Ground roll attenuation using unsupervised deep learning
A machine-implemented method, at least one non-transitory computer-readable medium storing instructions, and a computing system are provided for attenuating noise. A computing system receives a seismic image and generates a first image using a first neural network configured to identify low-frequency ground roll in a seismic image, and a second image using a second neural network configured to identify reflections in the seismic image. A combined image is generated by combining the first image and the second image. The first neural network and the second neural network are adjusted to reduce a difference between the combined image and the seismic image using frequency constraint to guide separation of the seismic image into the first image and the second image.
1. A method for attenuating noise in seismic data, comprising:
receiving a seismic image;
generating a first image using a first neural network configured to identify low frequency noise in the seismic image;
generating a second image using a second neural network configured to identify reflections in the seismic image and to attenuate the low frequency noise;
generating a combined image by combining the first image and the second image; and
adjusting the first neural network and the second neural network to reduce a difference between the combined image and the seismic image using frequency constraint to guide separation of the seismic image into the first image and the second image.
2. The method of claim 1 , further comprising:
before the generating of the first image and the second image, generating, by a computing system, a binary mask, the binary mask having a value of 1 in an area of first arrival and a value of 0 otherwise, the generating of the binary mask comprising:
binarizing a plurality of seismic images;
training an encoder-decoder neural network to generate a smooth image from the binarized seismic images; and
fitting in a vertical direction a 0-1 boundary with a sigmoid function.
3. The method of claim 2 , wherein:
total data loss is a sum of data loss, a product of a first coefficient with a first regularization term that imposes a first frequency constraint, and a product of a second coefficient with a second regularization term that imposes a second frequency constraint,
the data loss is equal to a quotient calculated by dividing, by a number of 2D data sections per patch, a product of a squared Frobenius norm of the seismic data, as originally received, subtracted from an element-wise multiplication of the binary mask with a summation of outputs of the first neural network and the second neural network,
the first regularization term is equal to a quotient of a first summation along a first discrete frequency domain in a vertical direction from zero through a window size in the first discrete frequency domain of an absolute value of a two-dimensional Fourier transform function of X, divided by a number of pixels for computing a mean value of the first summation,
the second regularization term is equal to a quotient of a second summation along the first discrete frequency domain in a vertical direction from one plus the window size in the first discrete frequency domain through Q of an absolute value of a two-dimensional Fourier transform function of Y, divided by the number of pixels for computing the mean value of the first summation subtracted from the number of 2D data sections per patch,
the first discrete frequency domain is 1, . . . , Q, and
a second discrete frequency domain in a horizontal direction is 1, . . . , P.
4. The method of claim 2 , further comprising:
applying the binary mask to the received seismic image to mask the noise before the area of first arrival in the received seismic image before the generating of the first image and the second image from the seismic image.
5. The method of claim 1 , wherein an architecture of each of the first neural network and the second neural network comprises:
a first plurality of stacks of first convolutional layers separated by respective down sampling;
a second plurality of stacks of second convolutional layers separated by respective up sampling; and
a relu activation function after each convolutional layer of the first and the second convolutional layers except for an output layer.
6. The method of claim 5 , wherein the architecture of each of the first neural network and the second neural network further comprises:
a skip connection from an output of a first stack of the first plurality of stacks to an input of a last stack of the second plurality of stacks.
7. The method of claim 1 , further comprising:
normalizing, by a computing system, seismic data from the seismic image before providing the seismic image to the first neural network and the second neural network.
8. At least one non-transitory computer-readable medium storing instructions that, when executed by at least one processor of a computing system, cause the computing system to perform operations, the operations comprising:
receiving a seismic image;
generating a first image using a first neural network configured to identify low frequency noise, including ground roll, in the seismic image;
generating a second image using a second neural network configured to identify reflections in the seismic image and to attenuate the low frequency noise;
combining the first image and the second image to generate a combined image; and
adjusting the first neural network and the second neural network to reduce a difference between the combined image and the seismic image using frequency constraint to guide separation of the seismic image into the first image and the second image.
9. The at least one non-transitory computer-readable medium of claim 8 , wherein the operations further comprise:
before the generating of the first image and the second image, applying a binary mask to the seismic image to remove noise before an area of first arrival in the seismic image.
10. The at least one non-transitory computer-readable medium of claim 9 , wherein:
total data loss is a sum of data loss, a product of a first coefficient with a first regularization term that imposes a first frequency constraint, and a product of a second coefficient with a second regularization term that imposes a second frequency constraint,
the data loss is equal to a quotient calculated by dividing, by a number of 2D data sections per patch, a product of a squared Frobenius norm of the seismic data, as originally received, subtracted from an element-wise multiplication of the binary mask with a summation of outputs of the first neural network and the second neural network,
the first regularization term is equal to a quotient of a first summation, along a first discrete frequency domain in a vertical direction from zero through a window size in the first discrete frequency domain, of an absolute value of a two-dimensional Fourier transform function of X, divided by a number of pixels for computing a mean value of the first summation,
the second regularization term is equal to a quotient of a second summation along the first discrete frequency domain in the vertical direction from one plus the window size in the first discrete frequency domain through Q of an absolute value of a two-dimensional Fourier transform function of Y, divided by the number of pixels for computing the mean value of the first summation subtracted from the number of 2D data sections per patch,
the first discrete frequency domain is 1, . . . , Q, and
a second discrete frequency domain in a horizontal direction is 1, . . . , P.
11. The at least one non-transitory computer-readable medium of claim 8 , wherein an architecture of each of the first neural network and the second neural network comprises:
a first plurality of stacks of first convolutional layers separated by respective down sampling;
a second plurality of stacks of second convolutional layers separated by respective up sampling; and
a relu activation function after each convolutional layer of the first and the second convolutional layers except for an output layer.
12. The at least one non-transitory computer-readable medium of claim 11 , wherein:
the down sampling comprises one of max pooling and average pooling, and
the up sampling comprises using a nearest-neighbor interpolation method.
13. The at least one non-transitory computer-readable medium of claim 11 , wherein the operations further comprise:
normalizing seismic data from the seismic image before providing the seismic image to the first neural network and the second neural network, the normalized seismic data being calculated by subtracting a mean value of the seismic data before the normalizing from the seismic data before the normalizing, and dividing a result of the subtracting by a standard deviation of the seismic data before the normalizing.
14. The at least one non-transitory computer-readable medium of claim 11 , wherein the architecture of each of the first neural network and the second neural network further comprises:
a skip connection from an output of a first stack of the first plurality of stacks to an input of a last stack of the second plurality of stacks.
15. A computing system for attenuating low-frequency ground roll, comprising:
one or more processors; and
a memory system comprising one or more non-transitory computer-readable media storing instructions that, when executed by at least one of the one or more processors, cause the computing system to perform operations, the operations comprising:
receiving a seismic image;
generating a first image using a first neural network configured to identify the low-frequency ground roll in the seismic image;
generating a second image using a second neural network configured to identify reflections in the seismic image;
combining the first image and the second image to generate a combined image; and
adjusting the first neural network and the second neural network to reduce a difference between the combined image and the seismic image using frequency constraint to guide separation of the seismic image into the first image and the second image.
16. The computing system of claim 15 , wherein the operations further comprise:
applying a binary mask to the seismic image, before the generating of the first image and the second image, to remove noise before an area of first arrival in the seismic image.
17. The computing system of claim 16 , wherein:
the operations further comprise normalizing seismic data from the seismic image before providing the seismic image to the first neural network and the second neural network, the normalized seismic data being calculated by subtracting a mean value of the seismic data before the normalizing from the seismic data before the normalizing, and dividing a result of the subtracting by a standard deviation of the seismic data before the normalizing,
total data loss is a sum of data loss, a product of a first coefficient with a first regularization term that imposes a first frequency constraint, and a product of a second coefficient with a second regularization term that imposes a second frequency constraint,
the data loss is equal to a quotient calculated by dividing, by a number of 2D data sections per patch, a product of a squared Frobenius norm of the seismic data, as originally received, subtracted from an element-wise multiplication of the binary mask with a summation of outputs of the first neural network and the second neural network,
the first regularization term is equal to a quotient of a first summation, along a first discrete frequency domain in a vertical direction from zero through a window size in the first discrete frequency domain, of an absolute value of a two-dimensional Fourier transform function of X, divided by a number of pixels for computing a mean value of the first summation,
the second regularization term is equal to a quotient of a second summation along the first discrete frequency domain in the vertical direction from one plus the window size in the first discrete frequency domain through Q of an absolute value of a two-dimensional Fourier transform function of Y, divided by the number of pixels for computing the mean value of the first summation subtracted from the number of 2D data sections per patch,
the first discrete frequency domain is 1, . . . , Q, and
a second discrete frequency domain in a horizontal direction is 1, . . . , P.
18. The computing system of claim 15 , wherein:
an architecture of each of the first neural network and the second neural network comprises:
a first plurality of stacks of first convolutional layers separated by respective down sampling,
a second plurality of stacks of second convolutional layers separated by respective up sampling, and
a relu activation function after each convolutional layer of the first and the second convolutional layers except for an output layer; and
the down sampling comprises one of max pooling and average pooling, and
the up sampling comprises using a nearest-neighbor interpolation method.
19. The computing system of claim 18 , wherein the architecture of each of the first neural network and the second neural network further comprises:
a skip connection from an output of a first stack of the first plurality of stacks to an input of a last stack of the second plurality of stacks.
20. The computing system of claim 15 , wherein the operations further comprise:
normalizing seismic data from the seismic image before providing the seismic image to the first neural network and the second neural network, the normalized seismic data being calculated by subtracting a mean value of the seismic data before the normalizing from the seismic data before the normalizing, and dividing a result of the subtracting by a standard deviation of the seismic data before the normalizing.