Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dime...Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dimensionally reduced,per frequency,compared to the time domain,which is useful for many applications,like full waveform inversion.However,our ability to attain such wavefield solutions depends often on the size of the model and the complexity of the wave equation.Thus,we use here a recently introduced framework based on neural networks to predict functional solutions through setting the underlying physical equation as a loss function to optimize the neural network(NN)parameters.For an input given by a location in the model space,the network learns to predict the wavefield value at that location,and its partial derivatives using a concept referred to as automatic differentiation,to fit,in our case,a form of the Helmholtz equation.We specifically seek the solution of the scattered wavefield considering a simple homogeneous background model that allows for analytical solutions of the background wavefield.Providing the NN with a reasonable number of random points from the model space will ultimately train a fully connected deep NN to predict the scattered wavefield function.The size of the network depends mainly on the complexity of the desired wavefield,with such complexity increasing with increasing frequency and increasing model complexity.However,smaller networks can provide smoother wavefields that might be useful for inversion applications.Preliminary tests on a two-box-shaped scatterer model with a source in the middle,as well as,the Marmousi model with a source at the surface demonstrate the potential of the NN for this application.Additional tests on a 3D model demonstrate the potential versatility of the approach.展开更多
Noise suppression is an essential step in many seismic processing workflows.A portion of this noise,particularly in land datasets,presents itself as random noise.In recent years,neural networks have been successfully ...Noise suppression is an essential step in many seismic processing workflows.A portion of this noise,particularly in land datasets,presents itself as random noise.In recent years,neural networks have been successfully used to denoise seismic data in a supervised fashion.However,supervised learning always comes with the often unachievable requirement of having noisy-clean data pairs for training.Using blind-spot networks,we redefine the denoising task as a self-supervised procedure where the network uses the surrounding noisy samples to estimate the noise-free value of a central sample.Based on the assumption that noise is statistically independent between samples,the network struggles to predict the noise component of the sample due to its randomicity,whilst the signal component is accurately predicted due to its spatio-temporal coherency.Illustrated on synthetic examples,the blind-spot network is shown to be an efficient denoiser of seismic data contaminated by random noise with minimal damage to the signal;therefore,providing improvements in both the image domain and down-the-line tasks,such as post-stack inversion.To conclude our study,the suggested approach is applied to field data and the results are compared with two commonly used random denoising techniques:FX-deconvolution and sparsity-promoting inversion by Curvelet transform.By demonstrating that blind-spot networks are an efficient suppressor of random noise,we believe this is just the beginning of utilising self-supervised learning in seismic applications.展开更多
Among the biggest challenges we face in utilizing neural networks trained on waveform(i.e.,seismic,electromagnetic,or ultrasound)data is its application to real data.The requirement for accurate labels often forces us...Among the biggest challenges we face in utilizing neural networks trained on waveform(i.e.,seismic,electromagnetic,or ultrasound)data is its application to real data.The requirement for accurate labels often forces us to train our networks using synthetic data,where labels are readily available.However,synthetic data often fail to capture the reality of the field/real experiment,and we end up with poor performance of the trained neural networks(NNs)at the inference stage.This is because synthetic data lack many of the realistic features embedded in real data,including an accurate waveform source signature,realistic noise,and accurate reflectivity.In other words,the real data set is far from being a sample from the distribution of the synthetic training set.Thus,we describe a novel approach to enhance our supervised neural network(NN)training on synthetic data with real data features(domain adaptation).Specifically,for tasks in which the absolute values of the vertical axis(time or depth)of the input section are not crucial to the prediction,like classification,or can be corrected after the prediction,like velocity model building using a well,we suggest a series of linear operations on the input to the network data so that the training and application data have similar distributions.This is accomplished by applying two operations on the input data to the NN,whether the input is from the synthetic or real data subset domain:(1)The crosscorrelation of the input data section(i.e.,shot gather,seismic image,etc.)with a fixed-location reference trace from the input data section.(2)The convolution of the resulting data with the mean(or a random sample)of the autocorrelated sections from the other subset domain.In the training stage,the input data are from the synthetic subset domain and the auto-corrected(we crosscorrelate each trace with itself)sections are from the real subset domain,and the random selection of sections from the real data is implemented at every epoch of the training.In the inference/application stage,the input data are from the real subset domain and the mean of the autocorrelated sections are from the synthetic data subset domain.Example applications on passive seismic data for microseismic event source location determination and on active seismic data for predicting low frequencies are used to demonstrate the power of this approach in improving the applicability of our trained NNs to real data.展开更多
Recorded seismic data are sensitive to the Earth’s elastic properties,and thus,they carry information of such properties in their waveforms.The sensitivity of such waveforms to the properties is nonlinear causing all...Recorded seismic data are sensitive to the Earth’s elastic properties,and thus,they carry information of such properties in their waveforms.The sensitivity of such waveforms to the properties is nonlinear causing all kinds of difficulties to the inversion of such properties.Inverting directly for the components forming the wave equation,which includes the wave equation operator(or its perturbation),and the wavefield,as independent parameters enhances the convexity of the inverse problem.The optimization in this case is provided by an objective function that maximizes the data fitting and the wave equation fidelity,simultaneously.To enhance the practicality and efficiency of the optimization,I recast the velocity perturbations as secondary sources in a modified source function,and invert for the wavefield and the modified source function,as independent parameters.The optimization in this case corresponds to a linear problem.The inverted functions can be used directly to extract the velocity perturbation.Unlike gradient methods,this optimization problem is free of the Born approximation limitations in the update,including single scattering and cross talk that may arise for example in the case of multi sources.These specific features are shown for a simple synthetic example,as well as the Marmousi model.展开更多
文摘Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dimensionally reduced,per frequency,compared to the time domain,which is useful for many applications,like full waveform inversion.However,our ability to attain such wavefield solutions depends often on the size of the model and the complexity of the wave equation.Thus,we use here a recently introduced framework based on neural networks to predict functional solutions through setting the underlying physical equation as a loss function to optimize the neural network(NN)parameters.For an input given by a location in the model space,the network learns to predict the wavefield value at that location,and its partial derivatives using a concept referred to as automatic differentiation,to fit,in our case,a form of the Helmholtz equation.We specifically seek the solution of the scattered wavefield considering a simple homogeneous background model that allows for analytical solutions of the background wavefield.Providing the NN with a reasonable number of random points from the model space will ultimately train a fully connected deep NN to predict the scattered wavefield function.The size of the network depends mainly on the complexity of the desired wavefield,with such complexity increasing with increasing frequency and increasing model complexity.However,smaller networks can provide smoother wavefields that might be useful for inversion applications.Preliminary tests on a two-box-shaped scatterer model with a source in the middle,as well as,the Marmousi model with a source at the surface demonstrate the potential of the NN for this application.Additional tests on a 3D model demonstrate the potential versatility of the approach.
文摘Noise suppression is an essential step in many seismic processing workflows.A portion of this noise,particularly in land datasets,presents itself as random noise.In recent years,neural networks have been successfully used to denoise seismic data in a supervised fashion.However,supervised learning always comes with the often unachievable requirement of having noisy-clean data pairs for training.Using blind-spot networks,we redefine the denoising task as a self-supervised procedure where the network uses the surrounding noisy samples to estimate the noise-free value of a central sample.Based on the assumption that noise is statistically independent between samples,the network struggles to predict the noise component of the sample due to its randomicity,whilst the signal component is accurately predicted due to its spatio-temporal coherency.Illustrated on synthetic examples,the blind-spot network is shown to be an efficient denoiser of seismic data contaminated by random noise with minimal damage to the signal;therefore,providing improvements in both the image domain and down-the-line tasks,such as post-stack inversion.To conclude our study,the suggested approach is applied to field data and the results are compared with two commonly used random denoising techniques:FX-deconvolution and sparsity-promoting inversion by Curvelet transform.By demonstrating that blind-spot networks are an efficient suppressor of random noise,we believe this is just the beginning of utilising self-supervised learning in seismic applications.
文摘Among the biggest challenges we face in utilizing neural networks trained on waveform(i.e.,seismic,electromagnetic,or ultrasound)data is its application to real data.The requirement for accurate labels often forces us to train our networks using synthetic data,where labels are readily available.However,synthetic data often fail to capture the reality of the field/real experiment,and we end up with poor performance of the trained neural networks(NNs)at the inference stage.This is because synthetic data lack many of the realistic features embedded in real data,including an accurate waveform source signature,realistic noise,and accurate reflectivity.In other words,the real data set is far from being a sample from the distribution of the synthetic training set.Thus,we describe a novel approach to enhance our supervised neural network(NN)training on synthetic data with real data features(domain adaptation).Specifically,for tasks in which the absolute values of the vertical axis(time or depth)of the input section are not crucial to the prediction,like classification,or can be corrected after the prediction,like velocity model building using a well,we suggest a series of linear operations on the input to the network data so that the training and application data have similar distributions.This is accomplished by applying two operations on the input data to the NN,whether the input is from the synthetic or real data subset domain:(1)The crosscorrelation of the input data section(i.e.,shot gather,seismic image,etc.)with a fixed-location reference trace from the input data section.(2)The convolution of the resulting data with the mean(or a random sample)of the autocorrelated sections from the other subset domain.In the training stage,the input data are from the synthetic subset domain and the auto-corrected(we crosscorrelate each trace with itself)sections are from the real subset domain,and the random selection of sections from the real data is implemented at every epoch of the training.In the inference/application stage,the input data are from the real subset domain and the mean of the autocorrelated sections are from the synthetic data subset domain.Example applications on passive seismic data for microseismic event source location determination and on active seismic data for predicting low frequencies are used to demonstrate the power of this approach in improving the applicability of our trained NNs to real data.
文摘Recorded seismic data are sensitive to the Earth’s elastic properties,and thus,they carry information of such properties in their waveforms.The sensitivity of such waveforms to the properties is nonlinear causing all kinds of difficulties to the inversion of such properties.Inverting directly for the components forming the wave equation,which includes the wave equation operator(or its perturbation),and the wavefield,as independent parameters enhances the convexity of the inverse problem.The optimization in this case is provided by an objective function that maximizes the data fitting and the wave equation fidelity,simultaneously.To enhance the practicality and efficiency of the optimization,I recast the velocity perturbations as secondary sources in a modified source function,and invert for the wavefield and the modified source function,as independent parameters.The optimization in this case corresponds to a linear problem.The inverted functions can be used directly to extract the velocity perturbation.Unlike gradient methods,this optimization problem is free of the Born approximation limitations in the update,including single scattering and cross talk that may arise for example in the case of multi sources.These specific features are shown for a simple synthetic example,as well as the Marmousi model.
