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Wavefield solutions from machine learned functions constrained by the Helmholtz equation

Artificial Intelligence in Geosciences 2021年第1期2卷 11-19页

作者： Tariq Alkhalifah Chao Song Umair bin Waheed Qi Hao Physical Sciences and Engineering Division King Abdullah University of Science and TechnologyThuwal23955Saudi Arabia Department of Geosciences King Fahd University of Petroleum and MineralsDhahran31261Saudi Arabia Center for Integrated Petroleum Research King Fahd University of Petroleum and MineralsDhahran31261Saudi Arabia

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 *** 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 ***,our ability to attain such wavefield solutions depends often on the size of the model and the complexity of the wave ***,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)*** 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 *** specifically seek the solution of the scattered wavefield considering a simple homogeneous background model that allows for analytical solutions of the background *** 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 *** size of the network depends mainly on the complexity of the desired wavefield,with such complexity increasing with increasing frequency and increasing model ***,smaller networks can provide smoother wavefields that might be useful for inversion *** 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 *** tests on a 3D model demonstrate the potential versatility of the approach.

关键词： Helmholtz equation wavefields Modeling Neural networks Deep learning

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