CN111695729A - Aftershock prediction method based on DMAP model - Google Patents
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Abstract
The invention discloses an aftershock prediction method based on a DMAP (Dimethylationpropane) model, which is based on a deep learning method, and utilizes a large amount of seismic data to learn the magnitude of the major shock, the spatial distance information between a predicted region and a major shock source and the correlation between stress change information caused by the major shock outbreak process to a related region and the outbreak of the aftershock, and meanwhile, the prediction capability of the model is improved and the variance of the model is reduced by combining a data enhancement method, and the magnitude information of the aftershock is added into a loss function of a sample to optimize the model, so that the prediction capability of the model is improved.
Description
Technical Field
The invention belongs to the technical field of earthquake prediction, and particularly relates to an aftershock prediction method based on a DMAP (multiple access point) model.
Background
A great deal of work and research has been carried out by geologists in the fields of earthquake early warning, earthquake prompt report, earthquake mechanism and the like for many years by using continuous waveform data recorded by an earthquake monitoring station, wherein tasks such as earthquake event detection, automatic earthquake phase pickup, earthquake magnitude quick estimation and the like are key points and hot points of relevant research. The earthquake event detection means that whether a certain section of data belongs to an earthquake event or not is detected for continuous waveform data recorded by the earthquake monitoring station, so that whether the earthquake occurs at a certain moment or not is judged; the automatic seismic phase pickup means that after a certain section of waveform data is known to belong to a seismic event, the exact time of the seismic wave propagation reaching a station is given; the task of quickly estimating the magnitude of earthquake is very important in earthquake early warning, and if accurate estimation of the magnitude of earthquake can be given in the first few seconds of the occurrence of an earthquake, great help can be brought to earthquake early warning and disaster relief work, and more time can be obtained.
As an earthquake is a natural disaster with great destructive power, the stress distribution around a fault is usually changed in the process of a major earthquake outbreak, a large number of experiments prove that the occurrence of aftershocks is closely related to the stress change caused by the main earthquake outbreak, and the occurrence of aftershocks usually causes secondary damage on the basis of the main earthquake, so that the effective prediction of the spatial distribution of the aftershocks is significant work.
Current aftershock prediction can be simply divided into two categories: the method is a physical quantity-based aftershock prediction method commonly used in the traditional seismology, namely the aftershock prediction is mainly carried out on the basis of physical quantities such as Coulomb fracture stress, maximum shear stress, paradigm equivalent stress and the like obtained by calculating stress change tensor of surrounding related regions caused by the main shock explosion process; the other type is to directly learn a complex mapping relation between stress change and aftershock based on a deep learning model.
In recent years, with the rapid development of deep learning, the application of deep learning to the earthquake related field gradually becomes a development trend, and typical research of aftershock prediction based on deep learning is thatDNN-based aftershock prediction work published in Nature journal of 2018 by DeVries et al [ DeVries P M R, Viegas F, Wattenberg M et al, Deeplearning of aftershock patterns following great earthquakes [ J].Nature，2018，560(7720):632.]DeVries directly utilizes six independent stress components delta sigma of stress change tensor delta sigma after aftershockxx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzBy means of the characteristics, a 6-layer DNN network is utilized to predict whether aftershocks occur in each grid in the next year, and as a result, the neural network is found to be capable of well learning the relation between delta sigma and the aftershocks.
The physical quantity-based aftershock prediction method in the traditional seismology has advantages in interpretability, but with the development of deep learning and the increase of data sets, the deep learning has certain advantages in the aftershock prediction effect. The DeVries residual earthquake prediction model based on DNN only considers the relation between stress change and residual earthquake, but does not consider the magnitude information of the main earthquake, the spatial distance information between the predicted area and the earthquake source and the lack of effective characteristic engineering on the stress change.
Disclosure of Invention
In view of the above, the invention provides an aftershock prediction method based on a DMAP Model, which trains a DMAP (deep Model for aftershock prediction) Model through a large amount of principal and aftershock data, and improves the capability of predicting aftershock.
A method for predicting aftershock based on a DMAP model comprises the following steps:
(1) collecting relevant information after an earthquake occurs, wherein the relevant information comprises main earthquake position information, main earthquake magnitude information, stress change information of a relevant area around the main earthquake and space distance information between the main earthquake and a main earthquake source;
(2) after the main earthquake occurs, taking a main earthquake source as a center, and performing plane two-dimensional grid division on peripheral areas of the main earthquake, wherein the size of each grid area is 5km multiplied by 5 km; calculating the dislocation caused by different grid areas at the periphery according to the main earthquake outbreak process to obtain the stress change tensor of each grid area;
(3) for any grid region, forming a characteristic sample by using the principal seismic magnitude, the stress change tensor of the grid region and the spatial distance between the principal seismic source and the principal seismic source; if the grid region has aftershock, taking the characteristic sample as a positive sample; if the grid region does not generate aftershock, taking the characteristic sample as a negative sample;
(4) and (3) constructing a DMAP model, training the DMAP model by using a large number of characteristic samples to obtain an aftershock prediction model, and performing aftershock prediction on the area to be tested around the main shock source by using the aftershock prediction model.
Further, the DMAP model in step (4) includes a hidden vector extraction module, a feature engineering module, an input layer, a feature extraction layer, and an output layer, where the hidden vector extraction module and the feature engineering module are connected to the input layer, the input layer is connected to the feature extraction layer, and the feature extraction layer is connected to the output layer.
Furthermore, a magnitude hidden vector matrix H of a major earthquake, a spatial distance hidden vector matrix L of a measured region from a major earthquake source, and a stress variation hidden vector matrix M of the measured region are built in the hidden vector extraction module, wherein the magnitude of the magnitude hidden vector matrix H is H × p, the magnitude of the spatial distance hidden vector matrix L is L × p, the magnitude of the stress variation hidden vector matrix M is M × p, H is the number of magnitude intervals after discretization, L is the number of spatial distance intervals after discretization, M is the number of stress components in a stress variation tensor, and p is a self-defined hidden vector dimension.
Furthermore, the hidden vector extraction module extracts a row vector corresponding to the principal seismic magnitude from the magnitude hidden vector matrix H as a principal seismic magnitude hidden vector after discretizing the principal seismic magnitude in the feature sample, and extracts a row vector corresponding to the spatial distance from the spatial distance hidden vector matrix L as a spatial distance hidden vector of the grid region after discretizing the spatial distance between the grid region and the principal seismic source in the feature sample; for the stress change tensor of the grid region in the feature sample, 6 stress components delta sigma are selected according toxx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzRespectively from the hidden vector of the stress variationExtracting a corresponding row vector from the matrix M, and multiplying the corresponding row vector by the stress component to obtain 6 stress component hidden vectors of the grid region, wherein delta sigmaxxIs a tensile or compressive force in the x direction, Δ σxyIs the torque force in the x-y plane, Δ σxzIs the torque force in the x-z plane, Δ σyyAs a tension or compression force in the y direction, Δ σyzIs the torque force in the y-z plane, Δ σzzAs a tension or compression force in the z direction.
Further, the feature engineering module is used for tensorially transforming 6 stress components Δ σ of stress variation tensors of the grid region in the feature samplexx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzAnd after the absolute value is taken, carrying out logarithm operation to form a logarithm stress change vector of the grid region, and simultaneously carrying out matrix transformation calculation on the stress change tensor of the grid region to obtain the maximum shearing stress and the normal equivalent stress of the grid region.
Further, Δ σ due to the stress componentxx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzThe directions x and y are equivalent to each other and the number of features can be data enhanced by interchanging.
Furthermore, the input layer adds the 6 stress component hidden vectors to form an effective stress vector, and then splices the effective stress vector with the dominant seismic magnitude hidden vector, the spatial distance hidden vector, the logarithmic stress variation vector, the maximum shear stress and the normal equivalent stress to form the input of the feature extraction layer; the characteristic extraction layer adopts DNN (deep neural network) to carry out characteristic extraction, and the obtained characteristic vector is sent to the output layer; the output layer is a layer of fully-connected network with the output dimensionality of 1, and the probability of aftershock of the grid area is obtained after Sigmoid activation function operation.
Further, the specific implementation process of training the DMAP model in step (4) is as follows: firstly, initializing the model parameters, including a weight matrix and a bias vector of each layer in a magnitude hidden vector matrix H, a spatial distance hidden vector matrix L and a stress change hidden vector matrix M, DNN, learning rate and an optimization algorithm; and then inputting the characteristic samples into the DMAP model one by one for training, calculating a loss function L between a prediction result output by the model and a true value of the corresponding characteristic sample, and continuously adjusting and updating parameters of the whole DMAP model through back propagation according to the loss function L until the loss function is minimum in convergence, thereby completing training and obtaining the aftershock prediction model.
Further, the expression of the loss function L is as follows:
wherein: p is a radical ofrThe true value of the r-th feature sample is a true value 1 if the feature sample is a positive sample; if the feature sample is a negative sample, its true value is 0,
d is the total number of the characteristic samples, and α is the weight coefficient.
Further, the magnitude of the weighting factor α is positively correlated with the magnitude of aftershock magnitude and α ═ Msub+1, for positive samples, MsubThe aftershock magnitude of the corresponding grid region; for negative samples, Msub＝0。
Further, the process of performing aftershock prediction on the region to be measured around the main seismic source by using the aftershock prediction model in the step (5) is as follows: after the main earthquake occurs, the characteristic quantity composed of the main earthquake magnitude, the stress change tensor of the region to be detected and the space distance with the main earthquake source is input to the aftershock prediction model, and the probability of the aftershock occurring in the region to be detected in the next period of time can be output and obtained.
Based on the technical scheme, the method utilizes a large amount of seismic data to learn the relationship among the magnitude of the major earthquake, the spatial distance information between the predicted region and the major earthquake source, and the stress change information caused by the major earthquake outbreak process to the relevant region and the outbreak of the aftershock, and simultaneously combines a data enhancement method to improve the prediction capability of the model and reduce the variance of the model, and in addition, the magnitude information of the aftershock is added into the loss function of the sample to optimize the model, thereby improving the prediction capability of the model.
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FIG. 1 is a schematic overall flow chart of the aftershock prediction method of the present invention.
FIG. 2 is a DMAP model architecture of the present invention.
Detailed Description
In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.
As shown in FIG. 1, the method for predicting the aftershock based on the DMAP model comprises the following steps:
(1) aiming at historical earthquakes occurring in the past, dividing a surrounding relevant area with a main earthquake as a center into plane grids, and collecting the magnitude information of the main earthquake, the spatial distance information of each grid from an earthquake source and the stress change tensor caused by the main earthquake outbreak process in each grid area.
The magnitude information of the main earthquake is characterized by continuous features, and the magnitude of the main earthquake is discretized by the specific method as follows:
1. determining a discretized bucket division interval: [ - ∞, m1),[m1,m2),[m2,m3),[m3,m4),[m4，+∞)；
2. And determining the interval of the main seismic magnitude of the sample to obtain the discretized one-hot value.
And obtaining the one-hot coding format through discretized main earthquake. The mapping of the space vector is performed by means of matrix multiplication, as follows:
vmainshock＝vo-main·H
wherein: v. ofo-mainThe vector is 1 × H, H represents the dimension of the discretized main earthquake, H is a matrix of H × p, and p is a self-defined hidden vector dimension, and based on the vector, the main earthquake magnitude information v encoded by one-hot can be obtainedo-mainCharacterised by v of dimension 1 × pmainshockAnd (5) vector quantity.
For the spatial distance between the predicted area and the main seismic source, the same method is adopted for the sub-barrelThe method firstly obtains the vector v of one-hot codingo-disAnd the following formula obtains the implicit vector characterization v of the distancedis。
vdis＝vo-dis·L
Six independent stress components Δ σ for the stress tensorxx，Δσxy，Δσxz，Δσyy，Δσyz，ΔσzzThe processing method is to use the weight of the implicit vector as the weight of the implicit vector, and the method for acquiring the implicit vector is as follows:
wherein:
representing a spatially mapped basis vector with the stress component direction mn.
The magnitude information of the main earthquake, the spatial distance information between the predicted area and the earthquake source and the stress component information are represented by high-dimensional hidden vectors, the hidden vectors are initialized by Gaussian distribution according to the following formula, and the hidden vectors are reversely propagated and adjusted by a neural network.
Wherein: μ is the mean of the distributions, set to 0; σ is the standard deviation of the distribution and is set to 0.1.
(2) The structure of the aftershock prediction model DMAP adopted by the invention is shown in figure 2, and the input of the DMAP model comprises the following four characteristics: the method comprises the following steps of firstly, based on master earthquake magnitude information represented by high-dimensional hidden vectors; the spatial distance information between the predicted area represented by the high-dimensional hidden vector and the seismic source is obtained; stress change information based on high-dimensional hidden vector representation; and fourthly, characteristic engineering based on stress tensor.
The input of the model is first Sum Pooling of 6 independent stress component vectors characterized by implicit vectors, as follows:
Emb＝∑Embmn
and then splicing the stress component vector subjected to SumPooling with the dominant seismic magnitude hidden vector, the spatial distance hidden vector and the characteristic engineering characteristic vector, and inputting the spliced stress component vector, the spatial distance hidden vector and the characteristic engineering characteristic vector into a DNN network layer, wherein a single-layer DNN grid formula is as follows:
hi＝σ(WThi-1+bi)
wherein: h isi-1Output vector representing the previous layer of network, biAs an offset vector, WTIs a network weight parameter, sigma is an activation function, hiRepresenting the output of the current layer; for initial input, a stress component vector after SumPoling is adopted, a dominant seismic magnitude hidden vector, a spatial distance hidden vector and a feature engineering feature vector are spliced to obtain a vector, and the activation function sigma adopts a Relu function.
The output layer of the model adopts a Sigmoid activation function, as follows:
y＝Sigmoid(hi)
(3) and reversely propagating the training network parameters through a large number of collected characteristic samples to obtain an effective network model.
SGD is used as a gradient descent method, the initial learning rate is set to be 0.1, and the learning rate is continuously reduced in combination with a quenching mode; relu is used as a deep network activation function to reduce the problem of gradient disappearance of the deep network; dropout is added to each layer of the DNN module to improve the generalization capability of the model and improve the stability of the model; set 80% of the data as the training set and 20% of the data as the test set, and use 5-fold cross-validation to adjust the model and parameters in the training set.
The following loss functions were used in training the model:
wherein: p is a radical ofrIs the true value in the r-th feature sample,
the prediction result corresponding to the r-th characteristic sample, D is the total number of the characteristic samples, α is the weightThe weight coefficient, the magnitude of which is positively correlated with the magnitude of aftershock, is specifically set as follows:
α＝Msub+1
wherein: msubRepresenting the magnitude of the aftershock, α is a value of 1 for samples with an aftershock magnitude of 0.
(4) For the real prediction problem, the earthquake magnitude information of the main earthquake, the spatial distance information between the predicted region and the earthquake source, the stress change information of the predicted region and the characteristic engineering characteristics based on the stress change are used as model inputs, and the probability of aftershocks of the predicted region is output through a Sigmoid activation function of the last layer of the model.
Table 1 shows the comparison of the effect of the method of the present invention with other prediction methods, and it can be seen that the method of the present invention is significantly improved in the aspect of prediction effect compared to other prediction methods in the prior art.
TABLE 1
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the invention. It will be readily apparent to those skilled in the art that various modifications to the above-described embodiments may be made, and the generic principles defined herein may be applied to other embodiments without the use of inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications to the present invention based on the disclosure of the present invention within the protection scope of the present invention.
Claims (10)
1. A method for predicting aftershock based on a DMAP model comprises the following steps:
(1) collecting relevant information after an earthquake occurs, wherein the relevant information comprises main earthquake position information, main earthquake magnitude information, stress change information of a relevant area around the main earthquake and space distance information between the main earthquake and a main earthquake source;
(2) after the main earthquake occurs, taking a main earthquake source as a center, and performing plane two-dimensional grid division on peripheral areas of the main earthquake, wherein the size of each grid area is 5km multiplied by 5 km; calculating the dislocation caused by different grid areas at the periphery according to the main earthquake outbreak process to obtain the stress change tensor of each grid area;
(3) for any grid region, forming a characteristic sample by using the principal seismic magnitude, the stress change tensor of the grid region and the spatial distance between the principal seismic source and the principal seismic source; if the grid region has aftershock, taking the characteristic sample as a positive sample; if the grid region does not generate aftershock, taking the characteristic sample as a negative sample;
(4) and (3) constructing a DMAP model, training the DMAP model by using a large number of characteristic samples to obtain an aftershock prediction model, and performing aftershock prediction on the area to be tested around the main shock source by using the aftershock prediction model.
2. The aftershock prediction method according to claim 1, characterized in that: the DMAP model in the step (4) comprises a hidden vector extraction module, a feature engineering module, an input layer, a feature extraction layer and an output layer, wherein the hidden vector extraction module and the feature engineering module are connected with the input layer, the input layer is connected with the feature extraction layer, and the feature extraction layer is connected with the output layer.
3. The aftershock prediction method according to claim 2, characterized in that: the hidden vector extraction module is internally provided with a magnitude hidden vector matrix H of a main earthquake, a spatial distance hidden vector matrix L of a detected region from the main earthquake source and a stress variation hidden vector matrix M of the detected region, wherein the magnitude of the magnitude hidden vector matrix H is H multiplied by p, the magnitude of the spatial distance hidden vector matrix L is L multiplied by p, the magnitude of the stress variation hidden vector matrix M is M multiplied by p, H is the number of magnitude intervals after discretization, L is the number of spatial distance intervals after discretization, M is the number of stress components in a stress variation tensor, and p is a self-defined hidden vector dimension.
4. The device of claim 3The earthquake prediction method is characterized by comprising the following steps: the hidden vector extraction module extracts a row vector corresponding to the main earthquake magnitude from the magnitude hidden vector matrix H after discretizing the main earthquake magnitude in the characteristic sample as a hidden vector of the main earthquake magnitude, and extracts a row vector corresponding to the spatial distance from the hidden vector matrix L of the spatial distance as a hidden vector of the spatial distance of the grid region after discretizing the spatial distance between the grid region and the main earthquake source in the characteristic sample; for the stress change tensor of the grid region in the feature sample, 6 stress components delta sigma are selected according toxx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzRespectively extracting a corresponding row vector from the stress change implicit vector matrix M, and multiplying the corresponding row vector by the stress component to obtain 6 stress component implicit vectors of the grid region, wherein delta sigmaxxIs a tensile or compressive force in the x direction, Δ σxyIs the torque force in the x-y plane, Δ σxzIs the torque force in the x-z plane, Δ σyyAs a tension or compression force in the y direction, Δ σyzIs the torque force in the y-z plane, Δ σzzAs a tension or compression force in the z direction.
5. The aftershock prediction method according to claim 4, characterized in that: the characteristic engineering module is used for tensorially transforming 6 stress components delta sigma of stress change of the grid region in the characteristic samplexx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzAnd after the absolute value is taken, carrying out logarithm operation to form a logarithm stress change vector of the grid region, and simultaneously carrying out matrix transformation calculation on the stress change tensor of the grid region to obtain the maximum shearing stress and the normal equivalent stress of the grid region.
6. The aftershock prediction method according to claim 5, characterized in that: due to the stress component Δ σxx、Δσxy、Δσxz、Δσyy、Δσyz、ΔσzzThe directions x and y are equivalent to each other and the number of features can be data enhanced by interchanging.
7. The aftershock prediction method according to claim 5, characterized in that: the input layer adds the 6 stress component hidden vectors to form an effective stress vector, and then the effective stress vector is spliced with the principal seismic magnitude hidden vector, the spatial distance hidden vector, the logarithmic stress variation vector, the maximum shear stress and the normal form equivalent stress to form the input of the feature extraction layer; the characteristic extraction layer adopts DNN to carry out characteristic extraction, and the obtained characteristic vector is sent to the output layer; the output layer is a layer of fully-connected network with the output dimensionality of 1, and the probability of aftershock of the grid area is obtained after Sigmoid activation function operation.
8. The aftershock prediction method according to claim 7, characterized by: the specific implementation process of training the DMAP model in the step (4) is as follows: firstly, initializing the model parameters, including a weight matrix and a bias vector of each layer in a magnitude hidden vector matrix H, a spatial distance hidden vector matrix L and a stress change hidden vector matrix M, DNN, learning rate and an optimization algorithm; and then inputting the characteristic samples into the DMAP model one by one for training, calculating a loss function L between a prediction result output by the model and a true value of the corresponding characteristic sample, and continuously adjusting and updating parameters of the whole DMAP model through back propagation according to the loss function L until the loss function is minimum in convergence, thereby completing training and obtaining the aftershock prediction model.
9. The aftershock prediction method according to claim 8, characterized by: the expression of the loss function L is as follows:
wherein: p is a radical ofrThe true value of the r-th feature sample is a true value 1 if the feature sample is a positive sample; if the feature sample is a negative sample, its true value is 0,
d is the total number of the characteristic samples, α is a weight coefficient with the magnitude positively correlated with the aftershock magnitude and α M is the prediction result corresponding to the r-th characteristic samplesub+1, for positive samples, MsubThe aftershock magnitude of the corresponding grid region; for negative samples, Msub＝0。
10. The aftershock prediction method according to claim 1, characterized in that: the process of performing aftershock prediction on the region to be measured around the main seismic source by using the aftershock prediction model in the step (5) is as follows: after the main earthquake occurs, the characteristic quantity composed of the main earthquake magnitude, the stress change tensor of the region to be detected and the space distance with the main earthquake source is input to the aftershock prediction model, and the probability of the aftershock occurring in the region to be detected in the next period of time can be output and obtained.
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| CN115494544A (en) * | 2022-07-06 | 2022-12-20 | 西南交通大学 | Maximum aftershock magnitude interval prediction method based on Bayesian theory |
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| CN114089410A (en) * | 2021-12-15 | 2022-02-25 | 中国地震台网中心 | Earthquake prediction method and device and electronic equipment |
| CN115494544A (en) * | 2022-07-06 | 2022-12-20 | 西南交通大学 | Maximum aftershock magnitude interval prediction method based on Bayesian theory |
| CN115494544B (en) * | 2022-07-06 | 2023-08-15 | 西南交通大学 | Maximum aftershock magnitude interval prediction method based on Bayesian theory |
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