Gaussian filter to process tracer breakthrough curves

Abstract

Breakthrough curves in hydrogeology are similar to seismograms in containing a variety of undesired noises and regular interferences characterized with high frequency. In this paper, Gaussian filter for processing seismic waves is used to retain low-frequency trend of breakthrough curves and remove away high-frequency fluctuations. At first, the mathematical fundamental of the filter is introduced. Then the filter is applied to process four breakthrough curves measured in laboratory experiments, in which Gaussian parameter is set to be 0.2 and 0.5. Finally, a breakthrough curve in field test is processed with different Gaussian parameters. The results demonstrate how the parameter controls the cutting-off frequency and the filter is well controllable and very efficient in acquiring the primary trend of the curves. Key words: Gaussian filter; convolution; breakthrough curves, cutting-off frequency, noises. Analiza sledilnih krivulj z Gaussovimi filtri Sledilne krivulje (krivulja casovne odvisnosti koncentracije povrnjenega sledila) v hidrogeologiji so podobno kot seizmogrami v geofiziki obremenjene z nezaželenimi visokofrekvencnimi sumi in interferencami. V tem clanku uporabimo Gaussov filter, primarno namenjen obdelavi seizmicnih podatkov, za odstanitev visokofrekvencnih sumov iz sledilnih krivulj. Najprej predstavimo matematicne osnove filtriranja, potem Gaussov filter z parametrom 0,2 in 0,5 uporabimo na stirih sledilnih krivuljah, dobljenih v laboratorijskih pogojih. Na koncu z razlicnimi Gaussovimi parametri obravnavamo sledilno krivuljo, dobljeno pri sledenju v naravi. Z rezultati prikažemo vpliv izbranih parametrov na mejno frekvenco ter prilagodljivost , ucinkovitost in uporabnost filtra za izluscenje primarnih znacilnosti sledilnih krivulj. Kljucne besede: Gaussov filter, konvolucija, sledilne krivulje, mejne frekvence, sum.