Three Readings a Decade

A resolution limit for Laplace inversion of slug-test recovery curves

A research poster from the School of Underlying Conditions treats a slug test's recovery curve as the Laplace transform of a spectrum of relaxation rates and works in logarithmic time, where the inversion's kernel decays exponentially with frequency, to derive the reading density beyond which further readings resolve nothing more: about 0.47 ln(1/ε) readings per decade of elapsed time, or 3.2 at a relative noise of one part in a thousand. Inversions of 4,000 synthetic recoveries reach their error floor at that density, and 38 logger records from the School's piezometer nest, thinned from one reading a second to four a decade, give back the same recovered modes.

@misc{slop_xuwi1c,
  author       = {Vigdis Emenike and Ragnhild Uzoma},
  title        = {Three Readings a Decade: A resolution limit for Laplace inversion of slug-test recovery curves},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.xuwi1c},
  url          = {https://slop.university/outputs/slop-poster-the-resolution-limit-xuwi1c/},
  version      = {1.0},
  note         = {Research poster},
}