A method for inversion imaging of seafloor sulfide spontaneous potential based on physical information constrained neural network

Abstract

The present invention relates to the technical field of measuring electrical variables, and in particular to a method for inverting the spontaneous potential of seabed sulfides based on a physical information constrained neural network. The method comprises: constructing a spontaneous potential inversion algorithm based on the constraints of a physical information neural network; obtaining topographic data of a target area and constructing a geological model; obtaining spontaneous potential data measured by an electric field sensor in the target area; performing inversion imaging on seabed sulfides based on the topographic data, the resistivity model, and the spontaneous potential data; obtaining the volume, position, and current density distribution of the seabed sulfides based on the inversion imaging; and evaluating the mining value and mining plan of the seabed sulfides based on the volume, position, and current distribution of the seabed sulfides. The present invention achieves the purpose of high-precision inversion imaging by combining physical drive and data drive as common constraints through a deep learning method, thereby realizing the precise exploration of deep-sea sulfide resources in complex terrain.

Description

Technical Field

[0001] The present invention relates to the technical field of measuring electrical variables, and in particular to a method for inverting and imaging the spontaneous potential of seabed sulfides based on a physical information constrained neural network. Background Art

[0002] Polymetallic sulfide deposits on mid-ocean ridges cross the interface and are exposed to different redox environments, which can cause natural polarization and generate natural potential anomalies. Mid-ocean ridge natural potential surveys are generally conducted in deepwater environments, where the terrain is complex and the data collection conditions are poor, resulting in data scarcity. In these complex environments and data scarcity, the use of natural potential methods to invert and image seafloor sulfides and determine their scale and location is of great significance for precise seafloor mining. In existing inversion imaging methods based on grid generation and data driving, the grid generation accuracy of complex terrain seriously affects the inversion accuracy, and the scarce observation data set also seriously restricts the inversion imaging quality. Summary of the Invention

[0003] The purpose of the present invention is to provide a natural potential inversion algorithm based on a physical information constrained neural network, which solves the problem that the existing grid-based inversion technology cannot effectively achieve high-precision inversion imaging of seabed sulfides under conditions of scarce observation data and complex terrain due to the high density of observation data required, complex terrain subdivision, and huge computing resources occupied.

[0004] The technical solution of the present invention:

[0005] The present invention provides a natural potential inversion algorithm based on a physical information constrained neural network, comprising:

[0006] Construct a natural potential inversion algorithm based on a physical information constrained neural network;

[0007] The natural potential control equation of its physical information constraint term is:

[0008]

[0009] is the potential generated by the redox reaction of seabed sulfides, is the electrical conductivity of the formation and seawater, is the density of the seabed current source;

[0010] Obtain topographic data of the target area and construct a geological model;

[0011] Obtaining the natural potential data measured by the electric field sensor in the target area;

[0012] Perform inversion imaging based on terrain data, resistivity models, and natural potential data;

[0013] Based on inversion imaging, the location, volume and current density distribution of seabed sulfides are obtained;

[0014] Based on the volume, location and current density distribution of seabed sulfides, their mining value and mining plan are evaluated.

[0015] Furthermore, in the natural potential inversion algorithm based on the physical information constrained neural network, a neural network is constructed to realize the mapping relationship between the spatial coordinate points and the natural potential and the seabed current source density, a loss function is established, and the neural network parameters are modified through the optimization algorithm to realize inversion imaging.

[0016] Furthermore, the neural network in the natural potential inversion algorithm based on physical information constrained neural network consists of two neural networks: forward modeling and inversion modeling. Specifically, the neural network inputs geospatial coordinates, topographic data and water-rock two-layer resistivity model, and the two networks output the potential generated by the redox reaction of seabed sulfides. and seabed current source density .

[0017] Furthermore, the forward network uses 4 hidden layers, each with 32 neurons, and the Tanh activation function is used between each layer; the inversion network uses 2 hidden layers, each with 16 neurons, and the Tanh activation function is used between each layer; the input layer of both the forward and inversion networks is 1-channel input, and the output layer is 1-channel output.

[0018] Furthermore, the input and output of each layer of neurons satisfy the linear transformation:

[0019]

[0020]

[0021] in, is the weight matrix, is the bias vector corresponding to this layer, is the output of the previous layer and also the input of this layer. Output of this layer.

[0022] Furthermore, the loss function in the spontaneous potential inversion algorithm based on the physical information constrained neural network includes:

[0023] Physically driven constraints governing the natural potential equation:

[0024] Its physical loss function for:

[0025]

[0026] in:

[0027]

[0028] In the formula is the number of spatial points participating in the physical term loss function, is the Laplace operator, for The resistivity model value entered at the coordinate point, is the predicted natural potential value output by the forward neural network, is the current source density value output by the inversion neural network.

[0029] Furthermore, it also includes:

[0030] Data-driven target region observation data loss term ,in:

[0031]

[0032] is the number of observation points along the survey line, The natural potential data obtained;

[0033] Boundary loss term satisfy:

[0034]

[0035] is the predicted value of the natural potential at each point on the boundary.

[0036] Furthermore, the total loss function of the inversion imaging method is :

[0037]

[0038] in 、 、 are the balance factors of physical constraints, observation data constraints, and boundary constraints respectively.

[0039] Specifically: The various balance factors in the total loss function control the inversion accuracy by controlling the proportion of each loss item.

[0040] Furthermore, the spontaneous potential inversion algorithm based on physical information constrained neural network also includes:

[0041] Selection of optimization algorithms: mainly Adam optimization algorithm, L-BFGS optimization algorithm, and Adam and L-BFGS combined optimization;

[0042] Choice of learning rate: The learning rate controls how much (or how fast, how big the step size) the model parameters are adjusted in each step of parameter update. The main learning rate used is within the interval;

[0043] Selection of spatial points participating in the neural network operation in each iteration: a certain number of spatial coordinate points are randomly selected in the study area.

[0044] Furthermore, the acquisition of topographic data of the target area and construction of a geological model include:

[0045] Create a three-dimensional space coordinate point set based on the regional range of the terrain data as the neural network input;

[0046] Create a three-dimensional resistivity model based on the regional extent of the terrain data, with the water layer above the terrain and the rock layer below the terrain;

[0047] Normalize the 3D spatial coordinate point set, 3D resistivity model and terrain data:

[0048]

[0049] in is the coordinate point of each dimensional space, X is the set of coordinate points of each dimensional space, is the normalized coordinate point of each dimensional space, and its value range satisfies .

[0050] Furthermore, the inversion imaging is performed based on the terrain data, resistivity model and spontaneous potential data, specifically:

[0051] The normalized spatial coordinate points of each dimension are flattened into a one-dimensional array, the terrain data is flattened into a one-dimensional array, and the resistivity model is flattened into a one-dimensional array and input into the inversion algorithm;

[0052] The inversion speed and accuracy can be adjusted by changing the balance factors, learning rate, and number of training points;

[0053] Finally, the inversion algorithm outputs the trained neural network, the curve of each loss value changing with the number of iterations, the predicted natural potential value, the predicted location of the underground current source, and the current density distribution.

[0054] The technical solution of the present invention has at least the following advantages and beneficial effects:

[0055] The present invention provides a natural potential inversion algorithm based on a physical information constrained neural network. It mainly achieves the purpose of high-precision inversion imaging by combining physical drive and data drive as common constraints through deep learning methods, thereby realizing accurate exploration of deep-sea sulfide resources in complex terrain. In the inversion algorithm designed by the present invention, due to the use of spatially selected coordinate points, there is no need for complex grid subdivision at the seabed interface. In addition, the observation data that controls the inversion quality no longer depends on the number of observation data but is controlled by the spatial distribution. Therefore, the inversion algorithm designed by the present invention effectively solves the problem that in the existing inversion imaging method based on grid subdivision and data drive, the grid subdivision accuracy of complex terrain seriously affects the inversion accuracy, and the scarce observation data set also seriously restricts the inversion imaging quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the structure of the spontaneous potential inversion imaging method of the present invention;

[0057] Figure 2 This is a diagram of the neural network architecture in the spontaneous potential inversion imaging method of the present invention;

[0058] Figure 3 Schematic diagram of 2D inversion results in an embodiment of the present invention; wherein a is a submarine current source model diagram, b is a submarine current source distribution inversion diagram, c is a spontaneous potential inversion diagram, d is a spontaneous potential forward simulation diagram, e is a comparison diagram of the observed data and the inversion data at the observation line, and f is an inversion loss curve diagram;

[0059] Figure 4 Schematic diagram of a geological model for 3D inversion imaging in an embodiment of the present invention;

[0060] Figure 5 3D inversion result diagram in an embodiment of the present invention; wherein, a is a schematic diagram of the 3D inversion structure, and b is a comparison diagram of the observation data and the inversion result at the observation line. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0062] Example

[0063] Please refer to Figure 1-Figure 5 The present invention provides a method for inversion imaging of seabed sulfide spontaneous potential based on a physical information constrained neural network, comprising:

[0064] Construct a natural potential inversion algorithm based on a physical information constrained neural network;

[0065] The natural potential control equation of its physical information constraint term is:

[0066]

[0067] is the potential generated by the redox reaction of seabed sulfides, is the conductivity of the formation and seawater, is the density of the seabed current source;

[0068] Obtain topographic data of the target area and construct a geological model;

[0069] Obtaining the natural potential data measured by the electric field sensor in the target area;

[0070] Perform inversion imaging based on terrain data, resistivity models, and natural potential data;

[0071] Based on inversion imaging, the location, volume and current density distribution of seabed sulfides are obtained;

[0072] Based on the volume, location and current density distribution of seabed sulfides, their mining value and mining plan are evaluated.

[0073] It is worth noting that this embodiment establishes a seabed sulfide inversion imaging method by building a neural network, combining physical drive and data drive as common constraints, and using the Adam optimization algorithm. After obtaining the topographic data of the target area, establishing a geological model and performing normalization processing, the inversion algorithm is used to obtain the position, volume and current source density distribution of seabed sulfides, providing technical support for achieving accurate seabed exploration. In the inversion algorithm of the embodiment, due to the use of spatially selected coordinate points, there is no need to perform complex grid subdivision at the seabed interface. In addition, the observation data that controls the inversion quality no longer depends on the number of observation data but is controlled by spatial distribution, which solves the problem that the grid subdivision accuracy of complex terrain seriously affects the inversion accuracy in the existing inversion imaging method based on grid subdivision and data drive, and the scarce observation data set also seriously restricts the inversion imaging quality.

[0074] It should be noted that in the natural potential control equation, The potential generated by the redox reaction of seabed sulfides, its unit is V; is the electrical conductivity of the formation and seawater, and its unit is S / m; is the density of the seabed current source, and its unit is A / m 3 .

[0075] It is worth noting that this embodiment constructs a neural network using spatial coordinate points as input, randomly selecting spatial points within the study area for computation during the inversion iteration process. This eliminates the existing gridding method of differential techniques, providing a new technical approach for reducing computing resources and improving the quality of complex terrain inversion imaging. Furthermore, by adding physical law constraints to the inversion constraints, this embodiment eliminates the dependence of inversion imaging quality on observation data density, improving inversion imaging quality even with sparse datasets.

[0076] Furthermore, the neural network in the spontaneous potential inversion algorithm based on physical information constrained neural network consists of two neural networks: forward and inverse. Figure 2 As shown, specifically: the neural network inputs geospatial coordinates, topographic data and water-rock two-layer resistivity model, and the two networks output the potential generated by the redox reaction of seabed sulfides and seabed current source density .

[0077] It should be noted that the neural network architecture of this case is as follows Figure 2 As shown in Figure 2, in this case, the forward network uses four hidden layers, each with 32 neurons, and a Tanh activation function between each layer; the inversion network uses two hidden layers, each with 16 neurons, and a Tanh activation function between each layer. The input layer of both the forward and inversion networks is single-channel input, and the output layer is single-channel output.

[0078] It should be noted that the input and output of each layer of neurons satisfy the linear transformation:

[0079]

[0080]

[0081] in, is the weight matrix, is the bias vector corresponding to this layer, is the output of the previous layer and also the input of this layer. Output of this layer.

[0082] It should be noted that each layer of the neural network undergoes a nonlinear neuron activation function operation:

[0083]

[0084] The Tanh activation function used in this case satisfies:

[0085]

[0086] Furthermore, the loss function in the spontaneous potential inversion algorithm based on the physical information constrained neural network includes:

[0087] Physically driven constraints governing the natural potential equation:

[0088] Its physical loss function for:

[0089]

[0090] in:

[0091]

[0092] In the formula is the number of spatial points participating in the physical term loss function, is the Laplace operator, for Resistivity model value entered at the coordinate point is the predicted natural potential value output by the forward neural network, is the current source density value output by the inversion neural network.

[0093] It should be noted that in the above formula 、 、 The three equations are obtained based on the automatic differentiation technology in the deep learning architecture PyTorch, and their principle is based on the chain rule:

[0094] For a certain node , assuming that its subsequent nodes are common , its derivative :

[0095]

[0096] The second-order derivative can be obtained by the chain rule.

[0097] Furthermore, it also includes:

[0098] Data-driven target region observation data loss term ,in:

[0099]

[0100] is the number of observation points along the survey line, The natural potential data obtained;

[0101] Boundary loss term satisfy:

[0102]

[0103] is the predicted value of the natural potential at each point on the boundary.

[0104] Furthermore, the total loss function of the inversion imaging method is :

[0105]

[0106] in 、 、 are the balance factors of physical constraints, observation data constraints, and boundary constraints respectively.

[0107] Specifically: The various balance factors in the total loss function control the inversion accuracy by controlling the proportion of each loss item.

[0108] It should be noted that the observation data is the corrosion electric field in seawater collected during the actual observation process, specifically the potential. In this case, it is obtained by using a neural network forward simulation constrained by physical information, as shown in the following example. Figure 3 As shown, Figure 3 -a is a 2D seabed current source model, and the black line is the observation line. Figure 3 The blue solid line in -e represents the observed data value. The boundary loss term needs to be input into the neural network based on the spatial points at the boundary of the target study area, so that the output natural potential at the boundary is set to 0.

[0109] It should be noted that each balance factor controls the “contribution degree” of each data in the inversion process. In this embodiment, 、 、 A large proportion of observation data will lead to faster convergence of the inversion results at the beginning. Appropriate values ​​of the balance factors will enable each data to play its role in the inversion process, thus accelerating the inversion speed and improving the inversion quality.

[0110] Furthermore, the spontaneous potential inversion algorithm based on physical information constrained neural network also includes:

[0111] Selection of optimization algorithms: mainly Adam optimization algorithm, L-BFGS optimization algorithm, and Adam and L-BFGS combined optimization;

[0112] Choice of learning rate: The learning rate controls how much (or how fast, how big the step size) the model parameters are adjusted in each step of parameter update. The main learning rate used is within the interval;

[0113] Selection of spatial points participating in the neural network operation in each iteration: a certain number of spatial coordinate points are randomly selected in the study area.

[0114] It should be noted that in this example, the optimizer only uses the Adam optimization algorithm. In practice, a combined optimization scheme of Adam and L-BFGS is more efficient and produces less error. The learning rate in this case is 0.001. A larger learning rate leads to faster convergence of the loss function, but also less stability in the inversion process. A smaller learning rate leads to slower convergence of the loss function and more stable inversion.

[0115] It is worth mentioning that the natural potential inversion algorithm based on physical information constrained neural network has been completed.

[0116] Furthermore, the acquisition of topographic data of the target area and construction of a geological model include:

[0117] Create a three-dimensional space coordinate point set based on the regional range of the terrain data as the neural network input;

[0118] Create a three-dimensional resistivity model based on the regional extent of the terrain data, with the water layer above the terrain and the rock layer below the terrain;

[0119] Normalize the 3D spatial coordinate point set, 3D resistivity model and terrain data:

[0120]

[0121] in is the coordinate point of each dimensional space, X is the set of coordinate points of each dimensional space, is the normalized coordinate point of each dimensional space, and its value range satisfies .

[0122] Furthermore, the inversion imaging is performed based on the terrain data, resistivity model and spontaneous potential data, specifically:

[0123] The normalized spatial coordinate points of each dimension are flattened into a one-dimensional array, the terrain data is flattened into a one-dimensional array, and the resistivity model is flattened into a one-dimensional array and input into the inversion algorithm;

[0124] The inversion speed and accuracy can be adjusted by changing the balance factors, learning rate, and number of training points;

[0125] Finally, the inversion algorithm outputs the trained neural network, the curve of each loss value changing with the number of iterations, the predicted natural potential value, the predicted location of the underground current source, and the current density distribution.

[0126] It's worth noting that the proposed spontaneous potential inversion algorithm, based on a physics-information-constrained neural network, is applicable to both 2D and 3D scenarios. In the 3D case, the acquired terrain data must be gridded. During the inversion process, increasing the number and density of observation data does not significantly improve the quality of the inversion image. Simply acquiring a small number of data points around the area of ​​spontaneous potential anomaly can yield high-quality images.

[0127] Optionally, the model complexity can be improved by increasing the number of neural network layers and neurons, thereby improving the fit of the inversion model and ultimately improving the inversion accuracy.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for inversion imaging of seabed sulfide spontaneous potential based on physical information constrained neural network, characterized in that: include: Construct a natural potential inversion algorithm based on a physical information constrained neural network; The natural potential control equation of its physical information constraint term is: ； Where, is the potential generated by the redox reaction of seabed sulfides, is the electrical conductivity of the formation and seawater, is the density of the seabed current source; Obtain topographic data of the target area and construct a geological model; Obtaining the natural potential data measured by the electric field sensor in the target area; Perform inversion imaging based on terrain data, resistivity models, and natural potential data; Based on inversion imaging, the location, volume and current density distribution of seabed sulfides are obtained; Based on the volume, location and current density distribution of seabed sulfides, their mining value and mining plan are evaluated.

2. The inversion imaging method according to claim 1, characterized in that: In the described natural potential inversion algorithm based on a physical information constrained neural network, a neural network is constructed to realize the mapping relationship between spatial coordinate points and natural potential and seabed current source density, a loss function is established, and the neural network parameters are modified through an optimization algorithm to achieve inversion imaging.

3. The inversion imaging method according to claim 2, characterized in that: The neural network consists of two neural networks, forward and inverse. The neural network inputs geospatial coordinates, topographic data and water-rock two-layer resistivity model. The two network outputs are the potential generated by the redox reaction of seabed sulfide. and seabed current source density .

4. The inversion imaging method according to claim 3, characterized in that: The forward network uses 4 hidden layers, each with 32 neurons, and the Tanh activation function is used between each layer; the inversion network uses 2 hidden layers, each with 16 neurons, and the Tanh activation function is used between each layer; the input layer of both the forward and inversion networks is 1-channel input, and the output layer is 1-channel output.

5. The inversion imaging method according to claim 4, characterized in that: The input and output of each layer of neurons satisfy the linear transformation: ； ； in, is the weight matrix, is the bias vector corresponding to this layer, is the output of the previous layer and also the input of this layer. Output of this layer.

6. The inversion imaging method according to claim 1, characterized in that: The loss term in the inversion algorithm is added with the constraint term of the physical driven natural potential control equation, specifically: Its physical loss function for: ； in: ； Where, is the number of spatial points participating in the physical term loss function, is the Laplace operator, for The resistivity model value entered at the coordinate point, is the predicted natural potential value output by the forward neural network, is the current source density value output by the inversion neural network.

7. The inversion imaging method according to claim 6, characterized in that: The loss function term in the inversion algorithm also includes: Data-driven target region observation data loss term ,in: ； Where, is the number of observation points along the survey line, The natural potential data obtained; Boundary loss term satisfy: ； is the predicted value of the natural potential at each point on the boundary.

8. The inversion imaging method according to claim 7, characterized in that: Total loss function : ； Where, 、 、 are the various balance factors; The various balance factors in the total loss function control the inversion accuracy by controlling the proportion of each loss item.

9. The inversion imaging method according to claim 1, characterized in that: The process of obtaining topographic data of the target area and constructing a geological model includes: Create a three-dimensional space coordinate point set based on the regional range of the terrain data as the neural network input; Create a three-dimensional resistivity model based on the regional extent of the terrain data, with the water layer above the terrain and the rock layer below the terrain; Normalize the 3D spatial coordinate point set, 3D resistivity model and terrain data: ； in, is the coordinate point of each dimensional space, X is the set of coordinate points of each dimensional space, is the normalized coordinate point of each dimensional space, and its value range satisfies .

10. The inversion imaging method according to claim 1, characterized in that: The inversion imaging based on terrain data, resistivity model and natural potential data includes: The normalized spatial coordinate points of each dimension are flattened into a one-dimensional array, the terrain data is flattened into a one-dimensional array, and the resistivity model is flattened into a one-dimensional array and input into the inversion algorithm; The inversion speed and accuracy can be adjusted by changing the balance factors, learning rate, and number of training points; Finally, the inversion algorithm outputs the trained neural network, the curve of each loss value changing with the number of iterations, the predicted natural potential value, the predicted location of the underground current source, and the current density distribution.

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