A multiscale convolution mangabey seismic data interpolation denoising synchronous processing method and system

Abstract

The application discloses a multiscale convolutional Mamba seismic data interpolation denoising synchronous processing method and system, solves the problems of error transmission of the existing serial process, strong dependence of fixed priori and difficulty of expressing two-dimensional long-range structure of a single convolutional network. The application constructs noisy missing input data through a sampling mask; a multiscale convolutional Mamba fusion network is constructed; in the encoding stage, four scales are used for step-by-step down-sampling, local detail features are extracted by a convolutional branch of each scale, a Mamba global branch is used for modeling cross-lane long-range dependence through two-dimensional selective scanning, and attention fusion is performed through a residual channel; meanwhile, discrete wavelet transform is used to decompose features into low-frequency large-scale and multi-directional high-frequency small-scale components; in the decoding stage, resolution is restored through inverse discrete wavelet transform, and multiscale features are fused through a skip connection; and a composite loss function is used for training. Through local-global collaboration and multiscale frequency band decomposition, the application can suppress noise and complete missing traces at the same time, and is used for synchronous processing of seismic data.

Description

Technical Field

[0001] A multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing method and system are proposed for high-fidelity reconstruction and denoising synchronous processing of seismic data under conditions of random missing traces, continuous missing traces, and random noise coupling. This method belongs to the fields of seismic data processing, artificial intelligence geophysics, and oil and gas exploration and development technology. Background Technology

[0002] Regular sampling and high signal-to-noise ratio recording of seismic data are crucial for obtaining reliable information about subsurface structures. During actual seismic acquisition, factors such as complex terrain, near-surface conditions, irregular observation systems, detector or shot point malfunctions, construction limitations, and instrument interference often result in random and continuous missing traces in seismic records. Furthermore, complex near-surface conditions, environmental vibrations, and differences in instrument response introduce random noise, disrupting the continuity, amplitude relationships, and phase characteristics of effective reflected signals.

[0003] Traditional seismic data processing typically treats missing trace interpolation and random noise suppression as two relatively independent steps performed sequentially. Common interpolation methods include fx predictive filtering, Fourier domain interpolation, compressed sensing reconstruction, low-rank reconstruction, curvelet or Seislet sparse representation, etc.; common denoising methods include predictive filtering, structure-guided filtering, wavelet thresholding, curvelet thresholding, dictionary learning, and low-rank denoising, etc. These methods have clear mathematical or physical priors, but most rely on assumptions such as locally linear phase axes, sparse spectra, low-rank structures, stable dip angles, or fixed transform bases. When seismic data contains complex structures, curved phase axes, fault boundaries, continuous large-interval missing traces, or low signal-to-noise ratio weak reflections, fixed priors are prone to mismatch, leading to broken axes, amplitude deviations, or tectonic artifacts in the interpolation results.

[0004] Traditional serial interpolation denoising processes are prone to error propagation. In a process where interpolation precedes denoising, random noise may be misidentified as continuous, valid reflection signals and participate in missing trace reconstruction during the interpolation stage. Conversely, in a process where denoising precedes interpolation, weak reflections, small amplitude anomalies, and local phase information may be over-smoothed during the denoising stage, thereby reducing the reliability of subsequent interpolation constraints. For applications such as reservoir prediction, fracture system characterization, thin-layer identification, and time-lapse monitoring, weak reflections, local amplitude anomalies, and fracture boundaries often have significant geological implications. Therefore, interpolation denoising methods not only need to improve the accuracy of numerical reconstruction but also should strive to maintain the spatial continuity of phase axes, the relative amplitude relationships, and local boundary characteristics.

[0005] In recent years, deep learning methods have been gradually introduced into seismic data recovery tasks. Convolutional neural networks (CNNs) can learn the nonlinear mapping relationship between noisy, missing data and complete data through end-to-end training, demonstrating strong capabilities in random noise suppression, seismic interpolation, and image-based reconstruction. However, CNNs mainly rely on limited local receptive fields to extract features. Although stacked convolutions and encoder-decoder structures can expand the receptive range, they are still insufficient for expressing long-range structural dependencies across channels and time directions. Under conditions of continuous missing channels, high missing rates, and strong noise, relying solely on local convolutions can easily lead to phase axis breakage, local amplitude smoothing, and insufficient recovery of weak reflections.

[0006] The Mamba model offers a novel technical approach to long-sequence modeling. Through selective state updates based on input dependencies and a parallel scanning mechanism, the Mamba can model long-range dependencies with near-linear complexity. However, the standard Mamba is primarily designed for one-dimensional sequence data, while seismic profiles typically exhibit a two-dimensional organizational structure, with phase axis morphology controlled by both the temporal sampling direction and the seismic trace direction. Simply flattening a two-dimensional seismic feature map into a one-dimensional sequence may disrupt the original spatial adjacency relationships and directional information, affecting the continuity of phase axes at missing trace locations and the recovery of complex structural boundaries.

[0007] In summary, the existing technology has the following technical problems:

[0008] 1. Existing serial interpolation denoising processes are prone to error propagation;

[0009] 2. Traditional model-driven methods have the problem of relying heavily on fixed priors and the difficulty of a single convolutional network in representing two-dimensional long-range in-phase axis structures;

[0010] 3. When existing sequence modeling methods are applied to two-dimensional seismic data, it is usually necessary to expand the two-dimensional features into a one-dimensional sequence along a single path. This can easily disrupt the original spatial adjacency and directional relationship between the time sampling direction and the seismic trace direction, limit the information propagation capability of reflection structures in different directions, and is not conducive to the recovery of bending phase axes, tilted reflections and fracture boundaries.

[0011] 4. Existing encoder-decoder networks typically use pooling operations for downsampling and interpolation or transposed convolution for upsampling. During scaling, high-frequency details such as weak reflections, thin-layer responses, local boundaries, and amplitude abrupt changes are easily lost. Furthermore, the upsampling process may introduce local reconstruction artifacts, affecting the waveform consistency and local structure fidelity of the recovered data.

[0012] 5. Existing seismic data recovery methods, under the condition of mixed missing data and random noise, have difficulty simultaneously taking into account the reconstruction of missing areas, the preservation of amplitude in effective observation areas, the continuity of the phase axis structure, and the protection of local boundaries. They are prone to problems such as insufficient noise suppression, damage to effective weak signals, or overly smooth reconstruction results.

[0013] Therefore, there is an urgent need for a seismic data interpolation and denoising synchronous processing method that can simultaneously utilize local waveform features, two-dimensional long-range structural relationships, and multi-scale frequency band information within a unified framework. Summary of the Invention

[0014] To address the aforementioned technical problems, the present invention aims to provide a method and system for synchronous processing of multi-scale convolutional Mamba seismic data interpolation and denoising, thereby solving problems such as the easy generation of error propagation in existing serial interpolation denoising processes, the strong dependence of traditional model-driven methods on fixed priors, and the difficulty of a single convolutional network in representing two-dimensional long-range in-phase axis structures.

[0015] To achieve the above objectives, the present invention adopts the following technical solution:

[0016] A method for simultaneous interpolation, denoising, and processing of multi-scale convolutional Mamba seismic data includes the following steps:

[0017] Step 1: Obtain the seismic data to be processed and construct the sampling mask. ;

[0018] Step 2: Based on the sampling mask Constructing noisy, missing input data:

[0019]

[0020] in, This indicates noisy and missing input data. Represents random noise, and ⊙ represents element-wise product. Represents complete target seismic data free of random noise;

[0021] Step 3: Construct a multi-scale convolutional Mamba fusion network, including an encoding stage and a decoding stage. The encoding stage includes a 1×1 convolutional layer that performs 1×1 convolution operations on noisy and missing input data and a sampling mask to obtain input features, connected sequentially; four encoding units that perform encoding operations on the input features sequentially; each encoding unit includes a local convolutional feature extraction branch that extracts local features and global state features of the input features at the corresponding encoding scale; a Mamba global state modeling branch based on visual state space; a residual channel attention fusion module that fuses local feature extraction and global state features; and a multi-scale wavelet transform downsampling layer that performs discrete wavelet transform on the features fused by the residual channel attention fusion module to obtain the input features at the next encoding scale.

[0022] The decoding stage uses inverse discrete wavelet transform to recover the spatial resolution of the output features of the deepest coding scale in the coding stage step by step, and receives the fused features of the corresponding scale in the coding stage through skip connections.

[0023] Step 4: Train a multi-scale convolutional Mamba fusion network using a composite loss function and dataset. The composite loss function includes partition reconstruction loss, structural similarity loss, and gradient consistency loss.

[0024] Step 5: Based on the trained multi-scale convolutional Mamba fusion network, perform missing trace completion and random noise suppression on pre-stack gathers or post-stack seismic profiles to obtain complete denoised seismic data.

[0025] Furthermore, the specific steps of step 1 are as follows:

[0026] Step 1.1: Obtain the seismic data to be processed, and determine the missing locations of random traces and continuous traces based on trace head information, seismic trace arrangement information, or preset missing patterns.

[0027] Step 1.2: Construct an entire-channel sampling mask based on the missing locations of random and continuous channels determined in Step 1.1. Specifically, this involves setting the mask value of all time sampling points for the seismic traces corresponding to the missing positions of the random and continuous traces to 0, and setting the mask value of all time sampling points corresponding to the remaining valid seismic traces to 1. Indicates the location of the missing lane. Indicates the location of the effective observation channel.

[0028] Furthermore, the local convolutional feature branch in step 3 includes two consecutive 3×3 convolutional layers, a batch normalization layer, and... The extraction process of local convolutional features in the activation function layer can be represented as follows:

[0029]

[0030]

[0031] in, Indicates the first Input features at each scale, when hour, The input features are obtained from a 1×1 convolutional layer, when hour, For the input features at the current coding scale, Indicates the first Local convolutional feature extraction branches at each scale The extracted first The output features of the coding unit at the i-th scale, that is, the i-th Local convolutional features mapped at each scale This represents the convolution operation of the first-level 3×3 convolutional layer. This represents the convolution operation of the second-level 3×3 convolutional layer. This indicates a batch normalization operation. This represents the activation function. express The input variables of the activation function, Represents the hyperbolic tangent function. Represents the natural logarithm function. Represents the natural constant;

[0032] Among them, the The 3×3 convolutional layer at level 3 is in the first stage. Location at each scale , No. The specific calculation process for each output channel is as follows:

[0033]

[0034] in, , Indicates the first The input features of the 3×3 convolutional layer at the location and the The response value on each input channel , Indicates the first The number of input channels for a 3×3 convolutional layer. Indicates the first In a 3×3 convolutional layer, the first The input channel and the first Between output channels, convolution kernel position The weight of the position, Indicates the first In a 3×3 convolutional layer, the first The bias term for each output channel.

[0035] Furthermore, the specific implementation steps of the Mamba global state modeling branch based on the visual state space in step 3 are as follows:

[0036] The first Input features at each coding scale The input Mamba global state modeling branch performs layer normalization and linear mapping on the input features sequentially to obtain intermediate features, namely two-dimensional seismic features:

[0037]

[0038] in, Representation layer normalization, This represents a linear projection operation;

[0039] Two-dimensional selective scanning was used to rearrange the two-dimensional seismic features, organizing them into multiple directional sequences along multiple scanning paths along the time sampling direction and the seismic trace direction:

[0040]

[0041] in, This indicates different scanning directions, including the time sampling direction and the seismic trace direction. Indicates the number of scan paths. Indicates the first Two-dimensional seismic feature sequences in each scanning direction, Indicates two-dimensional selective scanning;

[0042] Based on multiple direction sequences Selective state-space modeling is performed for each direction sequence. For the first... The state update and output process of the direction sequence corresponding to each scan path can be represented as follows:

[0043]

[0044] in, Indicates the first On the first scale The first scan path The hidden state of each location, Indicates the first On the first scale The first scan path Output features at each position, Indicates the first On the first scale The first scan path Input mapping parameters for each position, Indicates the first On the first scale The first scan path Output mapping parameters at each position, This represents the pass-through parameter from input to output. Indicates the first On the first scale The first scan path State transition parameters at each position, No. On the first scale The first scan path Input features at each location;

[0045] The output sequences obtained from each scanning direction are restored to the two-dimensional feature domain according to the corresponding scanning path, and then fused through a cross-merging operation to obtain the global state features output by the Mamba global state modeling branch:

[0046]

[0047]

[0048] in, Indicates the first The output sequence corresponding to each scan path. Indicates the first The total length of the sequence corresponding to each scan path. This involves restoring the output sequences from multiple directions to a two-dimensional feature domain and performing a cross-merging operation. This indicates a linear projection operation at the output. Indicates the first Mamba global state modeling branch at various scales Output global state characteristics;

[0049] Furthermore, the specific steps of the residual channel attention fusion module in step 3 are as follows:

[0050] First, channel mapping is performed using a 1×1 convolution, with the following formula:

[0051]

[0052] in, and These represent the local convolutional features, respectively. and global state features Perform channel projection operation. and They represent respectively to and The result after performing channel projection operation;

[0053] Next, the two types of features are concatenated along the channel dimension, and their joint feature is represented as:

[0054]

[0055] in, This indicates a channel-level concatenation operation;

[0056] joint features Global average pooling is performed using the following formula:

[0057]

[0058] in, No. The joint features of each scale in the first... Global statistical response on each channel and They represent the first Spatial dimensions of feature maps at each size Indicates the spatial location of joint features Passing the exam Response values ​​on each channel;

[0059] The first is generated through lightweight nonlinear mapping. Channel attention weights of each size:

[0060]

[0061] in, and Indicates learnable mapping parameters, Represents a non-linear activation function. express function, Indicates the first Channel attention weights of each size, Represents the global statistical response of each channel. The channel description vector is composed of;

[0062] Ultimately, the fusion process can be represented as:

[0063]

[0064] in, Represents element-wise product. Indicates output channel mapping. This is to integrate local and global features.

[0065] 6. The multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing method according to claim 5, characterized in that: the multi-scale wavelet transform downsampling layer in step 3 fuses the local and global features. Performing discrete wavelet transform yields low-frequency large-scale components and high-frequency small-scale components in multiple directions, as shown in the formula:

[0066]

[0067] in, Represents discrete wavelet transform. This represents the low-frequency, large-scale components, characterizing the overall trend of seismic reflections, background tectonics, and the continuity of large-scale phase axes. , and These represent high-frequency small-scale components in different directions, characterizing local boundaries, amplitude abrupt changes, thin-layer responses, small-scale texture changes, and discontinuous reflection details.

[0068] The low-frequency large-scale components and high-frequency small-scale components in multiple directions are concatenated along the channel dimension, and the number of channels is adjusted by 1×1 convolution to obtain the input features for the next scale. The formula is as follows:

[0069]

[0070] in, This indicates a channel-level concatenation operation. This represents a 1×1 convolution mapping operation. Indicates the first Input features at each scale.

[0071] Furthermore, in step 3, the decoding stage recovers the feature space resolution step by step according to the reverse scale order of the encoding stage. The specific steps are as follows:

[0072] Using the output features of the deepest coding scale as the initial input features for the decoding stage, for the data from the 3rd coding scale... The scale was restored to the first The decoding process at the nth scale, let the nth scale be... The decoding input features at each scale are During the initial decoding, The output features at the deepest coding scale will be used in subsequent decoding processes. The corresponding scale decoding features output by the previous decoding unit:

[0073]

[0074] in, This indicates a sub-band mapping operation. These represent the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions used for inverse wavelet reconstruction, respectively.

[0075] Subsequently, the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions are recovered to the nth level using inverse discrete wavelet transform. Spatial resolution at each scale:

[0076]

[0077] in, This represents the inverse discrete wavelet transform, which in turn represents upsampling. Represents the th wavelet after inverse wavelet transform. The scale feature refers to the first scale feature. Spatial resolution at various scales;

[0078] The features obtained during the encoding stage are a fusion of local and global features. The first obtained in the decoding stage Individual scale features The corresponding scale-skip connections are fused along the channel dimension, and the result is obtained through a convolutional thinning operation. Decoding output features at each scale:

[0079]

[0080] in, This indicates the subsequent convolution thinning operation;

[0081] Based on Perform step-by-step decoding to obtain the decoded output features at the highest spatial resolution scale. ;

[0082] Finally, the decoded output features are obtained through 1×1 convolution. Mapping to the single-channel seismic data space, we obtain the final interpolation and denoising results from the multi-scale convolutional Mamba fusion network:

[0083]

[0084] in, This represents the seismic data interpolation and denoising results output by the multi-scale convolutional Mamba fusion network.

[0085] Furthermore, in step 4:

[0086] The composite loss function is:

[0087]

[0088] Partition reconstruction loss is

[0089]

[0090] The structural similarity loss is:

[0091]

[0092] The gradient consistency loss is:

[0093]

[0094] in, represent the weights of the partition reconstruction loss, structural similarity loss, and gradient consistency loss, respectively. and These represent the weights of the missing region and the valid observation region, respectively. To prevent extremely small constants with a denominator of 0, Gradient operator along the direction of seismic trace arrangement, This represents the gradient operator along the time sampling direction. Describes the norm, Indicates the sampling mask. This represents complete target seismic data that is free of random noise.

[0095] A multi-scale convolutional Mamba seismic data interpolation and denoising synchronous processing system includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the multi-scale convolutional Mamba seismic data interpolation and denoising synchronous processing method.

[0096] Compared with the prior art, the beneficial effects of this invention are as follows:

[0097] I. This invention unifies interpolation and denoising into a reconstruction task under the same mask constraint, which can reduce the risk of interpolation error and denoising error amplifying each other in the serial process. That is, this invention models seismic data interpolation and random noise suppression in a unified manner, avoiding the error propagation problem that may occur in the traditional serial process of "interpolation first, then denoising" or "denoising first, then interpolation". It can suppress random noise while restoring missing samples, and improve the consistency and stability of the seismic data processing process.

[0098] Second, the local convolutional feature extraction branch and the Mamba global state modeling branch based on visual state space work together in this invention, enabling the multi-scale convolutional Mamba fusion network to have both the ability to preserve weak reflection details and the ability to continue long-range phase axes in continuous missing regions. That is, this invention extracts amplitude changes, short-period waveforms, weak reflection details and local boundary information within the neighborhood through the local convolutional feature extraction branch, which is beneficial to preserve the local amplitude characteristics, thin-layer response and small-scale reflection structure in the seismic profile, and reduces the problem of excessive smoothing of effective weak signals during interpolation and denoising. The Mamba global state modeling branch based on visual state space performs multi-directional state propagation and context aggregation of seismic features through two-dimensional selective scanning, which can simultaneously establish long-range structural connections in the time sampling direction and the seismic trace direction, and enhance the ability to continue phase axes in continuous missing traces, curved phase axes and complex tectonic backgrounds.

[0099] Third, the present invention uses a residual channel attention fusion module to adaptively fuse local convolutional features and global state features. It can dynamically allocate weights according to the contribution of different channel features to the current reconstruction task, which avoids the weakening of local weak reflections by global features and reduces the impact of local noise and texture on the reconstruction results, thereby improving the balance between local detail preservation and overall structural continuity.

[0100] Fourth, the wavelet scaling transform in this invention can preserve multi-band information during downsampling and upsampling, and reduce the loss of high-frequency details and reconstruction artifacts caused by traditional pooling and transposed convolution. This invention uses discrete wavelet transform to replace traditional max pooling for encoding downsampling, and uses inverse discrete wavelet transform to replace transposed convolution for decoding upsampling. It can preserve low-frequency construction trends and high-frequency boundary details during scaling, and reduce the loss of high-frequency information caused by conventional pooling and the reconstruction artifacts that may be introduced by transposed convolution.

[0101] V. The composite loss function in this invention simultaneously constrains amplitude fidelity, structural continuity, and local gradient consistency, which can improve the balance between missing trace completion, random noise suppression, and effective signal protection of seismic data.

[0102] VI. This invention is applicable to seismic data reconstruction scenarios with random missing traces, continuous missing traces, and random noise. It can improve the waveform consistency, phase axis continuity, and amplitude fidelity of missing trace completion results, providing higher quality basic data for subsequent migration imaging, attribute analysis, reservoir prediction, and seismic interpretation. Attached Figure Description

[0103] Figure 1 This is a schematic diagram of the seismic data interpolation, denoising, and synchronization processing method in this invention;

[0104] Figure 2 This is a schematic diagram of the structure of the multi-scale convolutional Mamba fusion network of the present invention;

[0105] Figure 3 These are the noisy missing data and label data for training input in this invention. The four images in the upper row are complete label data of four different random earthquake reflection structures. The lower row is the training input data formed by adding random noise and applying random and continuous trace missing masks to the corresponding images in the upper row.

[0106] Figure 4 These are the original data and input data in this invention. The first figure is the original complete seismic data after stacking for testing, and the second figure is the noisy missing seismic data formed by adding random noise to the original data after stacking and applying a full-channel missing mask.

[0107] Figure 5 These are the denoised reconstruction results and residual maps in this invention. The first map is the denoised prediction result of the post-stack seismic data interpolation output by the multi-scale convolutional Mamba fusion network, and the second map is the residual between the prediction result and the complete reference seismic data.

[0108] Figure 6The first figure shows the original data of a certain pre-stack shot set and the denoising and reconstruction results. The second figure shows the prediction results of the actual shot set after interpolation and denoising by a multi-scale convolutional Mamba fusion network.

[0109] Figure 7 The first figure is the fk spectrum comparison of the actual pre-stack shot set data and the denoised reconstruction prediction results in this invention. The second figure is the fk spectrum of the actual noisy missing shot set. Detailed Implementation

[0110] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0111] like Figure 1 As shown, a multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing method includes the following steps:

[0112] Step 1: Obtain the seismic data to be processed and construct the sampling mask. ;

[0113] The specific steps are as follows:

[0114] Step 1.1: Obtain the seismic data to be processed, and determine the missing locations of random traces and continuous traces based on trace head information, seismic trace arrangement information, or preset missing patterns.

[0115] Step 1.2: Construct an entire-channel sampling mask based on the missing locations of random and continuous channels determined in Step 1.1. Specifically, this involves setting the mask value of all time sampling points for the seismic traces corresponding to the missing positions of the random and continuous traces to 0, and setting the mask value of all time sampling points corresponding to the remaining valid seismic traces to 1. Indicates the location of the missing lane. Indicates the location of the valid observation channel, with the sampling mask as follows: ,in, Indicates the number of samples taken in the direction of the seismic trace. Indicates the number of time sampling points.

[0116] Step 2: Based on the sampling mask Constructing noisy, missing input data:

[0117]

[0118] in, This indicates noisy and missing input data, such as Figure 3 The bottom row shows and Figure 4 As shown in the second figure, Represents random noise, and ⊙ represents element-wise product. Represents complete target seismic data free of random noise, such as Figure 3 The top row shows and Figure 4 As shown in the first figure;

[0119] Step 3: Construct a multi-scale convolutional Mamba fusion network, such as... Figure 2 As shown, it includes an encoding stage and a decoding stage. The encoding stage includes a 1×1 convolutional layer that performs a 1×1 convolution operation on the noisy and missing input data and the sampling mask to obtain the input features, which are connected in sequence; four encoding units that perform encoding operations on the input features in sequence; each encoding unit includes a local convolutional feature extraction branch that performs local feature extraction and global state feature extraction on the input features at the corresponding encoding scale; a Mamba global state modeling branch based on the visual state space; a residual channel attention fusion module that fuses the local feature extraction and global state features; and a multi-scale wavelet transform downsampling layer that performs discrete wavelet transform on the features fused by the residual channel attention fusion module to obtain the input features at the next encoding scale.

[0120] The local convolution feature extraction branch is used to extract local features from seismic data, such as neighborhood waveforms, short-period in-phase axes, weak reflection details, amplitude abrupt change interfaces, and thin-layer responses.

[0121] The local convolutional feature branch includes two consecutive 3×3 convolutional layers, a batch normalization layer, and... An activation function layer is used to expand the effective receptive field and improve training convergence stability while maintaining a low number of parameters. The formula is as follows:

[0122]

[0123]

[0124] in, Indicates the first Input features at each scale, when hour, The input features are obtained from a 1×1 convolutional layer, when hour, For the input features at the current coding scale, Indicates the first Local convolutional feature extraction branches at each scale The extracted first The output features of the coding unit at the i-th scale, that is, the i-th Local convolutional features mapped at each scale This represents the convolution operation of the first-level 3×3 convolutional layer. This represents the convolution operation of the second-level 3×3 convolutional layer. This indicates a batch normalization operation. This represents an activation function whose continuous, smooth, and non-monotonic properties help maintain the continuity of weak reflections and small-amplitude anomalies in the propagation of deep features. express The input variables of the activation function, Represents the hyperbolic tangent function. Represents the natural logarithm function. Represents the natural constant;

[0125] Among them, the The 3×3 convolutional layer at level 3 is in the first stage. Location at each scale , No. The specific calculation process for each output channel is as follows:

[0126]

[0127] in, , Indicates the first The input features of the 3×3 convolutional layer at the location and the The response value on each input channel , Indicates the first The number of input channels for a 3×3 convolutional layer. Indicates the first In a 3×3 convolutional layer, the first The input channel and the first Between output channels, convolution kernel position The weight of the position, Indicates the first In a 3×3 convolutional layer, the first The bias term for each output channel.

[0128] To enhance the model's ability to perceive long-range structures such as continuous missing regions and curved in-phase axes, this invention sets up a Mamba global state modeling branch based on the visual state space, in addition to the local convolutional feature extraction branch. The Mamba global state modeling branch in the multi-scale convolutional Mamba fusion network is based on the state space model and achieves long-program sequence dependency modeling through a selective state update mechanism that depends on the input.

[0129] The specific implementation steps of the Mamba global state modeling branch based on the visual state space in step 3 are as follows:

[0130] The first Input features at each coding scale The input Mamba global state modeling branch performs layer normalization and linear mapping on the input features sequentially to obtain intermediate features, namely two-dimensional seismic features:

[0131]

[0132] in, Representation layer normalization, This represents a linear projection operation;

[0133] Two-dimensional selective scanning was used to rearrange the two-dimensional seismic features, organizing them into multiple directional sequences along multiple scanning paths along the time sampling direction and the seismic trace direction:

[0134]

[0135] in, This indicates different scanning directions, including the time sampling direction and the seismic trace direction. Indicates the number of scan paths. Indicates the first Two-dimensional seismic feature sequences in each scanning direction, Indicates two-dimensional selective scanning;

[0136] Based on multiple direction sequences Selective state-space modeling is performed for each direction sequence. For the first... The state update and output process of the direction sequence corresponding to each scan path can be represented as follows:

[0137]

[0138] in, Indicates the first On the first scale The first scan path The hidden state of each location, Indicates the first On the first scale The first scan path Output features at each position, Indicates the first On the first scale The first scan path Input mapping parameters for each position, Indicates the first On the first scale The first scan path Output mapping parameters at each position, This represents the pass-through parameter from input to output. Indicates the first On the first scale The first scan path State transition parameters at each position, No. On the first scale The first scan path Input features at each location;

[0139] The output sequences obtained from each scanning direction are restored to the two-dimensional feature domain according to the corresponding scanning path, and then fused through a cross-merging operation to obtain the global state features output by the Mamba global state modeling branch:

[0140]

[0141]

[0142] in, Indicates the first The output sequence corresponding to each scan path. Indicates the first The total length of the sequence corresponding to each scan path. This involves restoring the output sequences from multiple directions to a two-dimensional feature domain and performing a cross-merging operation. This indicates a linear projection operation at the output. Indicates the first Mamba global state modeling branch at various scales Output global state characteristics;

[0143] The local convolutional feature extraction branch primarily responds to weak reflection details, local boundaries, and short-period waveforms, while the Mamba global state modeling branch primarily responds to long-range structural dependencies across channels and time directions. To avoid imbalanced feature contributions caused by simple addition or concatenation, this invention employs a residual channel attention module to adaptively fuse the two types of features.

[0144] The specific steps of the residual channel attention fusion module in step 3 are as follows:

[0145] First, channel mapping is performed using a 1×1 convolution, with the following formula:

[0146]

[0147] in, and These represent the local convolutional features, respectively. and global state features Perform channel projection operation. and They represent respectively to and The result after performing channel projection operation;

[0148] Next, the two types of features are concatenated along the channel dimension, and their joint feature is represented as:

[0149]

[0150] in, This indicates a channel-level concatenation operation;

[0151] joint features Global average pooling is performed using the following formula:

[0152]

[0153] in, No. The joint features of each scale in the first... Global statistical response on each channel and They represent the first Spatial dimensions of feature maps at each size Indicates the spatial location of joint features Passing the exam Response values ​​on each channel;

[0154] The first is generated through lightweight nonlinear mapping. Channel attention weights of each size:

[0155]

[0156] in, and Indicates learnable mapping parameters, Represents a non-linear activation function. express function, Indicates the first Channel attention weights of each size, Represents the global statistical response of each channel. The channel description vector is composed of;

[0157] Ultimately, the fusion process can be represented as:

[0158]

[0159] in, Represents element-wise product. Indicates output channel mapping. This is to integrate local and global features.

[0160] The multi-scale wavelet transform downsampling layer in step 3 is set in the multi-scale coding stage to establish wavelet multi-scale constraints between adjacent coding scales; for the l-th coding scale, the fused features output by the residual channel attention fusion module are used. Discrete wavelet transform is performed to obtain low-frequency large-scale sub-band features and high-frequency small-scale sub-band features in multiple directions, so as to preserve the overall structural trend and local detail information at different scales respectively. The formula is as follows:

[0161]

[0162] in, Represents discrete wavelet transform. This represents the low-frequency, large-scale components, characterizing the overall trend of seismic reflections, background tectonics, and the continuity of large-scale phase axes. , and These represent high-frequency small-scale components in different directions, characterizing local boundaries, amplitude abrupt changes, thin-layer responses, small-scale texture changes, and discontinuous reflection details.

[0163] The low-frequency large-scale components and high-frequency small-scale components in multiple directions are concatenated along the channel dimension, and the number of channels is adjusted by 1×1 convolution to obtain the input features for the next scale. The formula is as follows:

[0164]

[0165] in, This indicates a channel-level concatenation operation. This represents a 1×1 convolution mapping operation. Indicates the first Input features at each scale.

[0166] The decoding stage uses inverse discrete wavelet transform to recover the spatial resolution of the output features of the deepest coding scale in the coding stage step by step, and receives the fused features of the corresponding scale in the coding stage through skip connections.

[0167] The decoding stage in step 3 restores the feature space resolution step by step in the reverse scale order of the encoding stage. The specific steps are as follows:

[0168] Using the output features of the deepest coding scale as the initial input features for the decoding stage, for the data from the 3rd coding scale... The scale was restored to the first The decoding process at the nth scale, let the nth scale be... The decoding input features at each scale are During the initial decoding, The output features at the deepest coding scale will be used in subsequent decoding processes. The corresponding scale decoding features output by the previous decoding unit:

[0169]

[0170] in, This indicates a sub-band mapping operation. These represent the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions used for inverse wavelet reconstruction, respectively.

[0171] Subsequently, the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions are recovered to the nth level using inverse discrete wavelet transform. Spatial resolution at each scale:

[0172]

[0173] in, This represents the inverse discrete wavelet transform, which in turn represents upsampling. Represents the th wavelet after inverse wavelet transform. The scale feature refers to the first scale feature. Spatial resolution at various scales;

[0174] The features obtained during the encoding stage are a fusion of local and global features. The first obtained in the decoding stage Individual scale features The corresponding scale-skip connections are fused along the channel dimension, and the result is obtained through a convolutional thinning operation. Decoding output features at each scale:

[0175]

[0176] in, This indicates the subsequent convolution thinning operation;

[0177] Based on Perform step-by-step decoding to obtain the decoded output features at the highest spatial resolution scale. ;

[0178] Finally, the decoded output features are obtained through 1×1 convolution. Mapping to the single-channel seismic data space, we obtain the final interpolation and denoising results from the multi-scale convolutional Mamba fusion network:

[0179]

[0180] in, This represents the seismic data interpolation and denoising results output by the multi-scale convolutional Mamba fusion network.

[0181] This invention employs discrete wavelet transform in the encoding stage. Instead of traditional max pooling for downsampling, inverse discrete wavelet transform is used in the decoding stage. Upsampling is performed instead of transposed convolution. This allows multi-scale convolutional Mamba fusion networks to simultaneously preserve low-frequency structural trends and high-frequency local details during scale changes, reducing high-frequency information loss caused by traditional pooling and mitigating local artifacts introduced by transposed convolution during reconstruction. Figure 5 The first figure shows the interpolated and denoised prediction results of post-stack seismic data output by the multi-scale convolutional Mamba fusion network; the second figure shows the residuals between the prediction results and the complete reference seismic data. Figure 6 The first figure is a real noisy missing shot set; the second figure is the prediction result of the multi-scale convolutional Mamba fusion network after interpolation and denoising of the real shot set.

[0182] To achieve a stable balance between interpolation recovery, noise suppression, and effective signal preservation in the multi-scale convolutional Mamba fusion network, this invention employs a composite loss function consisting of partition reconstruction loss, structural similarity loss, and gradient consistency loss. Partition reconstruction loss is used to constrain missing regions and effective observation regions separately; structural similarity loss is used to constrain the consistency of the in-phase axis and local texture structure; and gradient consistency loss is used to constrain gradient differences in the trace direction and temporal sampling direction. This loss helps preserve reflective interfaces, thin-layer boundaries, and local waveform variations, preventing important structures from being over-smoothed during denoising.

[0183] Step 4: Train a multi-scale convolutional Mamba fusion network using a composite loss function and dataset. The composite loss function includes partition reconstruction loss, structural similarity loss, and gradient consistency loss.

[0184] The composite loss function is:

[0185]

[0186] Partition reconstruction loss is

[0187]

[0188] The structural similarity loss is:

[0189]

[0190] The gradient consistency loss is:

[0191]

[0192] in, represent the weights of the partition reconstruction loss, structural similarity loss, and gradient consistency loss, respectively. and These represent the weights of the missing region and the valid observation region, respectively. To prevent extremely small constants with a denominator of 0, Gradient operator along the direction of seismic trace arrangement, This represents the gradient operator along the time sampling direction. It represents the first norm. The focus is on the accuracy of interpolation recovery at the missing locations. The focus is on noise suppression and amplitude fidelity at effective observation locations. Indicates the sampling mask. This represents complete target seismic data that is free of random noise.

[0193] The dataset is constructed using synthetic seismic profiles and pre-stack shot sets from the SEG Open Seismic Data Repository. Complete, noise-free seismic data serves as the supervision label, and noisy, missing traces are generated as training input by setting random missing traces, consecutive missing traces, and random noise. The original seismic profiles or trace sets are first divided into training, validation, and test regions based on spatial location, profile number, or trace set number. Within each independent region, fixed-size blocks (e.g., 128×128 blocks) are extracted using a sliding window with a step size of 64. The training, validation, and test regions can be divided in an 8:1:1 ratio. The training set can be augmented using data augmentation methods such as rotation, while the validation and test sets are not augmented. The network can be trained using the Adam optimizer, with an initial learning rate of 0.001, a batch size of 32, and 60 training epochs. The learning rate is adjusted during training based on the validation set error.

[0194] Step 5: Based on the trained multi-scale convolutional Mamba fusion network, perform missing trace completion and random noise suppression on pre-stack gathers or post-stack seismic profiles.

[0195] After training, the multi-scale convolutional Mamba fusion network can be applied to synchronous interpolation and denoising tasks of actual pre-stack gathers or post-stack seismic profiles. For actual data, a sampling mask can be constructed based on acquisition geometry, trace head information, invalid value markings for entire traces, continuous blank traces, or manual interpretation results. The actual noisy and missing seismic data and the sampling mask are then input into the trained multi-scale convolutional Mamba fusion network to output complete denoised seismic data.

[0196] In real-world data where completely clean reference labels are unavailable, quality control can be achieved through methods such as reconstructed profile comparison, observation domain residual analysis, local magnification, local similarity maps, and frequency-wavenumber domain fk spectrum analysis. If the residual profile mainly presents a random background without continuous in-phase axes, it indicates that the model effectively protects the effective reflection signal while suppressing noise. If the main energy region remains intact and the scattered noise energy is reduced in the fk spectrum, it indicates that the model can maintain the spatial coherence of the seismic reflection signal well in the frequency-wavenumber domain.

[0197] This invention introduces local convolution feature extraction, Mamba 2D global state modeling based on visual state space, residual channel attention fusion, and wavelet multi-scale decomposition and reconstruction into the seismic data interpolation-denoising synchronous processing task. It unifies missing channel completion and random noise suppression into the same end-to-end reconstruction framework, and can simultaneously utilize the local waveform features, cross-channel long-range structural dependence, and multi-scale frequency band information of seismic data to improve the reconstruction accuracy and structural fidelity of noisy missing seismic data. This invention, by adopting the above technical solutions, has the following advantages: It unifies seismic data interpolation and random noise suppression into a single model, avoiding the error propagation problems that may occur in traditional serial processes of "interpolation first, then denoising" or "denoising first, then interpolation." This allows for the suppression of random noise while recovering missing samples, improving the consistency and stability of the seismic data processing flow. Furthermore, this invention extracts amplitude variations, short-period waveforms, weak reflection details, and local boundary information within the neighborhood using a UNet local convolutional feature extraction branch. This helps maintain local amplitude characteristics, thin-layer responses, and small-scale reflection structures in the seismic profile, reducing the problem of excessive smoothing of effective weak signals during interpolation and denoising. Finally, this invention introduces a Mamba global state modeling branch based on visual state space. Through two-dimensional selective scanning, it performs multi-directional state propagation and context aggregation of seismic features, enabling the simultaneous establishment of long-range structural connections in both the time sampling direction and the seismic trace direction. This enhances the in-phase characteristics of continuous missing traces, curved phase axes, and complex tectonic backgrounds. Axis continuity capability: This invention employs a residual channel attention fusion module to adaptively fuse local convolutional features and global state features. It dynamically allocates weights based on the contribution of different channel features to the current reconstruction task, avoiding the weakening of local weak reflections by global features and reducing the impact of local noise and texture on the reconstruction results. This improves the balance between preserving local details and maintaining overall structural continuity. This invention uses discrete wavelet transform instead of traditional max pooling for encoding downsampling and inverse discrete wavelet transform instead of transposed convolution for decoding upsampling. This preserves low-frequency structural trends and high-frequency boundary details during scale transformation, reducing high-frequency information loss caused by conventional pooling and reconstruction artifacts that may be introduced by transposed convolution. This invention is applicable to seismic data reconstruction scenarios with random missing, continuous missing, and random noise data. It improves waveform consistency, phase axis continuity, and amplitude fidelity of missing trace completion results, providing higher-quality basic data for subsequent migration imaging, attribute analysis, reservoir prediction, and seismic interpretation.

[0198] Through the aforementioned wavelet multi-scale decomposition and reconstruction, this invention achieves local detail extraction, global dependency modeling, local-global adaptive fusion, and multi-band decomposition in the encoding stage. In the decoding stage, it recovers seismic data step by step through inverse discrete wavelet transform, skip connections, and convolutional refinement. This structure can simultaneously utilize neighborhood waveform information, long-range structural constraints, and band decomposition features to suppress random noise while recovering missing traces, and to preserve the continuity of phase axes, weak reflection details, local amplitude anomalies, and tectonic boundary features as much as possible. Therefore, it is more suitable for handling the problem of integrated interpolation and denoising reconstruction of seismic data where missing samples and random noise coexist.

[0199] The multi-scale convolutional Mamba fusion network is trained using a composite loss function consisting of partition reconstruction loss, structural similarity loss, and gradient consistency loss. In the missing region, the focus is on interpolation recovery constraints, while in the effective observation region, the focus is on noise suppression and amplitude preservation constraints. The trained network is then applied to the pre-stack gathers or post-stack seismic profiles to be processed, outputting complete denoised seismic data. The quality control of the processing results is performed through reconstructed profiles, residual profiles, local similarity, or FK spectrum analysis.

[0200] like Figure 7 The left image shows a more diffuse background energy distribution with stronger noise components; the right image shows a more concentrated main effective energy cluster, with significantly suppressed low-amplitude background energy. The results demonstrate that the method of this invention can suppress the incoherent spectral energy corresponding to random noise while maintaining the main frequency-wavenumber energy distribution corresponding to seismic reflection events. No significant overall loss of effective frequency bands or enhancement of anomalous spectral energy occurs, further validating the interpolation denoising effect of this method from a frequency-wavenumber domain perspective.

[0201] The above are merely representative embodiments among the many specific applications of this invention, and do not constitute any limitation on the scope of protection of this invention. All technical solutions formed by transformation or equivalent substitution fall within the scope of protection of this invention.

Claims

1. A method for simultaneous interpolation, denoising, and processing of multi-scale convolutional Mamba seismic data, characterized in that: Includes the following steps: Step 1: Obtain the seismic data to be processed and construct the sampling mask. ; Step 2: Based on the sampling mask Constructing noisy, missing input data: in, This indicates noisy and missing input data. Represents random noise, and ⊙ represents element-wise multiplication. Represents complete target seismic data free from random noise; Step 3: Construct a multi-scale convolutional Mamba fusion network, including an encoding stage and a decoding stage. The encoding stage includes a 1×1 convolutional layer that performs 1×1 convolution operations on noisy and missing input data and a sampling mask to obtain input features, connected sequentially; four encoding units that perform encoding operations on the input features sequentially; each encoding unit includes a local convolutional feature extraction branch that extracts local features and global state features of the input features at the corresponding encoding scale; a Mamba global state modeling branch based on visual state space; a residual channel attention fusion module that fuses local feature extraction and global state features; and a multi-scale wavelet transform downsampling layer that performs discrete wavelet transform on the features fused by the residual channel attention fusion module to obtain the input features at the next encoding scale. The decoding stage uses inverse discrete wavelet transform to recover the spatial resolution of the output features of the deepest coding scale in the coding stage step by step, and receives the fused features of the corresponding scale in the coding stage through skip connections. Step 4: Train a multi-scale convolutional Mamba fusion network using a composite loss function and dataset. The composite loss function includes partition reconstruction loss, structural similarity loss, and gradient consistency loss. Step 5: Based on the trained multi-scale convolutional Mamba fusion network, perform missing trace completion and random noise suppression on pre-stack gathers or post-stack seismic profiles to obtain complete denoised seismic data.

2. The method for simultaneous interpolation, denoising, and processing of multi-scale convolutional Mamba seismic data according to claim 1, characterized in that, The specific steps of step 1 are as follows: Step 1.1: Obtain the seismic data to be processed, and determine the missing locations of random traces and continuous traces based on trace head information, seismic trace arrangement information, or preset missing patterns. Step 1.2: Construct an entire-channel sampling mask based on the missing locations of random and continuous channels determined in Step 1.

1. Specifically, this involves setting the mask value of all time sampling points for the seismic traces corresponding to the missing positions of the random and continuous traces to 0, and setting the mask value of all time sampling points corresponding to the remaining valid seismic traces to 1. Indicates the location of the missing lane. Indicates the location of the effective observation channel.

3. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 2, characterized in that: The local convolutional feature branch in step 3 includes two consecutive 3×3 convolutional layers, a batch normalization layer, and... The extraction process of local convolutional features in the activation function layer can be represented as follows: in, Indicates the first Input features at each scale, when hour, The input features are obtained from a 1×1 convolutional layer, when hour, For the input features at the current coding scale, Indicates the first Local convolutional feature extraction branches at each scale The extracted first The output features of the coding unit at the i-th scale, that is, the i-th Local convolutional features mapped at each scale This represents the convolution operation of the first-level 3×3 convolutional layer. This represents the convolution operation of the second-level 3×3 convolutional layer. This indicates a batch normalization operation. This represents the activation function. express The input variables of the activation function, Represents the hyperbolic tangent function. Represents the natural logarithm function. Represents the natural constant; Among them, the The 3×3 convolutional layer at level 3 is in the 1st stage. Location at each scale , No. The specific calculation process for each output channel is as follows: in, , Indicates the first The input features of the 3×3 convolutional layer at the location and the Response values ​​on each input channel , Indicates the first The number of input channels for a 3×3 convolutional layer. Indicates the first In a 3×3 convolutional layer, the first The input channel and the first Between output channels, convolution kernel position The weight of the position, Indicates the first In a 3×3 convolutional layer, the first The bias term for each output channel.

4. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 3, characterized in that: The specific implementation steps of the Mamba global state modeling branch based on the visual state space in step 3 are as follows: The first Input features at each coding scale The input Mamba global state modeling branch performs layer normalization and linear mapping on the input features sequentially to obtain intermediate features, namely two-dimensional seismic features: in, Representation layer normalization, This represents a linear projection operation; Two-dimensional selective scanning was used to rearrange the two-dimensional seismic features, organizing them into multiple directional sequences along multiple scanning paths along the time sampling direction and the seismic trace direction: in, This indicates different scanning directions, including the time sampling direction and the seismic trace direction. Indicates the number of scan paths. Indicates the first Two-dimensional seismic feature sequences in each scanning direction, Indicates two-dimensional selective scanning; Based on multiple direction sequences Selective state-space modeling is performed for each direction sequence. For the first... The state update and output process of the direction sequence corresponding to each scan path can be represented as follows: in, Indicates the first On the first scale The first scan path The hidden state of each location, Indicates the first On the first scale The first scan path Output features at each position, Indicates the first On the first scale The first scan path Input mapping parameters for each position, Indicates the first On the first scale The first scan path Output mapping parameters at each position, This represents the pass-through parameter from input to output. Indicates the first On the first scale The first scan path State transition parameters at each position, No. On the first scale The first scan path Input features at each location; The output sequences obtained from each scanning direction are restored to the two-dimensional feature domain according to the corresponding scanning path, and then fused through a cross-merging operation to obtain the global state features output by the Mamba global state modeling branch: in, Indicates the first The output sequence corresponding to each scan path. Indicates the first The total length of the sequence corresponding to each scan path. This involves restoring the output sequences from multiple directions to a two-dimensional feature domain and performing a cross-merging operation. This indicates a linear projection operation at the output. Indicates the first Mamba global state modeling branch at various scales Output global state characteristics.

5. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 4, characterized in that: The specific steps of the residual channel attention fusion module in step 3 are as follows: First, channel mapping is performed using a 1×1 convolution, with the following formula: in, and These represent the local convolutional features, respectively. and global state features Perform channel projection operation. and They represent respectively to and The result after performing channel projection operation; Next, the two types of features are concatenated along the channel dimension, and their joint feature is represented as: in, This indicates a channel-level concatenation operation; joint features Global average pooling is performed using the following formula: in, No. The joint features of each scale in the first... Global statistical response on each channel and They represent the first Spatial dimensions of feature maps at each size Indicates the spatial location of joint features Passing the exam Response values ​​on each channel; The first is generated through lightweight nonlinear mapping. Channel attention weights of each size: in, and Indicates learnable mapping parameters, Represents a non-linear activation function. express function, Indicates the first Channel attention weights of each size, Represents the global statistical response of each channel. The channel description vector is composed of; Ultimately, the fusion process can be represented as: in, Represents element-wise product. Indicates output channel mapping. This is to integrate local and global features.

6. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 5, characterized in that: The multi-scale wavelet transform downsampling layer in step 3 fuses local and global features. Performing discrete wavelet transform yields low-frequency large-scale components and high-frequency small-scale components in multiple directions, as shown in the formula: in, Represents discrete wavelet transform. This represents the low-frequency, large-scale components, characterizing the overall trend of seismic reflections, background tectonics, and the continuity of large-scale phase axes. , and These represent high-frequency small-scale components in different directions, characterizing local boundaries, amplitude abrupt changes, thin-layer responses, small-scale texture changes, and discontinuous reflection details. The low-frequency large-scale components and high-frequency small-scale components in multiple directions are concatenated along the channel dimension, and the number of channels is adjusted by 1×1 convolution to obtain the input features for the next scale. The formula is as follows: in, This indicates a channel-level concatenation operation. This represents a 1×1 convolution mapping operation. Indicates the first Input features at each scale.

7. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 6, characterized in that: The decoding stage in step 3 restores the feature space resolution step by step in the reverse scale order of the encoding stage. The specific steps are as follows: Using the output features of the deepest coding scale as the initial input features for the decoding stage, for the data from the 3rd coding scale... The scale was restored to the first The decoding process at the nth scale, let the nth scale be... The decoding input features at each scale are During the initial decoding, The output features at the deepest coding scale will be used in subsequent decoding processes. The corresponding scale decoding features output by the previous decoding unit: in, This indicates a sub-band mapping operation. These represent the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions used for inverse wavelet reconstruction, respectively. Subsequently, the low-frequency large-scale subband features and the high-frequency small-scale subband features in different directions are recovered to the nth level using inverse discrete wavelet transform. Spatial resolution at each scale: in, This represents the inverse discrete wavelet transform, which in turn represents upsampling. Represents the th wavelet after inverse wavelet transform. The first scale feature, that is, the first scale feature. Spatial resolution at various scales; The features obtained during the encoding stage are a fusion of local and global features. The first obtained in the decoding stage Individual scale features The corresponding scale-skip connections are fused along the channel dimension, and the result is obtained through a convolutional thinning operation. Decoding output features at each scale: in, This indicates the subsequent convolution thinning operation; Based on Perform step-by-step decoding to obtain the decoded output features at the highest spatial resolution scale. ; Finally, the decoded output features are obtained through 1×1 convolution. Mapping to the single-channel seismic data space, we obtain the final interpolation and denoising results from the multi-scale convolutional Mamba fusion network: in, This represents the seismic data interpolation and denoising results output by the multi-scale convolutional Mamba fusion network.

8. The method for multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing according to claim 7, characterized in that: In step 4: The composite loss function is: Partition reconstruction loss is The structural similarity loss is: The gradient consistency loss is: in, represent the weights of the partition reconstruction loss, structural similarity loss, and gradient consistency loss, respectively. and These represent the weights of the missing region and the valid observation region, respectively. To prevent extremely small constants with a denominator of 0, Gradient operator along the direction of seismic trace arrangement, This represents the gradient operator along the time sampling direction. Describes the norm 1. Indicates the sampling mask. This represents complete target seismic data that is free of random noise.

9. A multi-scale convolutional Mamba seismic data interpolation, denoising, and synchronous processing system, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1-8.

Images