Subsurface models with uncertainty quantification

1. A method for modeling a subsurface region, comprising:

obtaining a training set of geologically plausible models for the subsurface region;

training an autoencoder with the training set;

extracting a decoder from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function;

using the decoder within an objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables;

performing an inversion by identifying one or more minima of the objective function to generate a set of prospective latent-space models for the subsurface region;

using the decoder to convert each of the prospective latent-space models to a respective output-space model;

identifying one or more geologic axes for parameters of the geologically plausible models;

identifying prospective latent-space models relating to maxima and minima along the geologic axes;

estimating an uncertainty in the set of prospective latent-space models based on the maxima and minima along the geologic axes; and

estimating an uncertainty in the set of output-spaced models based on the uncertainty in the set of prospective latent-space models.

2. The method of claim 1 , wherein identifying the one or more geologic axes comprises identifying latent parameters of an encoded space of the autoencoder.

3. The method of claim 1 , wherein identifying the one or more geologic axes comprises identifying linear combinations of latent parameters of an encoded space of the autoencoder.

4. The method of claim 1 , further comprising:

identifying a minimum in the objective function that minimizes a combination of data-misfit and deviation from a mean prospective latent-space model; and

identifying a best-fit model near a latent-space locus of the identified minimum.

5. The method of claim 1 , wherein:

the training set comprises multiple training libraries; and

training the autoencoder comprises generating a distinct decoder network for each of the multiple training libraries.

6. The method of claim 5 , wherein each of the distinct decoder networks is a non-linear, vector-valued function.

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

Full Wavefield Inversion;

seismic tomography;

seismic velocity model building;

potential fields inversion; and

reservoir history matching.

8. The method of claim 1 , wherein the inversion is based on at least one of:

well-logs;

seismic data;

time-lapsed seismic data;

electromagnetic data;

potential-fields data;

well pressure over time; and

well production rates over time by fluid type.

9. The method of claim 1 , wherein a training set model comprises at least one of:

a volumetric description of a porosity and permeability;

a volumetric description of a compressional-wave velocity;

a volumetric description of a shear-wave velocity;

a volumetric description of resistivity; and

a volumetric description of density.

10. A method for modeling a subsurface region, comprising:

obtaining a training set of geologically plausible models for the subsurface region;

training an autoencoder with the training set;

extracting a decoder from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function;

using the decoder within an objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables;

performing an inversion by identifying one or more minima of the objective function to generate a set of prospective latent-space models for the subsurface region;

using the decoder to convert each of the prospective latent-space models to a respective output-space model;

using dropout layers within the autoencoder to generate an ensemble of decoders; and

estimating an uncertainty in the set of output-space models based on the ensemble of decoders.

11. A method for modeling a subsurface region, comprising:

obtaining a training set of geologically plausible models for the subsurface region;

training an autoencoder with the training set;

using dropout layers within the autoencoder to generate an ensemble of decoders;

extracting the ensemble of decoders from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function;

for each decoder in the ensemble:

using the decoder within an objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables;

performing an inversion by identifying one or more minima of the objective function to generate a set of prospective latent-space models for the subsurface region; and

using the decoder to convert each of the prospective latent-space models to a respective output-space model; and

estimating an uncertainty in the set of output-space models based on the ensemble of decoders.

12. A method for modeling a subsurface region, comprising:

obtaining a training set of geologically plausible models for the subsurface region, wherein at least a portion of the training set is generated from a computer simulation;

training an autoencoder with the training set;

extracting a decoder from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function;

using the decoder within an objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables;

performing an inversion by identifying one or more minima of the objective function to generate a set of prospective latent-space models for the subsurface region; and

using the decoder to convert each of the prospective latent-space models to a respective output-space model.

13. The method of claim 12 , wherein the computer simulation comprises at least one of:

process stratigraphy;

basin and petroleum system modeling;

salt body plastic flow simulations; and

geomechanical simulations.

14. The method of claim 12 , wherein:

the training set comprises multiple training libraries; and

training the autoencoder comprises generating a distinct decoder network for each of the multiple training libraries.

15. The method of claim 14 , wherein each of the distinct decoder networks is a non-linear, vector-valued function.

16. The method of claim 12 , wherein the inversion comprises at least one of:

Full Wavefield Inversion;

seismic tomography;

seismic velocity model building;

potential fields inversion; and

reservoir history matching.

17. The method of claim 12 , wherein the inversion is based on at least one of:

well-logs;

seismic data;

time-lapsed seismic data;

electromagnetic data;

potential fields data;

well pressure over time; and

well production rates over time by fluid type.

18. The method of claim 12 , wherein a training set model comprises at least one of:

a volumetric description of a porosity and permeability;

a volumetric description of a compressional-wave velocity;

a volumetric description of a shear-wave velocity;

a volumetric description of resistivity; and

a volumetric description of density.

19. A method of hydrocarbon management comprising:

obtaining a training set of geologically plausible models for the subsurface region;

training an autoencoder with the training set;

extracting a decoder from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function;

using the decoder within an objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables;

performing an inversion by identifying one or more minima of the objective function to generate a set of prospective latent-space model for the subsurface region;

using the decoder to convert each of the prospective latent-space models to a respective output-space model;

identifying one or more geologic axes for parameters of the geologically plausible models;

identifying prospective latent-space models relating to maxima and minima along the geologic axes;

estimating an uncertainty in the set of prospective latent-space models based on the maxima and minima along the geologic axes;

estimating an uncertainty in the set of output-spaced models based on the uncertainty in the set of prospective latent-space models; and

making one or more hydrocarbon management decisions based on the estimated uncertainty in the set of output-space models.

20. The method of claim 19 , wherein identifying the one or more geologic axes comprises identifying latent parameters of an encoded space of the autoencoder.

21. The method of claim 19 , wherein identifying the one or more geologic axes comprises identifying linear combinations of latent parameters of an encoded space of the autoencoder.

22. The method of claim 19 , further comprising:

identifying a minimum in the objective function that minimizes a combination of data-misfit and deviation from a mean prospective latent-space model; and

identifying a best-fit model near a latent-space locus of the identified minimum.

23. The method of claim 19 , wherein:

the training set comprises multiple training libraries; and

training the autoencoder comprises generating a distinct decoder network for each of the multiple training libraries.

24. The method of claim 23 , wherein each of the distinct decoder networks is a non-linear, vector-valued function.

25. The method of claim 19 , wherein the inversion comprises at least one of:

Full Wavefield Inversion;

seismic tomography;

seismic velocity model building;

potential fields inversion; and

reservoir history matching.