Single and Multi-Objective Optimization of Distributed Acoustic Sensing Cable Layouts for Geophysical Applications

TL;DR

Problem addressed: optimising DAS cable layouts under terrain, accessibility, and exclusion-zone constraints to maximize information for seismic source location and surface-wave tomography. Approach: a spline-based, knot-parametrised cable representation with knot-based control points (yielding channel locations $\mathbf{c}_i$ and orientations $\mathbf{u}_i$) optimised by derivative-free evolutionary algorithms across single- and multi-objective criteria, including $EIG$ and $\Sigma_D$ (D-optimality). Contributions: adaption of linearised travel-time tomography and probabilistic source-location design to DAS directional sensitivity; demonstration on the Cuolm da Vi slope showing enhanced source-location and ambient-noise tomography performance; and a scalable island-model parallel framework. Significance: enables robust, constraint-aware DAS deployments with quantitative trade-offs across objectives for diverse geophysical applications.

Abstract

We present a systematic approach to optimise distributed acoustic sensing (DAS) fibre-optic cable layouts using global optimisation techniques. Our method represents cable geometries using splines, enabling efficient exploration of layouts while respecting physical deployment constraints. The use of evolutionary algorithms enables single and multi-objective optimisation, taking into account complex design constraints such as terrain, accesibility, exclusion zones and cable length, while allowing efficient parallelisation of the optimisation process. We demonstrate the approach on a real-world case study, optimising the layout of a DAS cable for monitoring slope stability in the Cuolm da Vi area of Switzerland. We adapt design criteria for seismic source location problems, and for ambient noise surface wave tomography, to account for the unique characteristics of DAS, such as directional sensitivity patterns. The results show significant potential for improvements in source location accuracy and surface wave tomographic resolution by optimising cable layouts, highlighting the potential of this approach for optimising DAS deployments in various geophysical applications.

Figures (16)

• Figure 1: Example of a DAS cable parametrisation with similar knots but different spline types: linear (k=1) and cubic (k=3).
• Figure 2: Top panel: Reduction in amplitude of seismic waves as a function of distance from source. Cylindrical decay of surface waves and spherical decay of body waves are shown alongside P- and S-wave decay derived from the local magnitude scale of Yin2023-EarthquakeRelation. Bottom panel: Attenuation of laser signal as a function of distance along the cable.
• Figure 3: Sensitivity (top) and SNR (bottom) for P-waves as a function of azimuth and distance to the source, for sources at different depths z in both homogeneous (left) and horizontally layered (right) velocity models. The SNR calculations assume a reference distance of $R_\text{ref} = 20 \text{km}$ using the local magnitude scale of Yin2023-EarthquakeRelation. The radius of each circle is set to $R_\text{ref}$. The channel receiver is positioned at the centre and oriented along the east-west direction for a horizontal cable. To the right, the layered velocity model used is shown.
• Figure 4: Sensitivity (top) and SNR (bottom) for S-waves as a function of azimuth and distance to the source, for sources at different depths z in both homogeneous (left) and horizontally layered (right) velocity models. The SNR calculations assume a reference distance of $R_\text{ref} = 20 \text{km}$ using the local magnitude scale of Yin2023-EarthquakeRelation. The radius of each circle is set to $R_\text{ref}$. The channel receiver is positioned at the centre and oriented along the east-west direction for a horizontal cable. To the right, the layered velocity model used is shown.
• Figure 5: Sensitivity for Rayleigh (center) and Love (right) waves as a function of the azimuths of the two channels relative to the wave propagation direction, which is set to have azimuth zero for the purposes of display. The sketch on the left illustrates the azimuths of the two channels $\theta_1$ and $\theta_2$ and the direction of the line connecting the two channels $\phi$. Adapted from Fang2023-DirectionalCalifornia.