A method, system, device and medium for underground ore body conductivity inversion based on differentiable FDTD

Abstract

The application discloses a kind of underground ore body conductivity inversion method, system, equipment and medium based on differentiable FDTD.It is low in accuracy, large in computation, dependent on training sample and other problems in complex scene for existing inversion method, the conductivity parameter field to be inverted is directly embedded in the differentiable finite-difference time-domain (FDTD) time step forward updating chain, the measured response waveform is used as observation constraint to construct loss function, the gradient is back propagated along the differentiable FDTD calculation chain using automatic differentiation mechanism, the conductivity parameter field is iteratively updated to convergence, and the position range and equivalent conductivity of the underground ore body are output.The application does not need to construct sensitivity matrix or numerical differentiation to obtain gradient, does not need large-scale training sample, under the premise of maintaining electromagnetic propagation physical consistency, significantly reduces the calculation and storage overhead, improves the accuracy, efficiency and stability of underground ore body conductivity inversion in complex terrain, strong non-uniform medium and multi-anomaly body scene.

Description

Technical Field

[0001] This invention relates to the field of geophysical electromagnetic detection and parameter inversion technology, and in particular to a method for inverting the conductivity of underground ore bodies by combining differential finite-difference time-domain (FDTD) electromagnetic field numerical simulation with gradient optimization algorithms. This method can be used for the identification and parameter estimation of underground anomalies in transient electromagnetic detection (TEM), low-frequency electromagnetic detection, and other active electromagnetic detection systems. Background Technology

[0002] Transient electromagnetic exploration (TEM) is an important method for detecting underground electrical structures and identifying ore body anomalies. It uses a transmitting coil to apply a pulsed current to create a primary field, which is then induced by underground conductors upon shutdown to form a secondary field. The receiving system records the response of the secondary field as it decays over time, and uses this response to invert the underground conductivity distribution. Current ore body inversion typically employs a "forward-inversion" framework: the forward side often uses methods such as layered medium analytical approximation, integral equations, finite element method, finite difference method, or FDTD to calculate the electromagnetic response corresponding to different underground models; the inversion side mainly includes schemes such as rapid interpretation of apparent parameters, Occam inversion, LCI lateral constraint imaging, and two-dimensional / three-dimensional nonlinear least squares inversion. Two-dimensional / three-dimensional inversion often requires repeated calls to numerical forward modeling and the construction of Jacobian matrices, or the acquisition of gradients through numerical perturbation differencing, to achieve iterative model updates. With the development of deep learning methods, some studies have attempted to use neural networks to establish a mapping relationship between "response data and underground parameters" to improve the inversion speed. These methods are highly efficient in the inference phase, but they typically rely on large-scale training data and are prone to declining generalization ability when the measurement system, noise type, or geological conditions are inconsistent with the distribution of the training samples. Further, some schemes combine neural networks with physical models. For example, they use implicit neural networks to represent the conductivity model with spatial coordinates as input, then combine this with finite-difference forward modeling to calculate the theoretical response, and train the network parameters through a loss function to obtain the conductivity distribution of the subsurface medium. This type of method enhances physical constraints compared to purely data-driven networks, but its core is still to train neural network parameters to indirectly represent the conductivity model, and it is mostly geared towards magnetotelluric frequency domain or periodic domain data. Overall, existing schemes still face the challenge of balancing inversion accuracy, computational efficiency, and result stability in complex terrain, highly heterogeneous media, and multi-orebody scenarios.

[0003] Existing underground electromagnetic inversion methods have the following main shortcomings: One approach is based on apparent parameter interpretation, Occam inversion, or LCI lateral constraint imaging. These approaches are typically built on the assumption of layered media or weak lateral variation. In complex terrain, strongly non-uniform background media, and multiple anomaly scenarios, they are difficult to accurately characterize the electromagnetic response caused by underground ore bodies. This can easily lead to overly smoothed inversion results, anomaly location shifts, and false anomalies, making it difficult to reliably characterize the location range and equivalent conductivity of ore bodies.

[0004] Second, although two-dimensional and three-dimensional deterministic inversion methods can improve imaging accuracy, they usually require repeated electromagnetic forward modeling calculations and explicit construction of sensitivity matrices or the use of numerical difference to obtain gradients. This results in problems such as large computational load, high memory consumption, sensitivity to difference step size, and easy introduction of numerical noise, leading to slow convergence speed and insufficient stability of inversion iteration.

[0005] Third, although the fast inversion method based on deep learning has a fast inference speed, it is highly dependent on large-scale training data and lacks explicit physical constraints on the electromagnetic propagation process. When the instrument response characteristics, noise level or geological conditions are inconsistent with the distribution of training samples, the generalization ability is prone to decline and the inversion results deviate from the true physical laws.

[0006] Fourthly, there are physics-driven inversion methods that combine neural network representation with finite-difference forward modeling. Although these methods do not rely on large-scale labeled training datasets, they still require sufficient measured observation data to constrain the conductivity model represented by the network. Furthermore, the inversion results are significantly affected by the network structure, activation function, and regularization term settings. The main optimization target of this type of method is the parameters of the implicit neural network, and it is primarily geared towards magnetotelluric frequency / period domain data.

[0007] In summary, existing technologies struggle to balance the accuracy, efficiency, and stability of conductivity inversion in underground ore bodies under complex scenarios while ensuring the physical consistency of electromagnetic propagation. Summary of the Invention

[0008] This invention aims to address the problems of low accuracy, high computational cost, difficulty in explicitly constructing the sensitivity matrix, and poor generalization ability resulting from reliance on large-scale training samples in existing underground ore body conductivity inversion methods under complex terrain and highly inhomogeneous media scenarios. To this end, this invention provides a method, system, device, and medium for underground ore body conductivity inversion based on differentiable finite difference time-domain (FDTD). By directly embedding the conductivity parameter field to be inverted into the forward update chain of a differentiable finite difference time-domain (FDTD) time step, using the measured response waveform as an observation constraint to construct the loss function, and utilizing an automatic differentiation mechanism to propagate the gradient backward along the differentiable FDTD computation chain, stable iterative updates of the conductivity parameter field are achieved. This invention, while maintaining the physical consistency of electromagnetic propagation, eliminates the need for explicit construction of the sensitivity matrix or numerical difference gradient calculation, significantly reducing computational and storage overhead and improving the accuracy, efficiency, and stability of underground ore body conductivity inversion in complex scenarios.

[0009] According to one aspect of the present invention, a method for inverting the conductivity of underground ore bodies based on differentiable FDTD is provided, comprising: Step 1: Based on the detection area information and the parameters of the transmitting and receiving systems, construct a differentiable finite difference time-domain FDTD inversion model, and set the calculation parameters, source terms, and receiver location and observation definitions of the model; Step 2: Establish an initial conductivity parameter field and map it onto the grid of the differentiable FDTD inversion model as the conductivity parameter field to be inverted; Step 3: Input the conductivity parameter field to be inverted into the differentiable FDTD inversion model, execute the differentiable FDTD time step forward update chain, and obtain the predicted response waveform under the current conductivity parameter field; Step 4: Using the measured response waveform as observation constraint data, construct the loss function between the predicted response waveform and the measured response waveform; Step 5: Using the automatic differentiation mechanism, backpropagate the gradient of the loss function along the forward update chain of the differentiable FDTD time step, and calculate the gradient of the loss function with respect to the conductivity parameter field to be inverted; Step 6: Based on the calculated gradient, the conductivity parameter field to be inverted is iteratively updated using the gradient optimization method; Step 7: Repeat steps 3 to 6 until the loss function converges, and output the final inverted conductivity parameter field to characterize the location range and equivalent conductivity of the underground ore body.

[0010] As a further technical solution, the process of constructing the loss function in step 4 includes: introducing a time window mask function to construct a weighted data error term, and combining it with a regularization term applied to the conductivity parameter field to be inverted, together forming the loss function.

[0011] As a further technical solution, the electromagnetic field discrete update process in the differentiable FDTD time-step forward update chain has update coefficients determined by local dielectric parameters and time step size. The local dielectric parameters include at least the conductivity parameter field to be inverted, relative permittivity, relative permeability and loss parameters, so that each time step update of the electromagnetic field is differentiable from the conductivity parameter field to be inverted.

[0012] As a further technical solution, the computational domain periphery of the differentiable FDTD inversion model adopts a fully matched convolutional layer CPML as an absorbing boundary condition.

[0013] As a further technical solution, the conductivity parameter field to be inverted is subject to non-negative constraints and preset upper and lower bound constraints during the iterative update process.

[0014] According to one aspect of the present invention, a system for inverting the conductivity of underground ore bodies based on differentiable FDTD is provided, comprising: The model building module is used to construct a differentiable finite difference time-domain FDTD inversion model based on the detection area information and the parameters of the transmitting and receiving systems, and to set the calculation parameters, source terms, and receiver location and observation definitions of the model. The parameter field initialization module is used to establish an initial conductivity parameter field and map it onto the grid of the differentiable FDTD inversion model as the conductivity parameter field to be inverted. The forward calculation module is used to input the conductivity parameter field to be inverted into the differentiable FDTD inversion model, execute the differentiable FDTD time step forward update chain, and obtain the predicted response waveform under the current conductivity parameter field. The loss function construction module is used to construct the loss function between the predicted response waveform and the measured response waveform using the measured response waveform as observation constraint data. The gradient calculation module is used to use an automatic differentiation mechanism to backpropagate the gradient of the loss function along the forward update chain of the differentiable FDTD time step, and calculate the gradient of the loss function with respect to the conductivity parameter field to be inverted. The parameter update module is used to iteratively update the conductivity parameter field to be inverted based on the calculated gradient using a gradient optimization method. The iteration and output module is used to control the forward calculation module, loss function construction module, gradient calculation module and parameter update module to perform iterative operations until the loss function converges and outputs the finally inverted conductivity parameter field.

[0015] According to one aspect of the present invention, an electromagnetic detection system for underground ore bodies based on differentiable FDTD is provided, comprising: A transmitting device used to project transient electromagnetic fields underground; A receiving device used to acquire measured response waveforms generated by induction in underground ore bodies; A computing processing device is connected to the transmitting device and the receiving device respectively. The computing processing device includes a memory and a processor. When the processor executes the computer program stored in the memory, it implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD as described in any one of claims 1 to 5, and outputs the location range and equivalent conductivity of the underground ore body according to the inversion result.

[0016] According to one aspect of the present invention, a device for calculating the conductivity inversion of underground ore bodies based on differentiable FDTD is provided, comprising: Memory, used to store computer programs; A processor, when executing the computer program, implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD as described in any one of claims 1 to 5.

[0017] According to one aspect of the present invention, a computer-readable storage medium for inverting the conductivity of underground ore bodies based on differentiable FDTD is provided, wherein a computer program is stored thereon, which, when executed by a processor, implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD.

[0018] As a further technical solution, the computing processing device is also used to preprocess the measured response waveform acquired by the receiving device. The preprocessing includes time alignment, resampling and interpolation operations, so that the preprocessed measured response waveform is consistent with the output of the differentiable FDTD inversion model in terms of sampling time and observation definition.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: First, there is no need to pre-build a large-scale forward response library or labeled training dataset. This invention directly uses the underground conductivity parameter field as the object to be optimized and embeds it into a differentiable FDTD time-step forward update chain. It uses measured electromagnetic field data as observation constraints and achieves gradient backpropagation and iterative updates through an automatic differentiation mechanism. Therefore, it does not rely on large-scale training samples or pre-generated forward response libraries, avoiding the problem of decreased generalization ability caused by inconsistent training sample distribution in data-driven methods.

[0020] Second, it avoids explicitly constructing the sensitivity matrix or using numerical differencing to calculate the gradient. This invention constructs the FDTD time-step update process, receiver response extraction process, and loss function calculation process as a differentiable computational chain. It utilizes an automatic differentiation mechanism to directly backpropagate from the loss function to the conductivity parameter field, eliminating the need for explicit Jacobian matrix calculation or numerical perturbation differencing. This significantly reduces the computational and memory overhead of traditional two-dimensional / three-dimensional deterministic inversion methods, eliminates sensitivity to differencing step size and the introduction of numerical noise, and improves the convergence speed and stability of the inversion iteration.

[0021] Third, it reduces the dependence on network structure, activation function, and prior samples. Unlike physical-driven inversion methods that indirectly characterize conductivity models through neural network parameters, this invention directly uses the conductivity parameter field as an optimizable variable. It does not require the design of specific network structures or activation functions, making the inversion results more interpretable. Furthermore, while maintaining the physical consistency of electromagnetic propagation, it can adapt to complex terrain, strongly non-uniform background media, and multiple anomaly conditions in active-source transient electromagnetic scenarios.

[0022] Fourth, stable inversion of the location range and equivalent conductivity of underground ore bodies was achieved. By constructing a coupling mechanism between a differentiable FDTD time-step forward update chain and an automatic differential reverse gradient backpropagation chain, the predicted response waveform gradually approximates the measured response waveform, and finally outputs the equivalent location range and equivalent conductivity parameters of the underground ore body. This approach balances accuracy, efficiency, and stability in inversion under complex exploration scenarios. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A schematic flowchart of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD provided in an embodiment of the present invention; Figure 2 A schematic diagram illustrating the principle of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD, as provided in this embodiment of the invention. Figure 3 This is a schematic diagram of the inversion model provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the inversion results provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the loss function change curve during the inversion training process provided in an embodiment of the present invention. Detailed Implementation

[0025] The technical problem to be solved by this application is to provide a method for inverting the conductivity of underground ore bodies based on differentiable FDTD. Under the premise of ensuring the physical consistency of the electromagnetic propagation process, this method can realize the stable gradient back-transmission and iterative update of the underground conductivity parameter field by the measured electromagnetic response. This reduces the computational and storage overhead caused by the explicit construction of the sensitivity matrix or the numerical difference gradient calculation in traditional two-dimensional and three-dimensional inversion, and improves the accuracy, efficiency and stability of underground ore body conductivity inversion in complex terrain, strongly non-uniform background media and multi-anomaly scenarios.

[0026] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0028] This invention provides a method for inverting the conductivity of underground ore bodies based on differentiable FDTD, such as... Figure 1 and Figure 2 As shown, it includes the following steps.

[0029] Step 1: Construct a differentiable FDTD inversion model

[0030] Based on the detection area information and the parameters of the transmitting and receiving systems, a differentiable finite-difference time-domain (FDTD) inversion model is constructed. Specifically, the model's computational parameters are set, including the computational domain range and grid size, the type and parameters of the absorbing boundary layer, the time step, and the computation window. In this embodiment, a fully matched convolutional layer (CPML) is used as the absorbing boundary condition around the computational domain to simulate the propagation of electromagnetic waves in an infinite space. Simultaneously, the model's source terms are set according to the measured transmitter parameters, including the transmitted current waveform I(t) (or equivalent magnetic moment), source location, coil size and number of turns, and its equivalent injection method in the FDTD; the receiver location and observation definitions (e.g., electric field components, magnetic field components, induced voltage, or dB / dt response at the receiver point) are set according to the receiving system information.

[0031] Step 2: Establish the initial conductivity parameter field

[0032] By combining regional lithology and empirical electrical property ranges, an initial background conductivity model is established and mapped onto the grid of the differentiable FDTD inversion model to form the conductivity parameter field to be inverted. (x,z) (taking a two-dimensional xz-plane TM model as an example). During the inversion process, the conductivity parameters are updated only within the inversion region, and non-negativity constraints and preset upper and lower bound constraints (e.g., ...) are applied to the conductivity parameter field to be inverted. min ≤ ≤ max This is to ensure the physical rationality of the inversion results.

[0033] Step 3: Forward calculation to obtain the predicted response waveform

[0034] The conductivity parameter field to be inverted is input into the differentiable FDTD inversion model, and a differentiable FDTD time-step forward update chain is executed. Taking the electromagnetic field update process in the two-dimensional xz-plane TM mode as an example, the field components to be updated include the electric field E. x E z and magnetic field H y At the same time, set auxiliary variables corresponding to the CPML absorption boundary. , , , Within each time step, first, based on the electric field at the current moment... , Calculate its discrete spatial curl components and update the magnetic field (half-time step). Then, calculate the discrete spatial curl components based on the half-time step magnetic field and update the electric field at the next time step. , (Integer time steps). Its discrete update relation can be expressed as:

[0035] (1) Magnetic field half-time step update: ,

[0036] in, and The magnetic field update coefficient is calculated from local medium parameters (such as relative permeability and magnetic loss parameters) and time step.

[0037] (2) Electric field integer time step update:

[0038] In obtaining Then, update the electric field component E. x E z : , Where J represents source term injection, , , , The electric field update coefficient is calculated from local dielectric parameters (such as conductivity and relative permittivity) and time step.

[0039] As can be seen from the discrete equations above, the changes in the underground conductivity parameter field will directly affect the field update results at each time step, and further affect the final predicted response.

[0040] Since the conductivity parameter in the updated coefficients is directly involved in the calculation, the field update result at each time step is differentiable from the conductivity parameter field to be inverted. After completing all time step iterations, the predicted response waveform d is extracted from the field quantity at the receiving point. sim (t).

[0041] Step 4: Construct the loss function

[0042] Before constructing the loss function, the measured received data is preprocessed, including time alignment (t0 or the off time), resampling / interpolation, and necessary data preprocessing, so that it is consistent with the model output in terms of sampling time and observation definition, and is used as observation constraint data input to the inversion model.

[0043] The measured response waveform d obs Using (t) as the observation constraint data, a loss function L is constructed between the predicted response waveform and the measured response waveform. To improve the inversion's focus on the effective time window and reduce the impact of noisy periods, this embodiment introduces a time window mask function M(t) to construct a weighted data error term, which, combined with a regularization term applied to the conductivity parameter field to be inverted, constitutes the loss function: , in, Here, λ is the regularization term for the conductivity parameter to be inverted, and λ is the regularization weight, using L2 form: , This is to suppress excessive increases in the parameters to be inverted and improve inversion stability. Where N is the total number of parameter units within the region to be inverted. This represents the conductivity parameter corresponding to the (i, j)th grid cell.

[0044] Step 5: Automatically differentiate and calculate the gradient

[0045] Since the aforementioned FDTD time step update process, receiver response extraction process, and loss function calculation process are all constructed as differentiable computational chains, the gradient of the loss function with respect to the conductivity parameter field to be inverted is calculated by using an automatic differentiation mechanism, starting from the loss function L, through the predicted response waveform, receiver field quantity extraction, FDTD time step update chain, and update coefficients, and then backpropagating layer by layer: .

[0046] Step 6: Iteratively update the conductivity parameter field

[0047] Based on the calculated gradient, the conductivity parameter field to be inverted is updated using gradient optimization methods (such as Adam, SGD, etc.): , in, and Let represent the conductivity parameter field in the k-th and k+1-th iterations, and η be the learning rate. During the update process, nonnegativity constraints and upper and lower bound constraints are applied simultaneously to ensure that the parameters are always within a physically reasonable range.

[0048] Through the aforementioned forward field update, predicted response extraction, loss construction, automatic differential gradient backpropagation, and parameter update processes, the predicted response waveform gradually approximates the measured received response waveform, thereby realizing the inversion of the equivalent location range and equivalent conductivity parameters of the underground ore body.

[0049] Step 7: Iterative Convergence and Output Results

[0050] Repeat steps 3 to 6 until the loss function L converges (e.g., the change in loss between two adjacent iterations is less than a preset threshold), and output the final inverted conductivity parameter field, which directly characterizes the equivalent location range and equivalent conductivity of the underground ore body.

[0051] To verify the effectiveness of the underground ore body conductivity inversion method based on differentiable FDTD described in this invention, a two-dimensional xz-plane simulation model can be constructed. The simulation region is set to 600m × 300m, with a horizontal length of 600m and a vertical depth of 300m. The spatial grid size is set to Δx = Δz = 6m, corresponding to 100 horizontal grids and 50 vertical grids. A CPML absorbing boundary layer is set at the boundary of the computational region to reduce the influence of boundary reflection on the received response.

[0052] Based on the stability condition of the two-dimensional FDTD, the time step is taken as... The emission source uses a transient electromagnetic emission current waveform I(t) or an equivalent magnetic moment source, with a turn-off time of 50 μs and a total calculation time window of 600 μs, corresponding to approximately 60,000 time steps.

[0053] The underground model can be preset with background conductivity. and high conductivity anomalies Simulated observation response waveforms are generated through theoretical models or numerical forward modeling. The response is then used as an observation constraint input to a differentiable FDTD inversion model to verify its ability to recover the location range and equivalent conductivity parameters of underground ore bodies.

[0054] Figure 3 and Figure 4 The inversion results are displayed in logarithmic form of resistivity, where resistivity and conductivity are reciprocals of each other. Therefore, this display method is equivalent to reflecting the spatial variation of the underground conductivity parameter field.

[0055] like Figure 3 As shown, a uniform background resistivity model is set up within the two-dimensional xz plane calculation region, and three electrical anomalies are placed in the shallow region. The left and right sides are high resistivity anomalies, and the middle is a low resistivity anomaly, used to simulate anomalies with different electrical characteristics underground. The color scale uses log10(ρ) to represent the logarithmic value of resistivity, with red areas representing relatively high resistivity anomalies, blue areas representing relatively low resistivity anomalies, and green areas representing the background medium.

[0056] like Figure 4As shown, after inversion, the approximate horizontal location, burial depth range, and high / low resistivity anomaly characteristics of the three anomalies can all be recovered. Compared with the real model, the boundaries of the anomalies in the inversion results exhibit a certain degree of smooth transition, and a blurred response diffuses into the depth below the anomalies. This is due to the inherent diffusion, limited resolution, and regularization constraints of the electromagnetic inversion problem itself. These results demonstrate that the underground ore body conductivity inversion method based on differentiable FDTD described in this invention can recover the approximate location range and equivalent resistivity characteristics of underground anomalies under observation response constraints, and is suitable for the identification and parameter estimation of underground ore bodies or electrical anomalies.

[0057] Figure 5 The figure shows the loss function variation curve during the inversion training process. As can be seen from the figure, with the increase of the number of iterations, the loss value decreases rapidly from an initial large value, and the error is significantly reduced in the early iteration stage. Subsequently, the rate of loss decrease gradually slows down and approaches stability after about 100 iterations, indicating that the difference between the predicted response waveform and the observed response waveform gradually decreases, and the inversion process reaches a convergent state. This result shows that the differentiable FDTD inversion model described in this invention can obtain an effective gradient through automatic differentiation and drive the iterative update of the underground conductivity parameter field, thereby achieving stable inversion under the constraint of observed response.

[0058] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a system for inverting the conductivity of underground ore bodies based on differentiable FDTD, used to perform the methods described in the above embodiments. This system includes the following functional modules: Model building module: Used to build a differentiable finite difference time-domain FDTD inversion model based on the detection area information and the parameters of the transmitting and receiving systems, and to set the model's calculation parameters, source terms, and the location of the receiving point and the definition of the observations.

[0059] Parameter field initialization module: used to establish an initial conductivity parameter field and map it onto the grid of the differentiable FDTD inversion model as the conductivity parameter field to be inverted.

[0060] Forward calculation module: used to input the conductivity parameter field to be inverted into the differentiable FDTD inversion model, execute the differentiable FDTD time step forward update chain, and obtain the predicted response waveform under the current conductivity parameter field.

[0061] The loss function construction module is used to construct a loss function between the predicted response waveform and the measured response waveform, using the measured response waveform as the observation constraint data. Specifically, a time window mask function is introduced to construct a weighted data error term, which, together with a regularization term applied to the conductivity parameter field to be inverted, constitutes the loss function.

[0062] Gradient calculation module: used to use an automatic differentiation mechanism to backpropagate the gradient of the loss function along the forward update chain of the differentiable FDTD time step, and calculate the gradient of the loss function with respect to the conductivity parameter field to be inverted.

[0063] Parameter update module: Iteratively updates the conductivity parameter field to be inverted based on the calculated gradient using gradient optimization method, and applies non-negativity constraints and preset upper and lower bound constraints during the update process.

[0064] Iteration and Output Module: This module controls the forward calculation module, loss function construction module, gradient calculation module, and parameter update module to perform iterative operations until the loss function converges, and outputs the final inverted conductivity parameter field.

[0065] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electromagnetic detection system for underground ore bodies based on differentiable FDTD, comprising: Transmitting device: Used to transmit transient electromagnetic fields underground. Specifically, the transmitting device can be a transmitting coil, which generates a primary field by applying a pulsed current.

[0066] Receiver: Used to acquire the measured response waveform generated by induction in underground ore bodies. The receiver can be a receiving coil or receiving electrodes, recording the response of the secondary field decaying over time.

[0067] Computational processing device: connected to the transmitting device and the receiving device respectively, the computational processing device includes a memory and a processor. When the processor executes the computer program stored in the memory, it implements the steps of the method embodiment of the underground ore body conductivity inversion method based on differentiable FDTD, and outputs the location range and equivalent conductivity of the underground ore body according to the inversion result.

[0068] Optionally, the computing processing device is further configured to preprocess the measured response waveform acquired by the receiving device. The preprocessing includes time alignment (aligning to the off time t0), resampling, and interpolation operations, so that the preprocessed measured response waveform is consistent with the output of the differentiable FDTD inversion model in terms of sampling time and observation definition.

[0069] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a device for calculating the conductivity inversion of underground ore bodies based on differentiable FDTD, comprising: Memory, used to store computer programs; The processor, when executing the computer program, implements the steps of the underground ore body conductivity inversion method based on differentiable FDTD described in the foregoing method embodiments.

[0070] The computing device can be a desktop computer, server, embedded computer, or GPU workstation, etc.

[0071] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a computer-readable storage medium for inverting the conductivity of underground ore bodies based on differentiable FDTD, wherein a computer program is stored thereon. When the computer program is executed by a processor, it implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD described in the foregoing method embodiments. The storage medium includes, but is not limited to, non-volatile storage media such as ROM, RAM, hard disk, optical disk, and USB flash drive.

[0072] In summary, the core of this invention lies in: realizing the inversion of the conductivity of underground ore bodies based on a differentiable FDTD update network. That is, under the constraint of measured electromagnetic field data, the conductivity parameter field to be inverted is directly embedded into the forward update chain of the differentiable FDTD time step and coupled with the automatic differential reverse gradient backpropagation chain to achieve stable iterative update of the underground conductivity, and finally output the location range and equivalent conductivity parameters of the underground ore body.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A microdifferentiable FDTD-based method for inversion of subsurface ore body conductivity, characterized in that, include: Step 1: Based on the detection area information and the parameters of the transmitting and receiving systems, construct a differentiable finite difference time-domain FDTD inversion model, and set the calculation parameters, source terms, and receiver location and observation definitions of the model; Step 2: Establish an initial conductivity parameter field and map it onto the grid of the differentiable FDTD inversion model as the conductivity parameter field to be inverted; Step 3: Input the conductivity parameter field to be inverted into the differentiable FDTD inversion model, execute the differentiable FDTD time step forward update chain, and obtain the predicted response waveform under the current conductivity parameter field; Step 4: Using the measured response waveform as observation constraint data, construct the loss function between the predicted response waveform and the measured response waveform; Step 5: Using the automatic differentiation mechanism, backpropagate the gradient of the loss function along the forward update chain of the differentiable FDTD time step, and calculate the gradient of the loss function with respect to the conductivity parameter field to be inverted; Step 6: Based on the calculated gradient, the conductivity parameter field to be inverted is iteratively updated using the gradient optimization method; Step 7: Repeat steps 3 to 6 until the loss function converges, and output the final inverted conductivity parameter field to characterize the location range and equivalent conductivity of the underground ore body.

2. The method for inverting the conductivity of underground ore bodies based on differentiable FDTD according to claim 1, characterized in that, The process of constructing the loss function in step 4 includes: introducing a time window mask function to construct a weighted data error term, and combining it with a regularization term applied to the conductivity parameter field to be inverted, which together constitute the loss function.

3. The method for inverting the conductivity of underground ore bodies based on differentiable FDTD according to claim 1, characterized in that, The electromagnetic field discrete update process in the differentiable FDTD time-step forward update chain has update coefficients determined by local dielectric parameters and time step size. The local dielectric parameters include at least the conductivity parameter field to be inverted, relative permittivity, relative permeability, and loss parameters, so that each time step update of the electromagnetic field is differentiable from the conductivity parameter field to be inverted.

4. The method for inverting the conductivity of underground ore bodies based on differentiable FDTD according to claim 1, characterized in that, The computational domain of the differentiable FDTD inversion model is surrounded by a fully matched convolutional layer (CPML) as an absorbing boundary condition.

5. The method for inverting the conductivity of underground ore bodies based on differentiable FDTD according to claim 1, characterized in that, During the iterative update process, the conductivity parameter field to be inverted is subject to non-negativity constraints and preset upper and lower bound constraints.

6. A system for inverting the conductivity of underground ore bodies based on differentiable FDTD, characterized in that, include: The model building module is used to construct a differentiable finite difference time-domain FDTD inversion model based on the detection area information and the parameters of the transmitting and receiving systems, and to set the calculation parameters, source terms, and receiver location and observation definitions of the model. The parameter field initialization module is used to establish an initial conductivity parameter field and map it onto the grid of the differentiable FDTD inversion model as the conductivity parameter field to be inverted. The forward calculation module is used to input the conductivity parameter field to be inverted into the differentiable FDTD inversion model, execute the differentiable FDTD time step forward update chain, and obtain the predicted response waveform under the current conductivity parameter field. The loss function construction module is used to construct the loss function between the predicted response waveform and the measured response waveform using the measured response waveform as observation constraint data. The gradient calculation module is used to use an automatic differentiation mechanism to backpropagate the gradient of the loss function along the forward update chain of the differentiable FDTD time step, and calculate the gradient of the loss function with respect to the conductivity parameter field to be inverted. The parameter update module is used to iteratively update the conductivity parameter field to be inverted based on the calculated gradient using a gradient optimization method. The iteration and output module is used to control the forward calculation module, loss function construction module, gradient calculation module and parameter update module to perform iterative operations until the loss function converges and outputs the finally inverted conductivity parameter field.

7. An electromagnetic detection system for underground ore bodies based on differentiable FDTD, characterized in that, include: A transmitting device used to project transient electromagnetic fields underground; A receiving device used to acquire measured response waveforms generated by induction in underground ore bodies; A computing processing device is connected to the transmitting device and the receiving device respectively. The computing processing device includes a memory and a processor. When the processor executes the computer program stored in the memory, it implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD as described in any one of claims 1 to 5, and outputs the location range and equivalent conductivity of the underground ore body according to the inversion result.

8. A calculation device for inverting the conductivity of underground ore bodies based on differentiable FDTD, characterized in that, include: Memory, used to store computer programs; A processor, when executing the computer program, implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD as described in any one of claims 1 to 5.

9. A computer-readable storage medium for inverting the conductivity of underground ore bodies based on differentiable FDTD, wherein a computer program is stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for inverting the conductivity of underground ore bodies based on differentiable FDTD as described in any one of claims 1 to 5.

10. The electromagnetic detection system for underground ore bodies based on differentiable FDTD according to claim 7, characterized in that, The computing processing device is also used to preprocess the measured response waveform acquired by the receiving device. The preprocessing includes time alignment, resampling and interpolation operations, so that the preprocessed measured response waveform is consistent with the output of the differentiable FDTD inversion model in terms of sampling time and observation definition.

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