Geologic cross-section (x,z) at Mont Terri

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). Horizontal borehole BPP-1 (20m) (1) Multiresolution wavelet analyzis of X(t) Spectral & correlation functions (univariate) Cross-spectral & cross-correl. analyses Cross-correl. Rxy() Transfer function Gxy() Auto-correlation function Rxx() Dyadic decomposition: scale/time diagrams… Time  frequency Time  frequency Isolation of the half-daily wavelet component of X(t) (select scale T  12h) Spectral densitySxx(f) of signal X(t) Frequency gain Gxy(f)of system X(t)Y(t) RAW SIGNALX(ti) (I) - Identify specific storativity Ss (m-1) using Bredehoeft’s relation (II) - Identify effective porosity Φ(m3/m3) via Barometric Efficiency... 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* Stats? (b) (a) STEP 2: Preliminary Reconstitution of the gaps: - R00: constant average, with Δt variable - R01: moving average, with Δt variable Statistics: M0x,C0xx,σx0 STEP 5 : Reconstitution of all missing and aberrant values: - R11: linear Interpolation - AR1: random autoregressive 24h 24h STEP 3: Detection of the aberrant values; automatic marking (« Inf » or «  ») STEP 4: Truncation of left and right gaps of X(t) 12h 12h STEP 7: Adjusting the length of the time series STEP 6:Homogenization of Δt(i)  Δt0 constant Fractioning in 2 subsequences (recursively) Stats? Time series reconstitued End of the pre-processing Analysis Atmospheric pressure signal with missing data & outliers Detection of outliers in time series : missing Time span : 02/04/1997 to 30/06/1998 : Outlier, spurious : Missing data Time(days) Time(days) Reconstitution of missing data with AR1 model : available pieces of the signal Time(days) : reconstituted pieces of the signal (5) 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. Fatmi1, R. Ababou 1, J.M. Matray 21 Institut de Mécanique des Fluides de Toulouse, Allée du Professeur Camille Soula, 31400 Toulouse, France. Email : fatmi@imft.fr; ababou@imft.fr2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire, Av. General Leclerc, BP n°17, 92262 Fontenay-aux-Roses, France. Email : jean-michel.matray@irsn.fr Study site: the Mont Terri underground laboratory in Switzerland (Jura) Geologic cross-section (x,z) at Mont Terri 3D positioning of tunnel, galleries and boreholes at Mont Terri (2) (3) (4) Statistical Analyses of Time Series: Statistical Analysesof (Pre-Processed) Signals,and Identification of Clay Material Properties. Pre-Processing of Time Series • Objective of this work. The Mont Terri time series (pATM(ti), p1(ti), ...) 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 PATM). • 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”. Pre-processed time series : X(t) = p(t)-pATM(t) and Y(t) = pATM(t) • 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). Flowchart of Pre-Processing Tasks Application (I):identification of SS (m-1) Raw pressure signal (1 month) Pre-processed signal (15 months) Pre-processing example:reconstruction of atmospheric pressure signal 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). 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). 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)