Machine learning-augmented geophysical inversion

1. A method of machine learning-augmented geophysical inversion, comprising:

obtaining measured data for a subsurface region;

obtaining prior subsurface data for the subsurface region;

iteratively:

partially training an autoencoder with the measured data and with learned weights from a previous iteration to learn a fraction of data space representations and generate a data space encoder;

partially training the autoencoder with the prior subsurface data and with learned weights from the previous iteration to learn a fraction of model space representations and generate a model space decoder;

forming an augmented forward model with the model space decoder, the data space encoder, and a physics based forward model; and

solving an inversion problem with the augmented forward model to generate an inversion solution.

2. The method of claim 1 , wherein the measured data comprises at least one of:

data acquired from a geophysical survey of the subsurface region;

data from a data library; and

synthetic data.

3. The method of claim 1 , wherein the prior subsurface data comprises at least one of:

subsurface geophysical models;

subsurface images;

analog subsurface geophysical models;

analog subsurface images;

well logs;

estimates of values of geophysical properties as a function of depth in the subsurface region; and

data from a subsurface library.

4. The method of claim 1 , wherein the inversion problem comprises at least one of:

full-wavefield inversion;

seismic tomography;

gravity inversion;

magnetic inversion; and

electromagnetic inversion; and

wherein solving the inversion problem comprises at least one of:

a global optimization method; and

a gradient-based optimization method.

5. The method of claim 1 , wherein an objective functional of the inversion problem is formulated in a super attribute space of the augmented forward model.

6. The method of claim 1 , wherein an objective functional of the inversion problem includes regularization terms in a super parameter space of the augmented forward model and a discretized space of the physics based forward model.

7. The method of claim 1 , wherein the model space decoder and the data space encoder comprise variational autoencoders.

8. The method of claim 7 , wherein the trainings are based on at least one of:

convolutional neural network architectures; and

densely-connected network architectures.

9. The method of claim 1 , wherein the model space decoder and the data space encoder comprise combined variational autoencoders and generative-adversarial network models.

10. The method of claim 1 , wherein the inversion solution comprises proposed subsurface geophysical models.

11. The method of claim 1 , further comprising utilizing the inversion solution to manage hydrocarbons.

12. The method of claim 1 , wherein solving the inversion problem with the augmented forward model to generate an inversion solution comprises partially solving the inversion problem.

13. The method of claim 12 , wherein partially solving of the inversion problem comprises:

performing iterations towards minimizing an inversion objective functional; and

terminating solving the inversion problem prior to the inversion solution converging to a predefined minimum.

14. The method of claim 1 , wherein in one iteration, partial training of the autoencoder is for learning one of only direct arrival events or only primary reflection events; and

wherein in another iteration, partial training of the autoencoder is for learning another of only direct arrival events or only primary reflection events.

15. A method of machine learning-augmented geophysical inversion, comprising:

obtaining measured data for a subsurface region;

obtaining prior subsurface data for the subsurface region;

(a) partially training a data autoencoder with the measured data to learn a fraction of data space representations and generate a data space encoder,

(b) partially training a model autoencoder with the prior subsurface data to learn a fraction of model space representations and generate a model space decoder;

(c) forming an augmented forward model with the model space decoder, the data space encoder, and a physics based forward model;

(d) solving an inversion problem with the augmented forward model to generate an inversion solution; and

iteratively repeating (a)-(d) until convergence of the inversion solution, wherein, for each iteration:

partially training the data autoencoder starts with learned weights from an immediately-previous iteration;

partially training the model autoencoder starts with learned weights from the immediately-previous iteration; and

solving the inversion problem starts with super parameters from the previous iteration.

16. The method of claim 15 , wherein the measured data comprises at least one of:

data acquired from a geophysical survey of the subsurface region;

data from a data library; and

synthetic data.

17. The method of claim 15 , wherein the prior subsurface data comprises at least one of:

subsurface geophysical models;

subsurface images;

analog subsurface geophysical models;

analog subsurface images;

well logs;

estimates of values of geophysical properties as a function of depth in the subsurface region; and

data from a subsurface library.

18. The method of claim 15 , wherein, for each iteration, the inversion problem comprises at least one of:

full-wavefield inversion;

seismic tomography;

gravity inversion;

magnetic inversion; and

electromagnetic inversion.

19. The method of claim 15 , wherein, for each iteration, solving the inversion problem comprises at least one of:

a global optimization method; and

a gradient-based optimization method.

20. The method of claim 15 , wherein, for each iteration, an objective functional of the inversion problem is formulated in a super attribute space of the augmented forward model.

21. The method of claim 15 , wherein, for each iteration, an objective functional of the inversion problem includes regularization terms in a super parameter space of the augmented forward model and a discretized space of the physics based forward model.

22. The method of claim 15 , wherein, for each iteration, the model space decoder and the data space encoder comprise variational autoencoders.

23. The method of claim 15 , wherein, for each iteration:

the autoencoder comprises a generative-adversarial network,

the data space encoder corresponds to a generative model of the generative-adversarial network, and

the model space decoder corresponds to a discriminator model of the generative-adversarial network.

24. The method of claim 15 , wherein, for each iteration, the model space decoder and the data space encoder comprise combined variational autoencoders and generative adversarial network models.

25. A method for generating an image of a subsurface region comprising:

obtaining measured data for a subsurface region;

obtaining prior subsurface data for the subsurface region;

iteratively:

partially training an autoencoder with the measured data and with learned weights from a previous iteration to learn a fraction of data space representations and generate a data space encoder;

partially training the autoencoder with the prior subsurface data and with learned weights from the previous iteration to learn a fraction of model space representations and generate a model space decoder;

forming an augmented forward model with the model space decoder, the data space encoder, and a physics based forward model;

solving an inversion problem with the augmented forward model to generate an inversion solution comprising a proposed geophysical model; and

generating an image of the proposed geophysical model.