Crosshole Seismic Tomography: CO2 Plume Inversion

Survey Geometry

Stations per borehole 8

CO₂ plume Δv (velocity drop) -20%

ART relaxation λ 0.25

Inversion

Display

slow (CO₂)

fast

Readouts

Sweep (iteration)

Rays / sweep

RMS travel-time residual

— ms

RMS velocity error vs true

— m/s

How it works

A seismic source in the left borehole fires at every receiver depth in the right borehole. Each straight ray path i crosses a grid of subsurface cells with unknown slowness s = 1/v. Its travel time is the line integral of slowness along the path:

t_i = ∫ s(x,z) dl  ≈  Σ_j  L_ij · s_j

L_ij = length of ray i inside cell j

This gives a large, sparse linear system t = L·s. The Algebraic Reconstruction Technique (ART), applying one Kaczmarz row-projection per ray, updates the model after every shot without ever inverting the full matrix:

residual_i = t_obs,i − Σ_j L_ij·s_j
Δs_j = λ · L_ij · residual_i / Σ_j L_ij²
s_j ← s_j + Δs_j   (for every cell j on ray i)

Sweeping over every source-receiver pair once is one iteration. As iterations accumulate, the reconstructed slowness field converges toward the true model — this is exactly the imaging step used in real crosshole seismic surveys that verify CO₂ stays confined in a storage reservoir: injected CO₂ replaces brine in the pore space, which (via the Gassmann relation) lowers the rock's bulk modulus and P-wave velocity by 10–30%, producing the low-velocity anomaly you are inverting for here. Denser station spacing (more rays crossing the plume from more angles) resolves the anomaly faster and more accurately — sparse coverage leaves it smeared or missed, the same trade-off field surveys face.

Borehole stations Rays (source→receiver)

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