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

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 protected]; [email protected]

2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire, Av. General Leclerc, BP n°17, 92262 Fontenay-aux-Roses, France. Email : [email protected]

Geologic cross-section (x,z) at Mont TerriStudy site: the Mont Terri underground laboratory in Switzerland (Jura)

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Horizontal borehole BPP-1 (20m)

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3D positioning of tunnel, galleries and boreholes at Mont Terri

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”.

Statistical Analyses of Time Series:Statistical Analyses of (Pre-Processed) Signals,and Identification of Clay Material Properties.

Fractioning in 2 subsequences (recursively)

RAW SIGNALX(ti) 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).

StatisticsMx*,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 SS (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).

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Pre-processed time series : X(t) = p(t)-pATM(t) and Y(t) = pATM(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 densitySxx(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 (m3/m3) via Barometric Efficiency...

Auto-correlation function Rxx()

(I) - Identify specific storativity Ss (m-1) using Bredehoeft’s relation

mnnmnn

nnn

NoiseXXt

sXXAR

;0::0:1 0

111

tR

s

XX

X

1)(

1

1

11

21

Detection of outliers, spurious values, or aberrations, based on dimensionless statistical criteria

Threshold criterion based on the distance between X(t) and its moving average :

Threshold criterion based on standard deviation of X(t) around its moving average :

3

~2

~)( ThresholdiXiX

X

4~2

~)( ThresholdiXiX

X

1. The simplified physical model of Bredhoeft:

hSs relates the amplitudes of fluctuations of: volumetric strain (m3/m3) relative pressure head h = (p-pATM)/g , via the specific storativity coefficient SS (m-1).

2. The amplitude of strain fluctuations Δε due to the (dominant) semi-diurnal component of earth tides is typically:

Δε 210-8 [m3/m3]

3. The amplitude of relative pressure head Δh is obtained from multiresolution wavelet analyzis of p(t)-pATM(t) (or PP1(t) here). The wavelet component with dyadic time scale close to semi-diurnal is isolated, and its amplitude evaluated using either rms standard deviation, or absolute mean deviation:

p 0.58 kPa h 0.058 m (a) p 0.60 kPa h 0.06 m (b)

4. The specific storativity is then evaluated :

17104.3 mSs . (a)

17103.3 mSs (b)

(the results obtained for (a) and (b) are close).

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Methods used in this work for reconstituting missing data

AR1 : AutoRegressive 1rst order model, for stationary random processes...

Linear interpolation (for short gaps) Weighted moving average (combined with others) Constant mean (used only as initial step for other methods)

4 August 8 August 13 August 18 August 22 August

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Normalized frequency(ADIM)

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Normalized frequency (ADIM)

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Reconstitution of missing data with AR1 model

: available pieces of the signal

: reconstituted pieces of the signal

Time(days)

12 avril 09 juin 06 aout 03 oct 29 nov 26 janv 25 mars 22 mai93.5

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: 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)