Towards Three Component Seismograms From One Component DAS Records; Finite Frames in Geophysics

TL;DR

This paper introduces a method using finite frame theory to reconstruct full three-component seismograms from single-component DAS records, enabling improved geophysical data analysis from limited measurements.

Contribution

It presents a novel reconstruction algorithm based on finite frame theory to recover 3C vectors from 1C DAS data, demonstrated on geothermal borehole data.

Findings

Successful recovery of high-precision 3C vectors from 1C DAS data.

Application to Utah FORGE geothermal data shows practical viability.

Reconstruction improves the utility of single-component measurements.

Abstract

Some geophysical observations commonly collect only one component (1C) of a three component (3C) vector field. For example, Distributed Acoustic Sensing (DAS) records seismograms derived from displacement differences along the axis of segments of a fiber optic cable. In practice, multiple observations from such 3C vector fields are available, but commonly along non-orthogonal directions -- i.e.\ desirable sets of observations along orthogonal basis vectors are not available. For DAS, the theory of (finite) frames allows the recovery of 3C vector observations as long as the set of measurements occur on axis-vectors that mathematically span 3D space. A reconstruction algorithm from finite frame theory is described and then applied to geometry data from a borehole at the Utah FORGE geothermal project. The results demonstrate recovery of high precision 3C vectors along the fiber optic cable from 1C input vector-projections.