Presentation on theme: "Statistical pre-processing and analyses of hydrometeorologic time series in a geologic clay site (methodology and first results for Mont Terri’s PP experiment)"— Presentation transcript:
Statistical pre-processing and analyses of hydrometeorologic time series in a geologic clay site (methodology and first results for Mont Terri’s PP experiment) H. Fatmi 1, R. Ababou 1, J.M. Matray 2 1 Institut de Mécanique des Fluides de Toulouse, Allée du Professeur Camille Soula, 31400 Toulouse, France. Email : email@example.com; firstname.lastname@example.org 2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire, Av. General Leclerc, BP n°17, 92262 Fontenay-aux-Roses, France. Email : email@example.com@firstname.lastname@example.org@irsn.fr Geologic cross-section (x,z) at Mont TerriStudy site: the Mont Terri underground laboratory in Switzerland (Jura) (2)(3) Horizontal borehole BPP-1 (20m) (4) 3D positioning of tunnel, galleries and boreholes at Mont Terri Pre-Processing of Time Series Objective of this work. The Mont Terri time series (p ATM (t i ), p 1 (t i ),...) are affected by several defects common to many such data banks. These defects need to be (i) detected and (ii) corrected. Here, the problems are : (i) Missing data (e.g., isolated gaps, but also, much longer gaps involving hundred’s of time steps). (ii) Variable time step t(i) (e.g. : t = 1 min, 30 min, 4 days…). (iii) Outliers or spurious data (“aberrations”), affected by very large measurement errors and bias, e.g. defective instruments or uncontrolled human intervention (for example, negative values of P ATM ). Note: “ Missing data ”and “variable time step” can be interchanged in some cases. Indeed, the raw time series from Mont Terri contain explicit markers of “missing data” – and have a variable sampling time step. In some cases, it may be necessary to pre- process the raw signals for the specific purpose of re-classifying unreasonably large time steps t(i) as additional “missing data”. Statistical Analyses of Time Series: Statistical Analyses of (Pre-Processed) Signals, and Identification of Clay Material Properties. Fractioning in 2 subsequences (recursively) RAW SIGNAL X(t i ) MARKERS: Manual marking of missing data with 1.0E101 (note: Δt(i) is variable). STEP 1: Truncation of left and right sequences of missing data, and extraction of longest continuous sequence X*(t). Statistics Mx*,Cx*x*, σx* STEP 2: Preliminary Reconstitution of the gaps: - R00: constant average, with Δt variable - R01: moving average, with Δt variable STEP 3: Detection of the aberrant values; automatic marking (« Inf » or « » ) STEP 5 : Reconstitution of all missing and aberrant values: - R11:linear Interpolation - AR1: random autoregressive STEP 6: Homogenization of Δt(i) Δt0 constant Time series reconstitued End of the pre- processing Statistics: M0x,C0xx,σx0 Stats? Analysis Stats? STEP 7: Adjusting the length of the time series STEP 4: Truncation of left and right gaps of X(t) Flowchart of Pre-Processing Tasks Pre-processing example : reconstruction of atmospheric pressure signal General objectives Evaluate direct and coupled pressure transfer processes involving fluctations of pore pressure under the influence of natural “forcings” (earth tides, barometric fluctuations, rainfall, humidity,...) at various time scales. Specific objectives Estimate the hydraulic properties (specific storativity, compressibility, porosity,...) of Mont Terri opaline clays, as well as their evolution in time over long time scales, and compare them to properties estimated from hydraulic tests (pulse and slug tests conducted over short time scales). Application (I): identification of S S (m -1 ) Raw pressure signal (1 month) Pre-processed signal (15 months) Reduced spectrum of PP1(t), the first difference of relative pore pressure PP1(t) (kPa) at Mont Terri. Time span Tmax 1 month (from 02/08/2002 to 04/09/2002). Time step: t = 30 min (sampling step: k=1). Multiresolution wavelet analyzis: time evolution of one of the dyadic components of PP1(t), obtained at time scale T=8h (near 12h). Note: unprocessed signal with Tmax 1 month and t = 30 min (same as above). Multiresolution wavelet analyzis: time evolution of one of the dyadic components of PP1(t) obtained at time scale T=8h (near 12h). Note: pre-processed signal with Tmax 15 months and t = 30 min (same as above). (6) Pre-processed time series : X(t) = p(t)-p ATM (t) and Y(t) = p ATM (t) Reduced spectrum of PP1(t), the first difference of relative pore pressure (kPa) at Mont Terri. Time span: 15 months (from 29/01/2004 to 12/04/2005). Time step of pre- processed signal: t = 30 min (and k=1). Abstract: This poster presents a set of statistical methods for pre- processing (or pre-conditioning) and analyzing multivariate hydrogeologic time series, such as pore pressure and its relation to atmospheric pressure. The signal processing methods aim at characterizing the hydraulic behavior of a porous clayey formation in the context of deep geologic disposal of radioactive waste. Introduction: The signal processing methods illustrated here were applied to measurements obtained over a period of ten years in the Opalinus clay at the underground research laboratory of Mont Terri in Switzerland (international consortium). Absolute pore pressures are monitored in the “chambers” PP ‑ 1 and PP ‑ 2 of the BPP1 borehole (niche PP). The BPP ‑ 1 borehole was selected because it provided the longest times series of pore pressure (sensors PP ‑ 1 and PP ‑ 2) over a period of roughly ten years (17/12/1996 to 30/06/2005). (1) Spectral & correlation functions (univariate) Cross-spectral & cross-correl. analyses Multiresolution wavelet analyzis of X(t) Cross-correl. Rxy( ) Transfer function Gxy( ) Dyadic decomposition: scale/time diagrams… Time frequency Spectral density Sxx(f) of signal X(t) Time frequency Frequency gain Gxy(f) of system X(t) Y(t) Isolation of the half-daily wavelet component of X(t) (select scale T 12h) (II) - Identify effective porosity Φ (m 3 /m 3 ) via Barometric Efficiency... Auto-correlation function Rxx( ) (I) - Identify specific storativity Ss (m -1 ) using Bredehoeft’s relation (5) (a) 24h 12h (b) 24h 12h Reconstitution of missing data with AR1 model : available pieces of the signal : reconstituted pieces of the signal Time(days) : missing Detection of outliers in time series Time(days) Atmospheric pressure signal with missing data & outliers : Outlier, spurious : Missing data Time span : 02/04/1997 to 30/06/1998 Time(days)
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