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We propose Generalized Forward-Inverse (GFI) framework based on two assumptions. First, according to the manifold assumption, we assume that the velocity maps v ∈ V and seismic
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waveforms p ∈ P can be projected to their corresponding latent space representations, v˜ and p˜,
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respectively, which can be mapped back to their reconstructions in the original space, vˆ and pˆ. Note
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that the sizes of the latent spaces can be smaller or larger than the original spaces. Further, the size
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of v˜ may not match with the size of p˜. Second, according to the latent space
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translation assumption, we assume that the problem of learning forward and inverse mappings in
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the original spaces of velocity and waveforms can be reformulated as learning translations in their
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