Seabed sulfide natural potential inversion imaging method based on physical information constraint neural network

Abstract

The invention relates to the technical field of electrical variable measurement, in particular to a submarine sulfide natural potential inversion imaging method based on a physical information constraint neural network, and the method comprises the steps: constructing a natural potential inversion algorithm based on the constraint of the physical information neural network; obtaining topographic data of the target area, and constructing a geologic model; acquiring natural potential data measured by the electric field sensor in the target area; performing inversion imaging on the seabed sulfide based on the topographic data, the resistivity model and the natural potential data; obtaining the volume, the position and the current density distribution of the submarine sulfide based on inversion imaging; and based on the volume, the position and the current distribution of the seabed sulfide, evaluating the mining value and the mining scheme. According to the invention, through a deep learning method, physical driving and data driving are combined as a common constraint term to achieve the purpose of high-precision inversion imaging, so that precise exploration of deep sea sulfide resources of complex terrains is realized.

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

[0005] 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.

[0006] Further, in the self-potential inversion algorithm based on the physics-informed neural network, the mapping relationship between the spatial coordinate points, the self-potential, and the seabed current source density is realized by building a neural network. A loss function is established, and the neural network parameters are modified through an optimization algorithm to achieve inversion imaging.

[0007] Further, the neural network in the self-potential inversion algorithm based on the physics-informed neural network consists of a forward neural network and an inverse neural network. Specifically, the neural network inputs geographical spatial coordinates, topographic data, and a water-rock two-layer resistivity model, and the outputs of the two networks are respectively the electric potential generated by the redox reaction of the seabed sulfide and the seabed current source body density .

[0008] Further, the forward neural network uses 4 hidden layers, with 32 neurons in each hidden layer, and the Tanh activation function is used between each layer; the inverse neural network uses 2 hidden layers, with 16 neurons in each hidden layer, and the Tanh activation function is used between each layer; the input layer of both the forward and inverse neural networks has 1-channel input, and the output layer has 1-channel output.

[0009] Further, the input and output of each layer of neurons satisfy a linear transformation:

[0010]

[0011] where 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, is the output of this layer.

[0012] Further, the loss function in the self-potential inversion algorithm based on the physics-informed neural network includes: The physical-driven self-potential control equation constraint term: Its physical loss function term is:

[0013] where:

[0014] In the formula is the number of spatial points participating in the physical term loss function, is the Laplace operator, is the resistivity model value input at the coordinate point, is the predicted spontaneous potential value output by the forward neural network, is the current source density value output by the inverse neural network.

[0015] Furthermore, it also includes: The loss term of the observed data in the target area driven by data , where:

[0016] is the number of observation points on the survey line, is the obtained spontaneous potential data; The boundary loss term satisfies:

[0017] is the predicted value of the spontaneous potential at each point at the boundary.

[0018] Furthermore, the total loss function of the inverse imaging method :

[0019] where , , are the balance factors of the physical constraint term, the observed data constraint term, and the boundary constraint term respectively.

[0020] Specifically: The balance factors of each item in the total loss function control the inversion accuracy by controlling the proportion of each loss term.

[0021] Furthermore, the natural potential inversion algorithm based on the physics-informed neural network also includes: Selection of the optimization algorithm: mainly the Adam optimization algorithm, the L-BFGS optimization algorithm, and the joint optimization of Adam and L-BFGS; Selection of the learning rate: The learning rate controls how much (or how fast, what step size) the model parameters are adjusted in each step of parameter update. The main learning rate used is in the interval; Selection of the spatial points participating in the neural network operation in each iteration: A certain number of spatial coordinate points are randomly selected within the research area.

[0022] Furthermore, the terrain data of the target area is obtained and a geological model is constructed, where it includes: Create a three-dimensional spatial coordinate point set according to the regional range of the terrain data as the input of the neural network; Create a three-dimensional resistivity model according to the regional range of the terrain data, with an aquifer above the terrain and a rock layer below the terrain; Normalize the three-dimensional spatial coordinate points, three-dimensional resistivity model, and terrain data:

[0023] Among them is the spatial coordinate point of each dimension, X is the set of spatial coordinate points of each dimension, is the normalized spatial coordinate point of each dimension, and the value range satisfies .

[0024] Furthermore, based on the terrain data, resistivity model, and spontaneous potential data, perform inversion imaging. Specifically: Flatten the normalized spatial coordinate points of each dimension into a one-dimensional array, flatten the terrain data into a one-dimensional array, and flatten the resistivity model into a one-dimensional array and input them into the inversion algorithm; Regulate the inversion speed and inversion accuracy by changing various balance factors, learning rates, and the number of training points; Finally, the inversion algorithm outputs the trained neural network, the curves of various loss values changing with the number of iterations, the predicted spontaneous potential values, the predicted positions of underground current sources, and the current density distribution.

[0025] The technical solution of the present invention has at least the following advantages and beneficial effects: The present invention provides a spontaneous potential inversion algorithm based on a physics-informed neural network, which mainly uses the deep learning method, combines physical driving and data driving as common constraint terms to achieve the purpose of high-precision inversion imaging, and then realizes the precise exploration of deep-sea sulfide resources in complex terrain. In the inversion algorithm designed by the present invention, since coordinate points are selected in space and complex grid meshing is not required at the seabed interface, in addition, the observation data for controlling 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 problems that in the existing inversion imaging methods based on grid meshing and data driving, the grid meshing accuracy of complex terrain seriously affects the inversion accuracy, and the scarce observation data set also severely restricts the inversion imaging quality. Description of the Drawings

[0026] Figure 1 is a structural schematic diagram of the spontaneous potential inversion imaging method of the present invention; Figure 2 is a neural network architecture diagram in the spontaneous potential inversion imaging method of the present invention; Figure 3 is a schematic diagram of the 2D inversion result in the embodiment of the present invention; among them, a is a seabed current source model diagram, b is an inversion diagram of the seabed current source distribution, c is a spontaneous potential inversion diagram, d is a forward simulation diagram of the spontaneous potential, e is a comparison diagram of the observation data and the inversion data at the observation line, and f is an inversion loss curve diagram; Figure 4 Schematic diagram of the geological model for 3D inversion imaging in the embodiment of the present invention; Figure 5 3D inversion result diagram in the embodiment of the present invention; wherein, a is the schematic diagram of the 3D inversion structure, and b is the comparison diagram of the observed data and the inversion result at the observed survey line. Detailed implementation manners

[0027] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] Embodiment Please refer to Figures 1 - 5 simultaneously. The present invention provides a natural potential inversion imaging method for submarine sulfides based on a physics-informed neural network, including: Construct a natural potential inversion algorithm based on a physics-informed neural network; The natural potential control equation of its physics-informed constraint term is:

[0029] is the electric potential generated by the oxidation-reduction reaction of submarine sulfides, are the conductivities of the formation and seawater, is the volume density of the submarine current source; Obtain the terrain data of the target area and construct a geological model; Obtain the natural potential data measured by the electric field sensors in the target area; Based on the terrain data, resistivity model and natural potential data, perform inversion imaging; Based on the inversion imaging, obtain the position, volume and current density distribution of submarine sulfides; Based on the volume, position and current density distribution of submarine sulfides, evaluate its mining value and mining plan.

[0030] It should be noted that in this embodiment, a subsea sulfide inversion imaging method is established by building a neural network, combining physical drive and data drive as common constraint terms, and using the Adam optimization algorithm. After obtaining the terrain data of the target area, establishing a geological model and performing normalization processing, the position, volume, and current source density distribution of subsea sulfides are obtained using the inversion algorithm, providing technical support for realizing precise subsea exploration. In the inversion algorithm of the embodiment, since coordinate points are selected in space and complex grid meshing is not required at the subsea interface, in addition, the observation data for controlling the inversion quality is no longer dependent on the number of observation data but is controlled by the spatial distribution, solving the problems in the existing inversion imaging methods based on grid meshing and data drive, where the grid meshing accuracy of complex terrain seriously affects the inversion accuracy, and the scarce observation data set also severely restricts the inversion imaging quality.

[0031] It should be noted that in the natural potential control equation, is the electric potential generated by the redox reaction of subsea sulfides, and its unit is V; are the electrical conductivities of the formation and seawater, and their unit is S / m; is the subsea current source body density, and its unit is A / m 3 .

[0032] It should be noted that in this embodiment, by constructing spatial coordinate points and inputting them into the neural network, spatial points within the study area are randomly selected for calculation during the inversion iteration process, abandoning the grid meshing method of the existing differential technology, providing a new technical means for reducing computing resources and improving the inversion imaging quality of complex terrain. On the other hand, in this embodiment, by adding a physical law constraint term to the inversion constraint, the inversion imaging quality is no longer controlled by the observation data density, improving the inversion imaging quality in the case of sparse data sets.

[0033] Furthermore, the neural network in the natural potential inversion algorithm based on physics-informed neural network consists of a forward neural network and an inverse neural network as Figure 2 shown. Specifically: The neural network inputs geographical spatial coordinates, terrain data, and a water-rock two-layer resistivity model, and the outputs of the two networks are respectively the electric potential generated by the redox reaction of subsea sulfides and the subsea current source body density .

[0034] It should be noted that the neural network architecture of this case is as Figure 2 shown. In this case, the forward neural network uses 4 hidden layers, with 32 neurons in each hidden layer, and the Tanh activation function is used between each layer; the inverse neural network uses 2 hidden layers, with 16 neurons in each hidden layer, and the Tanh activation function is used between each layer. The input layer of both the forward and inverse neural networks is 1-channel input, and the output layer is 1-channel output.

[0035] It should be noted that the input and output of each layer of neurons satisfy a linear transformation:

[0036]

[0037] Among them, 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, is the output of this layer.

[0038] It should be noted that there is a non-linear neuron activation function operation between each layer of neural networks:

[0039] The Tanh activation function used in this case satisfies:

[0040] Furthermore, the loss function in the natural potential inversion algorithm based on the physics-informed neural network includes: The physical-driven natural potential control equation constraint term: Its physical loss function term is:

[0041] Among them:

[0042] In the formula is the number of spatial points participating in the physical term loss function, is the Laplace operator, is the resistivity model value input 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 inverse neural network.

[0043] It should be noted that in the above formula , , The three formulas are obtained based on the automatic differentiation technology in the deep learning framework PyTorch, and its principle is based on the chain rule: For a certain node , assuming its subsequent nodes are composed of in total ones, its derivative :

[0044] Among them, the second derivative can be obtained by the chain rule in the same way.

[0045] Furthermore, it further includes: The data-driven loss term of the observed data in the target area , where:

[0046] is the number of observation points on the survey line, is the obtained spontaneous potential data; The boundary loss term satisfies:

[0047] is the predicted value of the spontaneous potential at each point at the boundary.

[0048] Furthermore, the total loss function of the inversion imaging method :

[0049] where , , are the balance factors of the physical constraint term, the observed data constraint term, and the boundary constraint term, respectively.

[0050] Specifically: The balance factors of each item in the total loss function control the inversion accuracy by controlling the proportion of each loss term.

[0051] It should be noted that the observed data is the corrosion electric field in seawater collected during the actual observation process, specifically referring to the potential. In this case, it is obtained by the forward simulation of the neural network with physical information constraints, specifically as Figure 3 shown, Figure 3 In -a, it is a 2D seabed current source model, and the black line is the observation survey line, Figure 3 In -e, the blue solid line is the observed data value. The boundary loss term needs to input the spatial point positions at the boundary designed according to the target research area into the neural network, and make the output spontaneous potential at the boundary be 0.

[0052] It should be noted that the balance factors of each item control the "contribution degree" of each item of data in the inversion process. In this embodiment, , , are used. If the proportion of the observed data item is large, the inversion result will converge faster at the beginning. Appropriate values of the balance factors of each item will enable each item of data to play its role in the inversion process, accelerating the inversion speed and improving the inversion quality.

[0053] Furthermore, the natural potential inversion algorithm based on the physics-informed neural network further includes: Selection of optimization algorithms: mainly including Adam optimization algorithm, L-BFGS optimization algorithm, and combined optimization of Adam and L-BFGS; Selection of learning rate: The learning rate controls how much (or how fast, what step size) the model parameters are adjusted in each parameter update. The main learning rate used is in the interval; Selection of spatial points participating in the neural network operation in each iteration: A certain number of spatial coordinate points are randomly selected within the study area.

[0054] It should be noted that in this embodiment, only the Adam optimization algorithm is used for the optimizer. In practice, the combined optimization scheme of Adam and L-BFGS has higher efficiency and less error. The learning rate of this case is 0.001. The larger the learning rate, the faster the loss function converges, but the more unstable the inversion process; the smaller the learning rate, the slower the loss function converges, and the more stable the inversion process.

[0055] It is worth noting that so far, the natural potential inversion algorithm based on the physics-informed neural network has been constructed.

[0056] Furthermore, for obtaining the terrain data of the target area and constructing a geological model, it includes: Creating a three-dimensional spatial coordinate point set according to the regional scope of the terrain data as the input of the neural network; Creating a three-dimensional resistivity model according to the regional scope of the terrain data, with an aqueous layer above the terrain and a rock layer below the terrain; Performing normalization processing on the three-dimensional spatial coordinate point set, the three-dimensional resistivity model, and the terrain data:

[0057] where is the spatial coordinate point of each dimension, X is the spatial coordinate point set of each dimension, is the normalized spatial coordinate point of each dimension, and the value range satisfies .

[0058] Furthermore, for performing inversion imaging based on the terrain data, resistivity model, and natural potential data, specifically: Flattening the normalized spatial coordinate points of each dimension into a one-dimensional array, flattening the terrain data into a one-dimensional array, and flattening the resistivity model into a one-dimensional array and inputting them into the inversion algorithm; Adjusting the inversion speed and inversion accuracy by changing various balance factors, learning rate, and number of training points; Finally, the inversion algorithm outputs the trained neural network, the curves of various loss values changing with the number of iterations, the predicted spontaneous potential values, the predicted positions of underground current sources, and the current density distribution.

[0059] It should be noted that the spontaneous potential inversion algorithm based on the physics-informed neural network of the present invention is applicable to 2D and 3D cases. In the 3D case, the obtained terrain data needs to be meshed. During the inversion process, increasing the quantity and density of encrypted observation data will not bring a qualitative leap to the inversion imaging quality. Only a small number of data points are required to be obtained around the spontaneous potential anomaly area to obtain a high imaging quality.

[0060] Optionally, the model complexity is increased by increasing the number of neural network layers and neurons, thereby improving the fitting degree of the inversion model and ultimately improving the inversion accuracy.

[0061] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A natural potential inversion imaging method for submarine sulfides based on a physics-informed neural network, characterized in that, Including: Construct a spontaneous potential inversion algorithm based on a physics-informed neural network; The governing equation of the spontaneous potential for its physics-informed constraint term is: ； In the formula, is the electric potential generated by the redox reaction of submarine sulfides, is the conductivity of the formation and seawater, is the volume density of the submarine current source; Obtain the terrain data of the target area and construct a geological model; Obtain the spontaneous potential data measured by the electric field sensors in the target area; Based on the terrain data, resistivity model, and spontaneous potential data, perform inversion imaging; Based on the inversion imaging, obtain the position, volume, and current density distribution of submarine sulfides; Based on the volume, position, and current density distribution of submarine sulfides, evaluate their mining value and mining plan.

2. The inversion imaging method according to claim 1, wherein In the above-mentioned spontaneous potential inversion algorithm based on a physics-informed neural network, the mapping relationship between spatial coordinate points, spontaneous potential, and submarine current source density is realized by building a neural network, 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, wherein, The neural network consists of two neural networks, a forward neural network and an inverse neural network. The neural network takes geospatial coordinates, topographic data, and a two-layer resistivity model of water and rock as inputs, and the outputs of the two networks are respectively the electric potential generated by the redox reaction of submarine sulfides and the density of the submarine current source .

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

5. The inversion imaging method according to claim 4, wherein The input and output of neurons in each layer satisfy a linear transformation: ； ； Among them, 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, is the output of this layer.

6. The inversion imaging method according to claim 1, wherein In the loss term of the above-mentioned inversion algorithm, a constraint term of the physics-driven governing equation of the spontaneous potential is added. Specifically: Its physical loss function term is as follows: ； Where: ； In the formula, is the number of spatial points participating in the physical term loss function, is the Laplace operator, is the resistivity model value input at the coordinate point, is the predicted spontaneous 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 above-mentioned inversion algorithm also includes: Data-driven target area observation data loss term , where: ； In the formula, is the number of observation points on the survey line, is the obtained spontaneous potential data; Boundary loss term Satisfy: ； is the predicted value of spontaneous potential at each point at the boundary.

8. The inversion imaging method according to claim 7, wherein Total loss function : ； In the formula, , , are the balance factors of each item; The balance factors of each term in the total loss function control the inversion accuracy by controlling the proportion of each loss term.

9. The inversion imaging method according to claim 1, wherein The above-mentioned obtaining the terrain data of the target area and constructing a geological model includes: Create a three-dimensional spatial coordinate point set according to the regional scope of the terrain data as the input of the neural network; Create a three-dimensional resistivity model according to the regional scope of the terrain data, with an aqueous layer above the terrain and a rock layer below the terrain; Perform normalization processing on the three-dimensional spatial coordinate point set, three-dimensional resistivity model, and terrain data: ； Among them, are the coordinate points in each dimension space, and X is the set of coordinate points in each dimension space, are the normalized coordinate points in each dimension space, and the value range satisfies .

10. The inversion imaging method according to claim 1, characterized in that, The above-mentioned performing inversion imaging based on the terrain data, resistivity model, and spontaneous potential data includes: Flatten the normalized spatial coordinate points in each dimension into a one-dimensional array, flatten the terrain data into a one-dimensional array, and flatten the resistivity model into a one-dimensional array and input them into the inversion algorithm; Regulate the inversion speed and inversion accuracy by changing the balance factors, learning rate, and number of training points; Finally, the inversion algorithm outputs the trained neural network, the curve of the change of each loss value with the number of iterations, the predicted natural electric potential value, and the predicted underground current source position and current density distribution.

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