Incorporation of Magnetic Resonance Sounding data into groundwater models through coupled and joint inversion

8th Annual Meeting of DWRIP 2014 JANUARY 30

T.N. Vilhelmsen, A.A. Behroozmand, S. Christensen, E. Auken, and A.V. Christiansen

• Coupled vs. Joint inversion (MRS and groundwater model)

• Mapping the groundwater table using MRS

• Results from coupled inversion tests (synthetic model)

• Perspectives for 3d joint inversion

Outline

Coupled inversion

• Tight link directly through model forward responses

• Here: Groundwater flow model is used to simulate the thickness of the upper layer in an MRS model (unsaturated zone)

Joint vs. coupled inversion

Joint inversion

• Inversion setup is linked through shared parameter characteristics

• Here: Transmissivity derived from MRS (using petrophysical relation) is linked to transmissivity in a hydrological model (through regularization)

Coupled inversion using MRS

Layer 1w,T2*,lt.

Layer 2w,T2*,lt.

Layer 3w,T2*,lt.

MRS model:

Simulated by groundwater

model

The test model

After: Hill, et al., 2000

- Two aquifers separated by an aquitard

- Two recharge zones

- Well pumping from lower aquifer

- Flow in from adjoining hill side

- Flow out through river

- Model observations generated using heterogeneous parameter fields

Reference model (50 realiazations):- Heterogeneous k-

fields (calculated from water content and decay time fields)

- 10 head obs. - 1 river discharge

obs.- 1 MRS sounding

(located at prediction point)

PEST

The inversion setup:

Groundwater model parameter files:

- Hydraulic conductivity zones

- River bed conductance- Recharge

Geophysical model parameter files:

- Holds all geo. phys. par. Except for layer 1 thick (unsaturated zone)

Groundwater model(MODFLOW-2005)

- Simulated heads- Simulated river flow

Geophysical model (AarhusInv)

- Simulated MRS resp.- Simulated TEM resp.

Thickness of unsat. zone

GF only GWM only Sequential Coupled

Mean pred. Error

-0.39 m 3.73 m 3.20 m 1.12 m

Pred. error var.

2.92 m2 7.73 m2 9.9 m2 3.04 m2

Inversion results (50 models)

- Error variance similar / mean error larger

- Independent geophysical inversion cannot improve groundwater model prediction

Goal: Achieve the most accurate prediction of head at MRS location

3d joint inversion of MRS and groundwater models

Goal:- Use MRS to improve estimate of hydraulic

conductivity heterogeneity in groundwater flow models

- Estimate parameters pertaining to the petrophysical relation together with MRS/TEM and hydrological parameters using a regularized coupling

The joint inversion methodology

PEST

Hydrologicalparameters

Groundwater model

Hydrologicalsimulation

Hydrologicaldata𝚽𝒅

Geophysicalparameters

Geophysical model

Geophysicalsimulation

Geophysicaldata

The joint inversion methodology

PEST

Hydrologicalparameters

Groundwater model

Hydrologicalsimulation

Hydrologicaldata𝚽𝒅

Geophysicalparameters

Geophysical model

Geophysicalsimulation

Geophysicaldata

Petrophysicalrelation

Petrophysical relation:Tmrs = [Cp * wa * (T2*)2 ]*lt

𝚽𝒓

𝚽𝒕

Regul. Obj. Fun.

Ristrup well field

Ristrup well field

MRS sounding

Ristrup well field

∑𝒊=𝟏

𝒏=𝒏𝒎𝒓𝒔∗𝒏𝒑𝒑

(𝒌𝒑𝒑∗ 𝒍𝒕𝒑𝒑−𝑻𝒎𝒓𝒔 , 𝒋 )𝒏∗𝝎𝒏=𝟎

MRS sounding

• Coupled inversion• Can reduce head prediction

error

• Will only work for unconfined conditions

• Will be most applicable in remote areas with limited (hydrological) data coverage

• Joint inversion• Expected to increase resolution

of hydraulic conductivity inhomogeneity

• Setup tested and works for a 2d case

• Using joint inversion MRS can be linked to several types of hydrological data (not only aquifer tests)

Perspectives and conclusions