is the flow point position; h (i, j) is the sea depth corresponding to the point (i, j); l is the study point to pour point distance; (x, y, z) is the flow point coordinate S L And S is B Representing longitude and latitude central zone integral halves, respectivelyCounting the diameter points; Δx and Δy represent grid sizes in the longitudinal and latitudinal directions, respectively; t (T) z For disturbance gravity, here, disturbance gravity is used to represent sea surface gravity anomaly; t (T) zz Is a gravity anomaly vertical gradient.
Further, the noise adding module 202 includes:
sea depth data of different relative accuracies are generated by the formula (3):
h err ＝h o +h no (3)
in the formula, h err Sea depths for different relative accuracies; h is a 0 Is the sea depth without error; h is a no Is sea depth Gaussian white noise corresponding to different relative precision sea depths, and the standard deviation of the sea depth Gaussian white noise is equal to the product of the error-free sea depth average value and the relative precision.
Further, in the difference making module 204, the forward gravity field element difference value is obtained according to the formula (4):
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling;
and->
Respectively representing ith gravity field element values obtained by forward modeling of sea depths with different relative precision and sea depths without errors; n is the number of the counted gravity difference values.
Further, in the statistics module 205, the difference result indicator includes:
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling; Δγ max 、△γ min 、△γ mean And Deltay std The maximum value, minimum value, average value and standard deviation of the difference values are represented, respectively.
In conclusion, the invention provides a calculation method for theoretical accuracy requirements of sea surface gravity anomaly and gravity anomaly vertical gradient measurement data under different inversion accuracy index requirements of submarine topography. The invention peels off the entanglement effect of algorithm errors and data errors, completely realizes the calculation of the accuracy requirement of the quality of the submarine topography inversion result on gravity input data from the input and output data layers, and reveals the internal correlation between gravity data (input data) and submarine topography data (output data).
The method has a beneficial value for exploring the requirements of different construction precision of submarine topography on the measurement precision of sea surface gravity data, reflecting the underwater topography as truly, completely, globally and accurately as possible according to the requirements, improving the global ocean information acquisition, analysis and prediction capability, enhancing the ocean cognition, ocean prediction and ocean information service capability, and realizing the prediction and prediction capability of the global ocean mesoscale and key ocean area hundred-meter level.
The foregoing is merely illustrative of the preferred embodiments of this invention, and it will be appreciated by those skilled in the art that changes and modifications may be made without departing from the principles of this invention, and it is intended to cover such modifications and changes as fall within the true scope of the invention.
Claims (4)
1. A method for calculating influence of sea surface gravity data measurement accuracy on submarine topography inversion results is characterized by comprising the following steps:
step 1: the sea depth is used as input data, and the gravity field meta-information generated by the sea depth is calculated by using a strict prism integration method, so that an effective integration radius is obtained; the step 1 comprises the following steps:
solving gravitational field element information generated by sea depths by using a strict prism integration method, wherein the gravitational field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient:
in the method, in the process of the invention,
wherein G is the gravitational constant and takes the value of 6.672 multiplied by 10 -8 cm 3 /(g·s 2 )；ρ c And ρ w Respectively representing the crust density and the sea water density; (i) p ,j p ) To study the point location; (i, j) is the flow point position; h (i, j) is the sea depth corresponding to the point (i, j); l is the study point to pour point distance; (x, y, z) is the flow point coordinates; s is S L And S is B Points of integration radius of the central area in the longitude and latitude directions are respectively represented; Δx and Δy represent grid sizes in the longitudinal and latitudinal directions, respectively; t (T) z For disturbance gravity, here, disturbance gravity is used to represent sea surface gravity anomaly; t (T) zz Is a gravity anomaly vertical gradient;
step 2: adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depth, so as to generate sea depth data with different relative precision; the step 2 comprises the following steps:
sea depth data of different relative accuracies are generated by the formula (3):
h err ＝h 0 +h no (3)
in the formula, h err Sea depths for different relative accuracies; h is a 0 Is the sea depth without error; h is a no Is sea depth Gaussian white noise corresponding to sea depths with different relative precision, and the standard deviation of the sea depth Gaussian white noise is equal to the product of the average value of the sea depths without errors and the relative precision;
step 3: taking the effective integral radius obtained in the step 1 as a basis, respectively taking the sea depth data without errors and with different relative precision obtained in the step 2 as input, and forward modeling to obtain gravity field element results corresponding to the sea depth data without errors and with different relative precision;
step 4: the gravity field element result obtained by forward modeling of the sea depth data with different relative precision in the step 3 is differenced with the gravity field element result obtained by forward modeling of the sea depth without error, so as to obtain a forward modeling gravity field element difference value; in the step 4, the forward gravity field element difference value is obtained according to the formula (4):
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling;
and->
Respectively representing ith gravity field element values obtained by forward modeling of sea depths with different relative precision and sea depths without errors; n is the number of the counted gravity difference values;
step 5: taking the difference value obtained in the step 4 as input, and counting a difference value result index; in the step 5, the difference result index includes:
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling; Δγ max 、△γ min 、△γ mean And Deltay std The maximum value, minimum value, average value and standard deviation of the difference values are represented, respectively.
2. The utility model provides a sea surface gravity data measurement accuracy influences calculation device to submarine topography inversion result which characterized in that includes:
the resolving module is used for resolving gravitational field meta-information generated by sea depth by using a strict prism integration method by taking sea depth as input data to acquire an effective integration radius; the resolving module is specifically configured to:
solving gravitational field element information generated by sea depths by using a strict prism integration method, wherein the gravitational field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient:
in the method, in the process of the invention,
wherein G is the gravitational constant and takes the value of 6.672 multiplied by 10 -8 cm 3 /(g·s 2 )；ρ c And ρ w Respectively representing the crust density and the sea water density; (i) p ,j p ) To study the point location; (i, j) is the flow point position; h (i, j) is the sea depth corresponding to the point (i, j); l is the study point to pour point distance; (x, y, z) is the flow point coordinates; s is S L And S is B Points of integration radius of the central area in the longitude and latitude directions are respectively represented; Δx and Δy represent grid sizes in the longitudinal and latitudinal directions, respectively; t (T) z For disturbance gravity, here, disturbance gravity is used to represent sea surface gravity anomaly; t (T) zz Is a gravity anomaly vertical gradient;
the noise adding module is used for adding sea depth Gaussian white noise corresponding to sea depths with different relative precision on the basis of error-free sea depths so as to generate sea depth data with different relative precision; the noise adding module is specifically used for:
sea depth data of different relative accuracies are generated by the formula (3):
h err ＝h 0 +h no (3)
in the formula, h err Sea depths for different relative accuracies; h is a 0 Is the sea depth without error; h is a no Is sea depth Gaussian white noise corresponding to sea depths with different relative precision, and the standard deviation of the sea depth Gaussian white noise is equal to the product of the average value of the sea depths without errors and the relative precision;
the forward modeling module is used for taking the effective integral radius obtained by the resolving module as a basis, respectively taking sea depth data with different relative precision obtained by the error-free sea depth and noise adding module as input, and obtaining the gravity field element results corresponding to the error-free sea depth and the sea depth data with different relative precision through forward modeling;
the forward modeling module is used for modeling the sea depth data of different relative precision according to the difference value of the forward modeling module; and in the difference making module, obtaining a forward gravity field element difference value according to the formula (4):
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling;
and->
Respectively representing ith gravity field element values obtained by forward modeling of sea depths with different relative precision and sea depths without errors; n is the number of the counted gravity difference values;
the statistics module is used for taking the difference value of the difference making module as input and counting a difference value result index; in the statistics module, the difference result index includes:
wherein, gamma i Representing the gravity field element difference value of the ith forward modeling; Δγ max 、△γ min 、△γ mean And Deltay std The maximum value, minimum value, average value and standard deviation of the difference values are represented, respectively.
3. The device for calculating the influence of sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 2, wherein the gravity field element comprises sea surface gravity anomaly and gravity anomaly vertical gradient.
4. The device for calculating the influence of sea surface gravity data measurement accuracy on the submarine topography inversion result according to claim 2, 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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| CN113109883B (en) * | 2021-05-26 | 2023-01-03 | 湖南科技大学 | Method for forward modeling satellite gravity field based on isoparametric transformation global discrete grid spherical coordinates |
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| CN112965124A (en) * | 2021-02-08 | 2021-06-15 | 中国人民解放军92859部队 | Method for calculating abnormal vertical gradient of external gravity by considering local guarantee conditions |
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