HELICAL OPTICAL FIBERS FOR STRAIN MEASUREMENT
A method for measuring a strain field involves determining an expected source mechanism of the strain field, based on the expected source mechanism, estimating strain field tensors of the strain field in an area of interest, determining principal strain vectors from the strain field tensors, identifying the most extensional principal strain vectors, ε 3 , from the principal strain vectors, establishing a trajectory of a fiber optic path through the area of interest, discretizing the fiber optic path to obtain directions of fiber axial strain, ε a , comparing ε a against ε 3 , and based on the comparison, optimizing the fiber optic path for an alignment of ε a with ε 3 .
1 . A method for measuring a strain field, the method comprising:
determining an expected source mechanism of the strain field;
based on the expected source mechanism, estimating strain field tensors of the strain field in an area of interest;
determining principal strain vectors from the strain field tensors;
identifying the most extensional principal strain vectors, ε 3 , from the principal strain vectors;
establishing a trajectory of a fiber optic path through the area of interest;
discretizing the fiber optic path to obtain directions of fiber axial strain, ε a ;
comparing ε a against ε 3 ; and
based on the comparison, optimizing the fiber optic path for an alignment of ε a with ε 3 .
2 . The method of claim 1 , further comprising:
determining corrections to misaligned orientations of ε 3 against ε a .
3 . The method of claim 1 , further comprising:
manufacturing a fiber optic system based on the optimized fiber optic path.
4 . The method of claim 3 ,
wherein the fiber optic system comprises one selected from a group consisting of a plug and a pipe supporting one or more layers of fiber coiled according to the optimized fiber optic path.
5 . The method of claim 3 , further comprising:
deploying the fiber optic system to measure the strain field in the area of interest.
6 . The method of claim 1 , wherein determining the expected source mechanism of the strain field comprises:
receiving the expected source mechanism from an operator.
7 . The method of claim 1 , wherein estimating the strain field tensors of the strain field in the area of interest comprises one selected from a group consisting of:
obtaining an analytical solution for the expected source mechanism of the strain field, and
executing a simulation model for the expected source mechanism of the strain field.
8 . The method of claim 1 , wherein determining the principal strain vectors from the strain field tensors comprises:
computing the eigenvalues of the strain field tensors.
9 . The method of claim 1 , wherein the trajectory of the fiber optic path through the area of interest is one selected from a group consisting of:
a linear fiber optic path,
a helical fiber path, and
a contra-helical fiber path.
10 . The method of claim 1 , wherein discretizing the fiber optic path to obtain directions of fiber axial strain, ε a comprises:
quantifying an orientation of the fiber optic path using unit vectors representing a tangential direction of the fiber optic path average over a gauge length of a fiber associated with the fiber optic path.
11 . The method of claim 1 , wherein comparing ε a against ε 3 comprises:
generating a histogram for a distribution of ε 3 .
12 . The method of claim 1 , wherein optimizing the fiber optic path for an alignment of ε a with ε 3 comprises at least one selected from a group consisting of:
adjusting a wrap angle of the fiber optic path of a helical fiber,
adjusting a number of fibers on the fiber optic path, and
adjusting a length of a fiber on the fiber optic path.
13 . The method of claim 1 , wherein optimizing the fiber optic path for an alignment of Ea with ε 3 comprises one selected from a group consisting of:
a regression analysis, and
machine learning.
14 . The method of claim 1 , further comprising:
determining statistical characteristics of ε 3 ,
wherein the optimizing the fiber optic path for an alignment of ε a with ε 3 is performed using the statistical characteristics of ε 3 .
15 . A system for measuring a strain field, the system comprising:
a computer system configured to:
determine an expected source mechanism of the strain field;
based on the expected source mechanism, estimate strain field tensors of the strain field in an area of interest;
determine principal strain vectors from the strain field tensors;
identify the most extensional principal strain vectors, ε 3 , from the principal strain vectors;
establish a trajectory of a fiber optic path through the area of interest;
discretize the fiber optic path to obtain directions of fiber axial strain, ε a ;
compare ε a against ε 3 ; and
based on the comparison, optimize the fiber optic path for an alignment of ε a with ε 3 .
16 . The system of claim 15 , wherein estimating the strain field tensors of the strain field in the area of interest comprises one selected from a group consisting of:
obtaining an analytical solution for the expected source mechanism of the strain field, and
executing a simulation model for the expected source mechanism of the strain field.
17 . The system of claim 15 , wherein the trajectory of the fiber optic path through the area of interest is one selected from a group consisting of:
a linear fiber optic path,
a helical fiber path, and
a contra-helical fiber path.
18 . The system of claim 15 , wherein discretizing the fiber optic path to obtain directions of fiber axial strain, ε a comprises:
quantifying an orientation of the fiber optic path using unit vectors representing a tangential direction of the fiber optic path average over a gauge length of a fiber associated with the fiber optic path.
19 . The system of claim 15 , wherein optimizing the fiber optic path for an alignment of ε a with ε 3 comprises at least one selected from a group consisting of:
adjusting a wrap angle of the fiber optic path of a helical fiber, adjusting a number of fibers on the fiber optic path, and
adjusting a length of a fiber on the fiber optic path.
20 . A non-transitory machine-readable medium comprising a plurality of machine-readable instructions executed by one or more processors, the plurality of machine-readable instructions causing the one or more processors to perform operations comprising:
determining an expected source mechanism of a strain field;
based on the expected source mechanism, estimating strain field tensors of the strain field in an area of interest;
determining principal strain vectors from the strain field tensors;
identifying the most extensional principal strain vectors, ε 3 , from the principal strain vectors;
establishing a trajectory of a fiber optic path through the area of interest;
discretizing the fiber optic path to obtain directions of fiber axial strain, ε a ;
comparing ε a against ε 3 ; and
based on the comparison, optimizing the fiber optic path for an alignment of ε a with ε 3 .