A background noise empirical green's function interpolation method based on a conditional diffusion model

Abstract

The present application relates to the technical field of underground structure detection, and discloses a background noise empirical Green function interpolation method based on a conditional diffusion model, which comprises the following steps: collecting empirical Green function signals between station pairs formed by all seismographs in a target area and position coordinates of all seismographs as a training data set; inputting the empirical Green function signal containing noise, position coordinates of two seismographs in a station and a current denoising step number into a denoising neural network; taking the original empirical Green function signal in the training data set as a training target, inputting corresponding position coordinates of any two target points without seismographs into the trained denoising neural network, and generating an interpolated empirical Green function signal between the two target points. The method is more accurate than a traditional empirical Green function signal interpolation algorithm, can replace real observation data to a certain extent in a scenario where the number of seismographs is insufficient, and improves the underground structure detection capability.

Description

Technical Field

[0001] This invention relates to the field of underground structure detection technology, specifically to a background noise empirical Green's function interpolation method based on a conditional diffusion model. Background Technology

[0002] Seismic background noise imaging is an important method for detecting underground structures and is now widely used in various scenarios such as groundwater monitoring, identification of underground seismogenic environments, and underground mineral exploration. Seismic background noise imaging relies on the extraction of the empirical Green's function (EGF) signal for background noise. By performing cross-correlation operations on noise signals recorded by two seismographs over a long period, the EGF between the stations can be extracted. The extracted EGF contains information on seismic surface wave propagation between the two stations, which can be used to determine the surface wave velocity below the station pair, thereby obtaining the elastic properties of different geological structures in the study area.

[0003] However, the imaging quality of background noise is affected by the number of seismometers deployed in the study area. An increase in the number of seismometers leads to more empirical Green's functions between station pairs, resulting in richer seismic surface wave information reflecting subsurface structures. However, due to limitations such as deployment costs and geological conditions, it is difficult to deploy a large number of seismometers to form a dense seismic array in any study area. Therefore, developing data interpolation algorithms to accurately infer the empirical Green's function between two points without deployed stations using known empirical Green's functions between station pairs holds promise for achieving high-precision subsurface detection at a lower cost.

[0004] However, accurately interpolating the empirical Green's function (ERF) signal for background noise presents certain challenges. Most traditional interpolation algorithms in seismology, such as predictive filtering (Spitz, 1991), rank decomposition (Oropeza and Sacchi, 2011), and domain transformation (Shang et al., 2017), are typically suitable for processing two-dimensional or three-dimensional seismic data. However, the ERF for background noise is a five-dimensional seismic data, determined by five variables: time, longitude, and latitude of the two stations. The aforementioned algorithms are difficult to directly apply to ERF interpolation. While the radial basis function method (Song et al., 2017) can be used for interpolating high-dimensional seismic data, it suffers from the drawback of smooth interpolation results, making it difficult to accurately recover the phase characteristics of different frequency components in the ERF signal. In recent years, with the development of artificial intelligence (AI) technology, various seismic data interpolation algorithms based on deep neural networks have been proposed, outperforming traditional algorithms (Mousavi et al., 2024). However, attempts to apply AI technology to interpolating high-dimensional data such as the ERF for background noise remain relatively few.

[0005] To more accurately recover the empirical Green's function signals of uncollected points, this invention proposes an empirical Green's function interpolation algorithm based on a conditional diffusion probability model. The algorithm embeds the coordinates of the station pairs as prior information into a deep neural network, guiding the network to progressively denoise from Gaussian random noise, thereby obtaining the empirical Green's function signals of the corresponding station pairs. This algorithm provides empirical Green's function interpolation results superior to traditional algorithms, accurately recovering the phase information of different frequency components in the signal and effectively improving the quality of underground structure detection based on seismic background noise methods. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a background noise empirical Green's function interpolation method based on a conditional diffusion model. This invention learns the empirical Green's function characteristics corresponding to different coordinate points using a conditional diffusion model, thereby solving for the posterior probability of the empirical Green's function corresponding to any two station coordinates. This enables empirical Green's function interpolation at points where no seismographs have been deployed, accurately recovering the phase information of different frequency components in unknown empirical Green's function signals, and helping to improve the detection effect of underground structures based on empirical Green's function signals.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] An empirical Green's function interpolation method for background noise based on a conditional diffusion model includes:

[0009] The empirical Green's function signals between every two seismograph pairs in the target area, as well as the location coordinates of all seismographs, are collected as the training dataset.

[0010] To add noise to the empirical Green's function signal in the training dataset, the noisy empirical Green's function signal, the position coordinates of two seismographs in the station, and the current denoising step number are input into the denoising neural network. Using the original empirical Green's function signal in the training dataset as the training target, the denoising neural network is trained by minimizing the difference between the noise predicted by the denoising neural network and the actual added noise, so that the denoising neural network learns to generate the posterior probability distribution of the corresponding empirical Green's function signal under the given position coordinates of any pair of stations.

[0011] For any two target points where no seismometers are deployed, the corresponding position coordinates are input into a trained denoising neural network. The denoising neural network starts with Gaussian noise and generates an interpolated empirical Green's function signal between the two target points through a multi-step iterative denoising process.

[0012] In one embodiment, adding noise to the empirical Green's function signal in the training dataset specifically includes:

[0013] Noise is gradually added to the original empirical Green's function signal:

[0014] ;

[0015] in, The empirical Green's function signal for the training dataset, It is an artificially defined constant at step t. The empirical Green's function signal after adding noise at step t. Represents the conditional probability distribution. Indicates a Gaussian distribution. Represents the identity matrix.

[0016] In one embodiment, the denoising neural network employs a U-net structure.

[0017] In one embodiment, the step of inputting the noisy empirical Green's function signal, the position coordinates of two seismometers at the station, and the current denoising step count into the denoising neural network specifically includes:

[0018] The position coordinates of the two seismographs are input into the station coordinate encoding network to obtain the station coordinate encoding vector;

[0019] The current denoising step number is input into the denoising step encoding network to obtain the denoising step encoding vector;

[0020] The noisy empirical Green's function signal is used as the input to the downsampling process of the U-net structure, and the station coordinate encoding vector and the denoising step encoding vector are embedded into the upsampling process of the U-net structure.

[0021] In one embodiment, the process of embedding the station coordinate encoding vector and the denoising step encoding vector into the upsampling process of the U-net structure specifically includes:

[0022] Let the station coordinate encoding vector output by the station coordinate encoding network be... The denoising step encoding vector output by the denoising step encoding network is The original upsampling feature map of the U-net structure upsampling process is as follows: The feature map after embedding the station coordinate encoding vector and the encoding vector after the denoising step for:

[0023] .

[0024] In one embodiment, the original empirical Green's function signal in the training dataset is used as the training target. The denoising neural network is trained by minimizing the difference between the noise predicted by the denoising neural network and the actual added noise, specifically including:

[0025] ;

[0026] Describe the objective function. Represents the parameters of the neural network. The empirical Green's function signal for the training dataset, This represents the position coordinates of the station pair consisting of the i-th and j-th seismographs. , Let i be the longitude and latitude of the i-th seismograph. Let j be the longitude and latitude of the j-th seismograph. This represents the empirical distribution consisting of all samples in the training dataset. This represents noise sampled from a standard normal distribution. Represents the standard normal distribution. Representing a neural network; when noise is progressively added to the original empirical Green's function signal, the artificially defined constant at step t is defined as... intermediate variables ; This indicates the current number of denoising steps.

[0027] In one embodiment, the denoising neural network starts with Gaussian noise and generates an interpolation empirical Green's function signal between two target points through a multi-step iterative denoising process, specifically including:

[0028] ;

[0029] The empirical Green's function signal after adding noise at step t. It is an artificially defined constant at step t; when noise is gradually added to the original empirical Green's function signal, the artificially defined constant at step t is defined as... intermediate variables ; Represents a neural network. Indicates random noise. Indicates the current denoising step number. , Let i be the longitude and latitude of the i-th seismograph. Let be the longitude and latitude of the j-th seismograph.

[0030] Compared with the prior art, the beneficial technical effects of the present invention are:

[0031] This invention proposes a background noise empirical Green's function interpolation method based on a conditional diffusion model. This method uses a probabilistic model to learn the empirical Green's function obtained from the cross-correlation of background noise recorded by seismometers deployed in the study area, effectively inferring the empirical Green's function between the coordinates of any two points in the area. The proposed method is more accurate than traditional empirical Green's function signal interpolation algorithms and can, to some extent, replace real observation data in scenarios where the number of seismometers is insufficient, improving the ability to detect underground structures and playing a role in applications such as underground mineral exploration and disaster assessment. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram of the implementation process in an embodiment of the present invention.

[0034] Figure 3 This is a schematic diagram illustrating the principle of generating empirical Green's function signals corresponding to coordinates of a given arbitrary station pair based on a conditional diffusion probability model in an embodiment of the present invention.

[0035] Figure 4 This is a schematic diagram of a denoising neural network structure based on the U-net structure in an embodiment of the present invention.

[0036] Figure 5 This is a distribution map of seismic stations in an embodiment of the present invention.

[0037] Figure 6 This is a direct comparison of the interpolation results of the proposed method and the radial basis function method on a portion of the test dataset.

[0038] Figure 7 The figure shows the quantitative evaluation results of the interpolation results of the test dataset using the method and radial basis function method proposed in this invention. Detailed Implementation

[0039] A preferred embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] like Figure 1 As shown, the background noise empirical Green's function interpolation method based on a conditional diffusion model in this invention includes the following steps:

[0041] S1 collects the empirical Green's function signals between every two seismograph pairs in the target area, as well as the location coordinates of all seismographs, as the training dataset.

[0042] S2, add noise to the empirical Green's function signal in the training dataset. Input the noisy empirical Green's function signal, the position coordinates of the two seismographs in the station, and the current denoising step number into the denoising neural network. Using the original empirical Green's function signal in the training dataset as the training target, train the denoising neural network by minimizing the difference between the noise predicted by the denoising neural network and the actual added noise, so that the denoising neural network learns to generate the posterior probability distribution of the corresponding empirical Green's function signal under the given position coordinates of any station pair.

[0043] S3. For any two target points where no seismographs are deployed, the corresponding position coordinates are input into a trained denoising neural network. The denoising neural network starts with Gaussian noise and generates an interpolation empirical Green's function signal between the two target points through a multi-step iterative denoising process.

[0044] This invention first collects real empirical Green's function signals between station pairs consisting of all seismometers in the target area and records the latitude and longitude coordinates of all seismometers. These empirical Green's function signals and seismometer location coordinates are used as training data to train the conditional diffusion model. Before training the model, the empirical Green's function signals need to be preprocessed, such as filtering to remove non-target frequency components and amplitude normalization to simplify signal features, in order to reduce training difficulty and improve model generalization. Then, the preprocessed training dataset is used to train the conditional diffusion model, enabling the model to learn to generate near-realistic empirical Green's function signals corresponding to the coordinate positions of two stations. Finally, the trained conditional diffusion model is used to predict the empirical Green's function signal characteristics between two spatial points where no seismometers are deployed. Figure 2 The above process is illustrated more vividly: the conditional diffusion model learns the empirical Green's function signal characteristics corresponding to coordinate pairs of different stations in the training dataset. The trained model then uses this learned experience to infer the empirical Green's function signals between spatial points without seismographs (i.e., virtual stations in the figure). The following is a description of the implementation details and evaluation metrics of the conditional diffusion model.

[0045] Figure 2 The black triangles in the figure represent actual seismographs deployed in the study area, while the red triangles mark virtual seismic stations, representing spatial locations in the study area where no seismographs are deployed. The empirical Green's function signal (the black waveform in the figure) between two actual deployed seismographs is modeled using a conditional diffusion model, and the empirical Green's function signal (the red waveform in the figure) between two spatial locations where no seismographs are deployed is inferred, thus completing the interpolation.

[0046] 1. Method and Principle.

[0047] This invention uses a conditional diffusion probability model to solve for the posterior probability of the empirical Green's function corresponding to any given pair of station coordinates. Define the... The latitude and longitude of each seismograph are respectively and , No. The latitude and longitude of each seismograph are respectively and Empirical Green's function is used If this is expressed, then the problem is transformed into solving a given... back Posterior probability: .

[0048] To solve for the above posterior probability, this invention first defines a Markov process that progressively adds noise to the original empirical Green's function signal:

[0049] (1)

[0050] in, The empirical Green's function signal for the training dataset, These are a series of artificially defined constants, usually following... The value increases with each increase, and the specific value can be adjusted according to needs. In the following embodiments, a general setting is used. It is 0.0001, and the value increases with... Increase linearly until The value is 0.02. Formula (1) above guides how to... Add noise to obtain a signal with richer noise components in the next time step. The noise-adding process continues. Next, make This can be approximated as Gaussian noise sampled from a standard normal distribution. (Number of noise additions) It also needs to be manually defined, and is usually several hundred to a thousand times. In the example below, it is set to 500.

[0051] The process described by formula (1) realizes the transformation from target sample to Gaussian noise. Therefore, the inverse process of formula (1) represents the reversal process from Gaussian noise to target sample, which can be derived as follows:

[0052] (2)

[0053] in, , , This represents noise sampled from a standard normal distribution.

[0054] The process described by formula (2) can be used to extract Gaussian noise. To the target empirical Green's function The gradual generation of [the neural network]. Next, we define the neural network. Learn to generate coordinate pairs corresponding to different stations. The noise to be removed when using the empirical Green's function. :

[0055] (3)

[0056] in, This represents the empirical distribution consisting of all samples in the training dataset.

[0057] Neural Networks Using empirical Green's function samples from the training set Station coordinates and the current number of denoising steps As input, the empirical Green's function and station coordinates from the training dataset are substituted into formula (3), and the result is obtained by minimizing... Optimize neural network parameters In order to maximize the conditional probability The goal.

[0058] After the neural network is trained, it can be used as a basis for... Generate the empirical Green's function corresponding to any two station coordinates. (2) Replace with neural network We can obtain:

[0059] (4)

[0060] in, It is random noise.

[0061] Repeat the above iterative process. Secondly, it can be derived from Gaussian noise. Different samples were taken from the middle The corresponding purely empirical Green's function signal . Figure 3 The mathematical expression of the above method's principle is summarized in diagrams. Figure 3 The green arrow in the middle describes the process shown in formula (1), that is, gradually adding noise to the empirical Green function; the trained neural network gradually removes noise through the content described in formula (4). During the noise removal process, the coordinates of the i-th and j-th seismographs are always used as part of the neural network input, guiding the finally generated empirical Green function to conform to the empirical Green function characteristics corresponding to the coordinate positions of these two stations.

[0062] 2. Model structure and training strategy.

[0063] Based on the above method principle, this invention does not require specifying a particular neural network structure to implement the denoising process; it only requires the neural network to satisfy the noisy empirical Green's function, station coordinates, and the current number of denoising steps. The input is the noise signal to be removed at the current denoising step, and the output is the noise signal to be removed at the current denoising step. In implementation, this invention uses a U-net network as the main network structure, receives the noisy empirical Green's function as input and predicts the noise; simultaneously, two different fully connected neural networks are used to encode the station's position coordinates. and noise reduction steps The encoded vectors output from the two fully connected neural networks are then embedded into the feature map of the U-net. See the detailed network structure below. Figure 4 As shown by the green and orange arrows in the figure, the encoded vector is embedded in a portion of the feature map within the U-net. Assume the encoded vector output by the station coordinate encoding network is... The denoising step involves the encoding vector output by the encoding network. The original upsampled feature map is The feature map after embedding the encoding vector is The feature map can then be encoded according to the following formula:

[0064] (5)

[0065] The above neural network minimizes the objective function shown in formula (3). To achieve optimization, a mini-batch stochastic gradient descent method was used, with a batch size of 256, and the Adam algorithm was employed. During implementation, the optimizer iteration count was fixed at 1,000,000, and the learning rate decreased linearly from 0.0001 to 0 with each iteration step.

[0066] Figure 4 (a) shows the backbone structure based on U-net, including coordinate location information and denoising steps. The features are encoded into different feature vectors using two independent encoding networks, and then embedded into the feature map of U-net as shown by the green and orange arrows in the diagram. The encoding network is based on a two-layer fully connected neural network, such as... Figure 4 As shown in (b) and (c) in the figure.

[0067] 3. Interpolation effect evaluation indicators.

[0068] To quantitatively evaluate the difference between the interpolated empirical Green's function signal and the true empirical Green's function signal, three evaluation indicators are introduced: maximum time-shift cross-correlation coefficient, time-shift amount, and zero-time-shift cross-correlation coefficient. First, the true empirical Green's function... and the empirical Green's function obtained by interpolation Perform time-shift cross-correlation to obtain the time-shift cross-correlation coefficient. :

[0069] (6)

[0070] in, and These are the mean values ​​of the true empirical Green's function and the interpolated empirical Green's function signals, respectively.

[0071] Maximum time-shift cross-correlation coefficient That is, the maximum correlation between the two signals under the optimal time shift:

[0072] (7)

[0073] Time shift That is, the delay time when obtaining the maximum time-shifted cross-correlation number:

[0074] (8)

[0075] It describes the time delay between two signals and their similarity after alignment.

[0076] In addition to these two metrics, the zero-time-shift cross-correlation coefficient is used to describe the correlation between the two misaligned signals. The zero-time-shift cross-correlation coefficient is... Time-shift cross-correlation coefficient ( This indicator reflects the similarity of two signals without considering time delay.

[0077] This invention proposes an interpolation algorithm for background noise empirical Green's function (EGF) signals. This algorithm can accurately infer the EGF signals for uncollected points based on the EGF signals collected by seismographs at some locations. The EGF is obtained by cross-correlating noise signals recorded by two seismographs over a long period. It reflects the propagation information of seismic surface waves between two stations and is widely used in underground structure detection. The detection capability of the EGF for underground structures is affected by the number of seismographs in the study area. However, deploying a large number of seismographs is costly, and some locations are difficult to deploy instruments due to geological conditions. Therefore, accurately interpolating the EGF signals for points without seismographs using the EGF signals from known points is a potential alternative to deploying dense seismograph arrays. This invention proposes an EGF signal interpolation method based on a conditional diffusion model, enabling accurate inference of the EGF signal at any location in the study area, which can effectively improve the detection results for underground structures.

[0078] Example

[0079] This embodiment attempts to apply the background noise empirical Green's function interpolation method proposed in this invention to a practical empirical Green's function signal interpolation task. The data used comes from the North American continental background noise empirical Green's function signal collected by the Earth Lens Project, which is publicly available for download online. Data from 460 seismographs within the continental United States were selected as the training and validation sets for the model proposed in this invention. The distribution of these stations is as follows: Figure 5 As shown. Among them, 400 stations ( Figure 5 The empirical Green's function between the station pairs (formed by the red dots in the diagram) is used as the training set of the model, and the remaining empirical Green's function signals are used as the test set to compare the interpolation effect of the proposed method with other methods.

[0080] Figure 5 The dots in the diagram represent all the stations used. The empirical Green's function signal between the two stations indicated by the two blue dots is used as the training set for the model proposed in this invention. The empirical Green's function signal between the stations indicated by one blue dot and one red dot, and the empirical Green's function between the two stations indicated by the two red dots are used as the test dataset for the method of this invention.

[0081] The dataset records empirical Green's functions with periods ranging from 8 to 300 seconds, a total recording duration of 3600 seconds, and a sampling frequency of 1 Hz. For method validation, a frequency band with a relatively high signal-to-noise ratio of 20 to 50 seconds was used, and the data was resampled to 0.25 Hz. To reduce computational cost, only the first 2000 seconds of the recorded signal were used, as this data is sufficient to describe the propagation of seismic surface waves in the continental United States. Since amplitude information has limited importance in background noise imaging, each empirical Green's function signal was normalized so that the maximum absolute value of the signal was always 1, thereby reducing the difficulty of model training and improving generalization.

[0082] The radial basis function (RBF) method is used as a comparison object for the proposed method in this invention. To ensure a fair comparison, both methods learn only the empirical Green's function signals in the training set and use the same test set data to verify their effectiveness. Figure 6 The interpolation effects of the proposed method and the radial basis function method on a portion of the waveforms in the test dataset were directly compared. A direct comparison of the waveforms shows that while the radial basis function method can learn the approximate envelope characteristics of the empirical Green's function signal, it cannot precisely recover the phase information in the waveform; whereas the method proposed in this invention can more accurately recover the phase information of waveforms at different station spacings. Since underground structure imaging based on the empirical Green's function of background noise mainly relies on the phase changes of different frequency components in the empirical Green's function signal, accurate recovery of phase information is helpful for the detailed detection of underground structures.

[0083] Figure 6The black waveform represents the empirical Green's function signal recorded in reality, while the red waveform represents the interpolation results of the two methods. Figure 6 In the figure, (a) represents the interpolation result of the method proposed in this invention. Figure 6 (b) in the figure represents the interpolation result of the radial basis function method.

[0084] Figure 7 The interpolation results of the two methods were quantitatively compared using three evaluation indicators: zero-time-shift cross-correlation coefficient, maximum time-shift cross-correlation coefficient, and time shift amount. As shown in Figure 7, the proposed method consistently outperforms the radial basis function algorithm across all station spacing ranges. Specifically, the zero-time-shift cross-correlation coefficient of the proposed method remained consistently high across different station spacing ranges, while the radial basis function method showed near-zero or even negative correlation between its interpolation results and the actual records for most station pairs. The maximum time-shift correlation coefficients of the two methods differed relatively little, indicating that both methods could achieve high correlation after a small time adjustment, meaning the radial basis function method could also accurately recover waveform morphology characteristics. However, the time shift amount comparison showed that the radial basis function method required a much larger time shift to achieve maximum correlation than the proposed method, indicating that while the radial basis function method could capture the coarse waveform morphology, it easily introduced significant phase deviations, reducing overall similarity and making its interpolation effect less stable than that of the proposed method.

[0085] Figure 7 The interpolation results are differentiated according to the spacing between stations corresponding to the empirical Green's function, and different values ​​on the x-axis reflect the statistical results of different spacing ranges. Figure 7 (a), (b), and (c) respectively count the three indicators: zero time-shift cross-correlation coefficient, maximum time-shift cross-correlation coefficient, and time-shift amount. Figure 7 The dots in the table represent the median of the statistical indicators, and the error bars represent the 25th-75th percentile range of the statistics within each interval.

[0086] Qualitative and quantitative comparative analysis of the interpolation results of empirical Green's function data collected in the continental United States demonstrates that the method of this invention can accurately interpolate empirical Green's function signals, and can, to a certain extent, replace the observation signals collected by actual seismographs, saving exploration costs. Given the important role of background noise imaging in geological hazard assessment, underground resource exploration, and seismogenic environment analysis, the data interpolation method proposed in this invention has significant engineering application value.

[0087] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0088] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple steps or stages, which are not necessarily completed at the same time, but may be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but may be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0089] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0091] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A background noise empirical Green's function interpolation method based on a conditional diffusion model, characterized in that, include: The empirical Green's function signals between every two seismograph pairs in the target area, as well as the location coordinates of all seismographs, are collected as the training dataset. To add noise to the empirical Green's function signal in the training dataset, the noisy empirical Green's function signal, the position coordinates of two seismographs in the station, and the current denoising step number are input into the denoising neural network. Using the original empirical Green's function signal in the training dataset as the training objective, the denoising neural network is trained by minimizing the difference between the noise predicted by the denoising neural network and the actual added noise. This enables the denoising neural network to learn the posterior probability distribution of generating the corresponding empirical Green's function signal given any station pair's location coordinates. Specifically, this includes: ； Describe the objective function. Represents the parameters of the neural network. The empirical Green's function signal for the training dataset, This represents the position coordinates of the station pair consisting of the i-th and j-th seismographs. , Let i be the longitude and latitude of the i-th seismograph. Let j be the longitude and latitude of the j-th seismograph. This represents the empirical distribution consisting of all samples in the training dataset. This represents noise sampled from a standard normal distribution. Represents the standard normal distribution. Representing a neural network; when noise is progressively added to the original empirical Green's function signal, the artificially defined constant at step t is defined as... intermediate variables ; Indicates the current denoising step number. The index for the number of denoising steps. , This represents the artificially defined constant in the s-th step when noise is progressively added to the original empirical Green's function signal; For any two target points where no seismometers are deployed, the corresponding position coordinates are input into a trained denoising neural network. The denoising neural network starts with Gaussian noise and generates an interpolated empirical Green's function signal between the two target points through a multi-step iterative denoising process.

2. The background noise empirical Green's function interpolation method based on a conditional diffusion model according to claim 1, characterized in that, Adding noise to the empirical Green's function signal in the training dataset specifically includes: Noise is gradually added to the original empirical Green's function signal: ； in, The empirical Green's function signal after adding noise at step t. Represents the conditional probability distribution. Indicates a Gaussian distribution. Represents the identity matrix.

3. The background noise empirical Green's function interpolation method based on a conditional diffusion model according to claim 1, characterized in that, The denoising neural network adopts the U-net structure.

4. The background noise empirical Green's function interpolation method based on a conditional diffusion model according to claim 3, characterized in that, The process of inputting the noisy empirical Green's function signal, the position coordinates of the two seismometers at the station, and the current denoising step count into the denoising neural network specifically includes: The position coordinates of the two seismographs are input into the station coordinate encoding network to obtain the station coordinate encoding vector; The current denoising step number is input into the denoising step encoding network to obtain the denoising step encoding vector; The noisy empirical Green's function signal is used as the input to the downsampling process of the U-net structure, and the station coordinate encoding vector and the denoising step encoding vector are embedded into the upsampling process of the U-net structure.

5. The background noise empirical Green's function interpolation method based on a conditional diffusion model according to claim 4, characterized in that, The process of embedding the station coordinate encoding vector and the denoising step encoding vector into the upsampling process of the U-net structure specifically includes: Let the station coordinate encoding vector output by the station coordinate encoding network be... The denoising step encoding vector output by the denoising step encoding network is The original upsampling feature map of the U-net structure upsampling process is as follows: The feature map after embedding the station coordinate encoding vector and the encoding vector after the denoising step for: 。 6. The background noise empirical Green's function interpolation method based on a conditional diffusion model according to claim 1, characterized in that, The denoising neural network starts with Gaussian noise and generates an interpolated empirical Green's function signal between two target points through a multi-step iterative denoising process, specifically including: ； The empirical Green's function signal after adding noise at step t; intermediate variables ; Represents a neural network. This represents random noise.

Images