Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity, and others) from surface-based geophysical measurements (e.g., seismic, electric\/magnetic (EM) data). The problems are governed by partial differential equations~(PDEs) like the wave or Maxwell’s equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from geophysical measurements to the geophysical property directly.<\/p>\n
In this paper, we show that such a mapping can be well modeled by a \\textit{very shallow}~(but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: \\textit{a near-linear relationship between the input and output, after applying integral transform in high dimensional space.} In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer block to reverse the integral of velocity.<\/p>\n
Experiments show that this interesting property holds for two geophysics inversion problems over four different datasets. Compared to much deeper InversionNet~\\cite{wu2019inversionnet}, our method achieves comparable accuracy, but consumes significantly fewer parameters.<\/p>\n","protected":false},"excerpt":{"rendered":"
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity, and others) from surface-based geophysical measurements (e.g., seismic, electric\/magnetic (EM) data). The problems are governed by partial differential equations~(PDEs) like the wave or Maxwell’s equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those 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