METHODS AND SYSTEMS FOR AN ONLINE MACHINE-LEARNED NON-LINEAR BEAMFORMING TUPLE SOLVER

1 . A method for determining a non-linear beamforming (NLBF) tuple, comprising:

receiving a seismic data set;

discretizing the seismic data set into a plurality of NLBF sub-problems;

solving a subset of the NLBF sub-problems with a non-linear optimizer creating final NLBF tuples;

periodically training a machine-learned model with a subset of the NLBF sub-problems and final NLBF tuples data;

obtaining intermediate NLBF tuple predictions from the trained machine-learned model;

using the intermediate NLBF tuple predictions as initial values in the non-linear optimizer to create final NLBF tuples or accepting the intermediate NLBF tuple predictions obtained directly from the trained machine-learned model as final NLBF tuples; and

storing the final NLBF tuples.

2 . The method of claim 1 , further comprising:

determining a non-linear beamformed data set with enhanced traces based on the final NLBF tuples;

forming a seismic image based on the non-linear beamformed data set; and

planning and drilling a wellbore based on the seismic image.

3 . The method of claim 1 , further comprising electing of a move-out surface function and electing an objective function.

4 . The move-out surface of claim 3 , wherein the move-out function is a second-order expansion.

5 . The method of claim 1 , wherein the machine-learned model is a deep neural network.

6 . The method of claim 1 , wherein a frequency of the periodic training of the machine-learned model is determined by a training scheduler.

7 . The method of claim 1 , wherein the machine-learned model is trained by optimizing a semblance-like objective function.

8 . The method of claim 1 , wherein the intermediate NLBF tuple prediction is accepted based on a comparative analysis with a calculated semblance-like value.

9 . The method of claim 1 , wherein the final NLBF tuples are stored in a data storage system.

10 . A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:

receiving a seismic data set;

discretizing the seismic data set into a plurality of NLBF sub-problems;

solving a subset of the NLBF sub-problems with a non-linear optimizer creating final NLBF tuples;

periodically training a machine-learned model with a subset of the NLBF sub-problems and final NLBF tuples data;

obtaining intermediate NLBF tuple predictions from the trained machine-learned model;

using the intermediate NLBF tuple predictions as initial values in the non-linear optimizer to create final NLBF tuples or accepting the intermediate NLBF tuple predictions obtained directly from the trained machine-learned model as final NLBF tuples; and

storing the final NLBF tuples.

11 . The non-transitory computer readable medium of claim 10 , further comprising:

determining a non-linear beamformed data set with enhanced traces based on the final NLBF tuples;

forming a seismic image based on the non-linear beamformed data set; and

planning and drilling a wellbore based on the seismic image.

12 . The non-transitory computer readable medium of claim 10 , further comprising an election of a move-out surface function and the election of an objective function.

13 . The move-out surface of claim 12 , wherein the move-out function is a second-order expansion.

14 . The non-transitory computer readable medium of claim 10 , wherein the machine-learned model is a deep neural network.

15 . The non-transitory computer readable medium of claim 10 , wherein a frequency of the periodic training of the machine-learned model is determined by a training scheduler.

16 . The non-transitory computer readable medium of claim 10 , wherein the machine-learned model is trained by optimizing a semblance-like objective function.

17 . The non-transitory computer readable medium of claim 10 , wherein the intermediate NLBF tuple prediction is accepted based on a comparative analysis with a calculated semblance-like value.

18 . The non-transitory computer readable medium of claim 10 , wherein the final NLBF tuples are stored in a data storage system.