Surface-consistent travel-times inversion with accuracy estimation

A system for performing seismic imaging of a subterranean formation, the system comprising:

• at least one processor;
• and
• a memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations comprising:
• receiving, by a computer system, data representing a plurality of seismic traces corresponding to seismic waves propagating in the subterranean formation;
• determining, from the plurality of seismic traces, travel time data representing observed travel times of refracted energy and a data covariance matrix representing uncertainty associated with the observed travel times for the plurality of seismic traces;
• determining, based on the travel time data, a prior velocity model and a prior model covariance matrix for a plurality of common midpoint locations associated with the plurality of seismic traces, wherein the prior velocity model represents an initial estimate of velocities for the plurality of common midpoint locations and the prior model covariance matrix represents an uncertainty of the prior velocity model;
• generating an objective function based on the travel time data, the data covariance matrix, the prior velocity model, and the prior model covariance matrix;
• determining, by minimizing the objective function, values for a plurality of one-dimensional velocity models and a set of accuracy values associated with the plurality of one-dimensional velocity models;
• generating, based on the values for the plurality of one-dimensional velocity models and the set of accuracy values, a pseudo-3D model and a set of accuracy values for the pseudo-3D model;
• and
• generating, based on the pseudo-3D model and the set of accuracy values for the pseudo-3D model, a seismic image representing the subterranean formation.

One or more non-transitory computer readable media storing instructions to perform seismic imaging of a subterranean formation, the instructions, when executed by at least one processor, configured to cause the at least one processor to perform operations comprising:

• receiving, by a computer system, data representing a plurality of seismic traces corresponding to seismic waves propagating in the subterranean formation;
• determining, from the plurality of seismic traces, travel time data representing observed travel times of refracted energy and a data covariance matrix representing uncertainty associated with the observed travel times for the plurality of seismic traces;
• determining, based on the travel time data, a prior velocity model and a prior model covariance matrix for a plurality of common midpoint locations associated with the plurality of seismic traces, wherein the prior velocity model represents an initial estimate of velocities for the plurality of common midpoint locations and the prior model covariance matrix represents an uncertainty of the prior velocity model;
• generating an objective function based on the travel time data, the data covariance matrix, the prior velocity model, and the prior model covariance matrix;
• determining, by minimizing the objective function, values for a plurality of one-dimensional velocity models and a set of accuracy values associated with the plurality of one-dimensional velocity models;
• generating, based on the values for the plurality of one-dimensional velocity models and the set of accuracy values, a pseudo-3D model and a set of accuracy values for the pseudo-3D model;
• and
• generating, based on the pseudo-3D model and the set of accuracy values for the pseudo-3D model, a seismic image representing the subterranean formation.