A UNet-based joint inversion method of receiving function and surface wave dispersion

Abstract

The application discloses a UNet-based joint inversion method of receiving function and surface wave dispersion, and comprises the following steps: S1, constructing a velocity model and performing forward calculation to obtain a training data set; S2, constructing a UNet, training by using the training data set, and taking the receiving function and the surface wave dispersion data to be inverted as the input of the UNet to obtain the velocity structure of the crust and the upper mantle. The UNet-based joint inversion method of receiving function and surface wave dispersion can reduce the non-uniqueness in inversion, improve the inversion efficiency and stability, and explore the applicability of the deep learning method in joint inversion, so that the method can be used as the replacement of conventional inversion, the defects of the conventional inversion are improved, and the foundation is laid for geophysical real-time inversion interpretation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of earth exploration, and particularly relates to a joint inversion method of receiver function and surface wave dispersion based on UNet. BACKGROUND

[0002] The receiver function is a kind of reflection seismology for detecting the crust and upper mantle structure under the station. Generally, teleseismic body waves contain the comprehensive effect of the source time function and the medium attribute on the propagation path. The purpose of the receiver function is to remove the source time function and the influence of the instrument, and obtain the P-SV converted phase from the station below, which contains the velocity information of the main discontinuous interface in the lithosphere. Compared with other seismological methods, the receiver function can realize depth measurement only with a single seismic station. Therefore, the receiver function is widely used in the research of lithospheric structure and Moho shape.

[0003] The inversion of the receiver function is generally considered to have strong non-uniqueness, which leads to weak constraints of the receiver function on the absolute velocity of the underground, and strong dependence of the inversion on the initial model. The surface wave dispersion can well reflect the overall seismic wave velocity value of the underground geological body, but cannot well invert the interface position of the geological body; the receiver function is just the opposite, it can well reflect the interface position below the station, but lacks the constraint ability of the absolute velocity, and this insensitivity comes from the trade-off property of velocity and depth, that is, the low-velocity structure in the shallow part and the high-velocity structure in the deep part have almost the same receiver function response, and the inversion of the receiver function with different slowness cannot eliminate the velocity uncertainty in the depth. Therefore, the joint inversion of surface wave and receiver function has its natural rationality, and through the joint inversion of the receiver function and the surface wave dispersion of the same station, the advantages of the two are complementary, and the S-wave velocity information below the station can be better constrained.

[0004] The neural network algorithm is one of the main contents of deep learning. In recent years, there are a large number of applications of using neural network technology for inversion of geophysical data. These applications mainly focus on the field of seismic exploration, electromagnetic exploration and natural earthquake research. Although machine learning has been widely used in the inversion of various single methods of geophysics, there is no systematic research on the joint inversion of receiver function and surface wave dispersion using deep learning technology. The supervised learning method uses a large number of data sets obtained by the forward algorithm to establish an effective mapping between the data and the model, so as to complete the inversion, and this idea is widely used in deep learning inversion and produces a large number of achievements. More importantly, the same neural network framework is easy to migrate to different data sets, even if two kinds of data come from completely different fields. This property enables us to build the same neural network model for the joint inversion of multiple data, such as the joint inversion of receiver function and surface wave dispersion. SUMMARY

[0005] The application proposes a UNet-based joint inversion method of receiver functions and surface wave dispersion to solve the above problems.

[0006] The technical scheme of the application is as follows: a UNet-based joint inversion method of receiver functions and surface wave dispersion comprises the following steps:

[0007] S1: constructing a velocity model and performing forward calculation to obtain a training data set;

[0008] S2: constructing a UNet, training by using the training data set, and taking the receiver function and surface wave dispersion data to be inverted as the input of the UNet to obtain the velocity structure of the crust and upper mantle.

[0009] Further, step S1 comprises the following sub-steps:

[0010] S11: constructing a four-layer velocity model comprising the upper crust, middle crust, lower crust and upper mantle;

[0011] S12: interpolating the four-layer velocity model to obtain a first data set and a second data set;

[0012] S13: performing forward calculation of the receiver function and surface wave dispersion on the first data set and the second data set to obtain the training data set.

[0013] Further, in step S12, when the perturbation of the velocity model is 10%, the four-layer velocity model is interpolated to obtain the first data set.

[0014] Further, in step S12, when the perturbation of the velocity model is 20%, each layer of the velocity model is divided into two sub-layers to obtain an eight-layer velocity model, and the eight-layer velocity model is interpolated to obtain the second data set.

[0015] Further, in step S2, the UNet comprises 17 convolution layers, 3 pooling layers and 3 transposed convolution layers.

[0016] Further, in step S2, the ELU function is the activation function of the convolution layer of the UNet.

[0017] Further, in step S2, the objective function of the UNet in the training process is The calculation formula is as follows:

[0018]

[0019] Wherein, N represents the total number of training samples, m i represents the label corresponding to the i-th sample, D(·) represents an inversion operator realized by deep learning, d iX represents input data, and represents hyperparameters that need to be updated in UNet back propagation.

[0020] The UNet-based joint inversion method of the receiving function and the surface wave dispersion has the beneficial effects that the non-uniqueness in inversion can be reduced, the inversion efficiency and stability can be improved, the applicability of the deep learning method in joint inversion can be explored, the method can be used as a substitute for conventional inversion, the defects of conventional inversion are improved, and a foundation is laid for real-time inversion and interpretation of geophysics. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A flowchart of the joint inversion method of the receiving function and the surface wave dispersion;

[0022] Figure 2 A synthetic one-dimensional layered crust-mantle model for UNet training;

[0023] Figure 3 A framework of the deep learning model for joint inversion;

[0024] Figure 4(a) is an evolution diagram of the loss function in the training process;

[0025] Figure 4(b) is a residual histogram of the prediction result and the label of part of the test set in the training process;

[0026] Figure 5 A UNet prediction result and uncertainty estimation diagram. DETAILED DESCRIPTION

[0027] The embodiments of the present application will be further described below with reference to the accompanying drawings.

[0028] Forward calculation: the process of calculating the receiving function and the surface wave dispersion data based on the earth velocity model and using the seismic wave propagation theory.

[0029] As shown in Figure 1 The present application provides a UNet network-based joint inversion method of the receiving function and the surface wave dispersion, comprising the following steps:

[0030] S1: constructing a velocity model and performing forward calculation to obtain a training data set;

[0031] S2: constructing a UNet, training using the training data set, and taking the receiving function and the surface wave dispersion data to be inverted as the input of the UNet to obtain the velocity structure of the crust and the upper mantle.

[0032] In the embodiments of the present application, step S1 comprises the following sub-steps:

[0033] S11: Construct a four-layer velocity model including the upper crust, middle crust, lower crust, and upper mantle;

[0034] S12: Interpolate the four-layer velocity model to obtain the first and second datasets;

[0035] S13: Perform forward modeling of the receiver function and surface wave dispersion on the first and second datasets to obtain the training dataset.

[0036] Steps S11-S13 describe the method for constructing the velocity model.

[0037] In this embodiment of the invention, in step S12, when the perturbation of the velocity model is 10%, the four-layer velocity model is interpolated to obtain the first dataset.

[0038] In this embodiment of the invention, in step S12, when the perturbation of the velocity model is 20%, each layer of the velocity model is divided into two sub-layers to obtain an eight-layer velocity model, and the eight-layer velocity model is interpolated to obtain a second dataset.

[0039] In this embodiment of the invention, for any neural network model, the training dataset plays a central role in optimizing model performance. It contains the features the model needs to learn and largely determines the prediction results. When the data is of sufficient quality, the model's parameter space has considerable flexibility. Within a given model hyperparameter space, despite setting different model parameters, the difference in training accuracy is relatively small.

[0040] For geophysical inversion, the core issue with training data lies in how to establish a reasonable and as comprehensive a set of geological models as possible. In this invention, the training dataset is generated based on a standard one-dimensional layered Earth model, using numerous models and forward modeling to obtain the receiver function waveforms. For example... Figure 2 As shown, a basic four-layer velocity model is first established, comprising the upper, middle, and lower crust and the upper mantle. The S-wave velocity V of the upper crust is... s The velocity gradually changes with depth, while the velocities in other layers vary randomly within a given perturbation R (10%), based on the standard Earth reference model. The corresponding P-wave velocity V... p Based on a fixed ratio V p / V s =1.73, calculated from the empirical relationship ρ = 0.77 + 0.32V. sThe four-layer model is interpolated to obtain a final 80-layer model, and 10,000 models are generated as the first data set, which enables the network to learn the basic crust-mantle structure characteristics. In order to improve the ability of the model to predict complex velocity structure, the value of R is expanded to 20%, and the basic four-layer model is expanded to eight layers, that is, each layer is divided into two sub-layers, and the velocity and depth of each layer are randomly changed within the R range, and each eight-layer model is interpolated to obtain a final 80-layer model, and 40,000 such models are generated as the second data set.

[0041] The present application uses a seismological computer program package to perform forward calculation (i.e. solving the observed response from the known velocity model) of the receiver function and the surface wave dispersion of the model. The effective time window of the receiver function is 5 seconds before the arrival of the P wave phase and 25 seconds after the arrival, and each receiver function has 300 sampling points with a sampling frequency of 10 Hz. In the forward calculation of the model, the ray parameter is set to a random value from 0.04 to 0.075 to improve the generalization ability of the model. The period range of the surface wave dispersion is 10-40s; the total number of frequency points is 16, which are set to be equidistant. Finally, 300 receiver functions and 16 dispersion data are interpolated to 80 sampling points as the two inputs of UNet.

[0042] In the embodiment of the present application, in step S2, the UNet includes 17 convolution layers, 3 pooling layers and 3 transposed convolution layers.

[0043] In the embodiment of the present application, in step S2, the ELU function is the activation function of the convolution layer of the UNet.

[0044] In the embodiment of the present application, in step S2, the objective function of the UNet in the training process is The calculation formula is:

[0045]

[0046] Where N represents the total number of training samples, m i represents the label corresponding to the i-th sample, D(·) represents the inversion operator realized by deep learning, d i represents the input data, and theta represents the hyperparameter that needs to be updated in the back propagation of the UNet.

[0047] The framework of the deep model used for joint inversion is as shown in Figure 3As shown, the network has four layers on each side, containing a total of 17 convolutional layers, 3 pooling layers, and 3 transposed convolutional layers. Because the receiving function data contains a large number of negative numbers, the ELU activation function is chosen to apply to the output of the convolutional layers. This activation function can avoid information loss in the negative values ​​and gradient vanishing. After the convolution operation, Batch normalization is used to standardize the data to further prevent gradient vanishing or gradient explosion, while also increasing the regularization effect.

[0048] The reason why the receiver function and surface wave dispersion can be considered as two parallel input channels is that these two types of data reflect the true nature of the model from different perspectives. Just as the input of an image can consist of three channels representing different pixels, each channel contains some features of the image.

[0049] Figure 4(a) shows the evolution of the loss function during training. Similar to the individual inversion of the receiver function, the errors in the training and test sets from the joint inversion gradually decrease with increasing iterations, eventually falling below 0.001. This indicates that the model can effectively learn the features in the training set. Figure 4(b) shows the residuals between the prediction results and labels for a portion of the test set. The histogram exhibits a normal distribution, with maxima almost at 0, demonstrating the least-squares assumption of the residual error and the good performance of the algorithm. It also shows that the joint inversion can effectively constrain the absolute velocity value of Vs.

[0050] After the UNet model is trained, the new receiver function and surface wave dispersion data are used as inputs. The network can quickly output the crustal velocity model, i.e. the prediction result, through forward propagation.

[0051] To demonstrate the effectiveness and applicability of the proposed inversion scheme, such as Figure 5 As shown, this invention presents multiple synthetic model inversion results from a test dataset, where Depth is the depth and V is the depth. s This represents the S-wave velocity. The thick line indicates the actual model, while the thick line with small dots represents the predicted result, which is the average of 100 models (represented by thin lines) estimated by applying 10% random noise to the observed data. A 10% random noise was applied to the receiver function of the "observed" data to further estimate the uncertainty of the inversion. The perturbation δr follows a uniform distribution δr~U(-σ,+σ), where σ is the uncertainty at each point. Each model corresponds to the receiver function waveforms and surface wave dispersion curves of 100 perturbations, which, together, are used as input to U-Net to predict the 1D shear wave velocity structure. The predicted models form a narrow band, indicating that U-Net has a certain noise resistance and can predict the subsurface V-wave velocity relatively well. s distributed.

[0052] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

Claims

1. A UNet-based joint inversion method of receiver functions and surface wave dispersion, characterized in that, The method comprises the following steps: S1: constructing a velocity model and performing forward calculation to obtain a training data set; comprising: S11: constructing a four-layer velocity model comprising the upper crust, the middle crust, the lower crust and the upper mantle; S12: interpolating the four-layer velocity model to obtain a first data set and a second data set; S13: performing forward calculation of the first data set and the second data set to obtain the training data set; S2: constructing a UNet, training the UNet by using the training data set, and taking the to-be-inverted receiver function and surface wave dispersion data as the input of the UNet to obtain the velocity structure of the crust and the upper mantle; wherein the UNet comprises 17 convolution layers, 3 pooling layers and 3 transposed convolution layers. Objective function of UNet in training process The calculation formula is: where, N denotes the total number of training samples, m i denotes the label corresponding to the i th sample, D (·) denotes the inversion operator implemented by deep learning, d i denotes the input data, θ denotes the hyperparameters that need to be updated in UNet backpropagation.

2. The UNet-based joint inversion method of the reception function and surface wave dispersion according to claim 1, characterized in that, In the step S12, when the perturbation of the velocity model is 10%, the four-layer velocity model is interpolated to obtain the first data set. 3.The UNet-based joint inversion method of receiver functions and surface wave dispersion according to claim 1, characterized in that, In the step S12, when the perturbation of the velocity model is 20%, each layer of the velocity model is divided into two sub-layers to obtain an eight-layer velocity model, and the eight-layer velocity model is interpolated to obtain the second data set. 4.The UNet-based joint inversion method of receiver functions and surface wave dispersion according to claim 1, characterized in that, In the step S2, the ELU function is the activation function of the convolution layer of the UNet.

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