gmg.ankara.edu.tr

ACKNOWLEDGEMENTS This work is supported by the Scientific and Technical Research Council of Turkey (TUBITAK) under Project No: 110Y309 and 114E076.

Joint Inversion of Direct Current Resistivity, Radio-Magnetotelluric and Seismic Refraction Data: its implementation on hydrogeological problems

İsmail DEMİRCİ1, M. Emin CANDANSAYAR1, Pantelis SOUPIOS2 and Antonis VAFIDIS2

1Ankara University, Faculty of Engineering, Department of Geophysical Engineering, Geophysical Modeling Group (GMG), 06830 Gölbaşı, Ankara-TURKEY 2Department of Natural Resources and Environment, Technological Educational Institute of Crete, 3 Romanou, 73133, Chalepa, Chania, Crete, GREECE

idemirci@eng.ankara.edu.tr| candansayar@ankara.edu.tr

Direct Current Resistivity, Radio-magnetotelluric and Seismic Refraction method was used by some researchers in the solution of hydrogeological problems and the collected data inverted with individual inversion algorithms. Resistivity and velocity models obtained from individual inversion algorithms interpreted simultaneously. We developed a new joint inversion algorithm for Direct Current Resistivity, Radio-magnetotelluric and Seismic Refraction data based on cross gradient approach. In addition, we proposed a new data weighting matrix to stabilize the convergence behavior of the inversion algorithms. To evaluate the performance of developed joint inversion algorithm, we used both synthetic and field data. Our results showed that more unique hydrogeological scenario was obtained especially in high conductive media with the developed joint inversion algorithm using proposed data weighting matrix.

1 SUMMARY 5 FIELD DATA

The main highlights of this study can be given as follows:

A new joint inversion algorithm for SR, DCR and RMT data was developed and the results was discussed with using synthetic and field data study. With the joint usage of these method, near surface and deeper structures were better solved if one compare with the real model in synthetic data inversion.

DCR method is mainly affected from resistive and RMT method is mainly influenced from conductive structures. Amplitude of the resistive and conductive model parameters can be obtained very close to real resistivity of subsurface structures with the joint usage of these two methods. The increased resolutions of resistivity model parameters affected the solution of velocity model parameters in positive direction and vice a versa.

We proposed and used a new data weighting matrix into the developed joint inversion algorithm. Thus, the solution of model parameters affected from all methods in equal rate. Joint inversion results of synthetic and field data was confirmed our suggestions especially in high conductive media.

6 CONCLUSIONS

In recent years various techniques have been proposed to jointly invert data sets obtained from different geophysical methods. Nowadays most accepted approach for joint inversion is structural approach (Haber and Oldenburg 1997; Gallardo and Meju 2003).

In many hydrogeological investigations, DCR and SR methods were often used (Choudhury et al. 2001; Abdalla et al. 2010) and jointly inverted to determine lithology and hydrogeology of the medium (Hamdan and Vafidis 2013). Especially, determination of resistive unit under the conductive unit is generally hard with using DCR method. Because of that, to improve the resistivity image quality, many researchers proposed the joint usage of Electric and EM methods (Candansayar and Tezkan 2008). In this study, we used Radio-magnetotelluric (RMT) method to improve the resolution of resistivity model parameters. Thus, in our joint inversion algorithm not only resistivity model parameters but also velocity model parameters affected positively from this improvement.

Nowadays, the most discussed topic on joint inversion algorithms is to obtain more stable results. Many researchers discussed their joint inversion algorithm results with different weighting approaches (Athanasiou et al. 2007; Gallardo et al. 2012; Lochbühler et al. 2013). In this study, we proposed and discussed the effect of new weighting operator to stabilize the convergence behavior of the joint inversion algorithms.

2 INTRODUCTION

Individual Inversion After the minimization of the objective function, parameter correction Δmx (x depicts DCR, RMT and SR methods), is given as follows:

Wdx Data weighting matrix Δdx Differences between measured and calculated data Ax Sensitivity (Jacobean) matrix Δmx Parameter correction vector C Laplacian operator αx Regularization parameter

In our individual inversion algorithms, parameter correction vector was solved using QR factorization and regularization parameter αx calculated by using cooling approximation (Candansayar 2008).

Joint Inversion with using Structural Constraints The mathematical formulation of this approach was introduced by Haber and Oldenburg (1997). According to this approach, the different physical parameters affect each other simultaneously. Nowadays, the most used approach is Cross Gradient Function introduced by Gallardo and Meju (2003). This function is used as a regularization parameter of objective function and as a result of the minimization of objective function, the parameter correction vector given as below;

Ω cross gradients for all cells making up the model B derivatives of Ω with respect to the model parameters

Data Weighting Matrix in Joint Inversion In joint inversion algorithms, many researchers proposed different weighting matrix (Lochbühler et al. 2013; Athanasiou et al. 2007). In this study, we proposed a new data weighting matrix given as below;

dx :denotes the number of data ax balancing operator protect the weight between resistivity and slowness parameters

Thus, each data set and each different physical parameter used in joint inversion algorithm was normalized in order to affect the solution of model parameters at the same rate by this multiplication.

3 INVERSION

mm

m

R

S

g

g g

g

DC

RMT

S

0

0 0

G GG

G

DC RMT

S

Bafra is a delta plain, which is located on the middle part of the Black Sea coast in Samsun-Turkey (Fig-3). Kızılırmak river passes through the plain in N-S direction. Because of that plain mainly consists of slightly sloped alluvium formations. The alluvium around the flooding area consists of sandy and silty gravels. The origin of the gravel basically comes from volcanic rocks and limestones. The alluvium field out of the flooding area is characterized by silty-clay, sandy-clay and clay minerals. Bafra plain involves two permeable geologic units and aquifer levels. Also, there was a borehole very close to our investigation area with approximately 21m depth. Five geological units are defined.

Data Collection Settings:

Fig-2:Location map of the study area showing the SR, DCR, RMT profile and sounding location.

Soil(0-2.2m)

Clay(2.2-4.5m)

Clayey Gravel (4.5-6.3m) Mixture of Gravel-Conglomerate (6.3-17.8m)

Clayey Gravel-Conglomerate (17.8-?m)

Fig-3:Sounding Log

Fig-4:Field data application: a1-b1-c1) Individual inversion results, a2-b2-c2) Joint inversion results with standard data weight, a3-b3-c3) Joint inversion results of proposed weighting operator for SR, DCR and RMT methods, respectively.

Fig-8:SR data measured and calculated data fittings for: a2) Individual inversion results, b2) Joint inversion results with standard data weight, c2) Joint inversion results of proposed weighting operator, respectively. Fig-7:Field data pseudo-sections

for DCR method, a) Measured data, b) Individual inversion, c) Joint inversion with standard data weight, d) Joint inversion with proposed weighting operator

Fig-9:Field data pseudo-sections for RMT method: pseudosection of measured data, individual inversion, Joint inversion with standard data weight and Joint inversion with proposed weighting operator (respectively): a1. b1. c1. d1. TE mode apparent resistivity, a2. b2. c2. d2. TM mode apparent resistivity a3. b3. c3. d3. TE mode impedance phase, a4. b4. c4. d4. TM mode impedance phase

First, we discussed our results with proposed data weighting matrix with equal balancing operator (ax=1) for all method (kSR=2.87,kDCR=3.44,kRMT=1). With this approximation, we only normalized the effect of data size. Visible improvement on conductive and resistive parameters was seen in joint inversion result of resistivity model. Also, similar improvements can be seen in velocity model parameters.

With our proposed data weighting matrix, not only effect of different methods but also different physical parameters balanced in joint inversion algorithm. Due to the use of this weighting matrix, significant improvement especially in velocity model can be occur. This improvement influenced the solution of resistivity parameters in positive direction. Also amplitude and position of the resistivity and velocity model parameters was very close to synthetic model compared to other solution results.

4 SYNTHETIC DATA

DCR RMT SR

Electrode/Station/geophone Interval (m) 5 5 2.5

Array/freq./Shot Dipole-Dipole 1MHz to 10 KHz (21 frequencies)

35 shot

Number of stations/electrode 56 56 48

Number of Data 762 2302 840

Abdalla OA, Ali M, Al-Higgi K, Al-Zidi H, El-Hussain I, Al-Hinai S (2010) Rate of seawater intrusion estimated by geophysical methods in an arid area:

Al Khabourah, Oman. Hydrogeology journal, 18(6), 1437-1445. doi: 10.1007/s10040-010-0606-0 Athanasiou EN, Tsourlos PI, Papazachos CB, Tsokas GN (2007). Combined weighted inversion of electrical resistivity data arising from different

array types. Journal of applied geophysics, 62(2), 124-140. doi:10.1016/j.jappgeo.2006.09.003 Candansayar ME (2008) Two-dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least-squares solution

with singular value decomposition algorithm. Geophysical Prospecting, 56(1), 141–157. doi: 10.1111/j.1365-2478.2007.00668.x. Candansayar ME, Tezkan B (2008) Two-dimensional joint inversion of radiomagnetotelluric and direct current resistivity data, Geophysical

Prospecting, 56(5), 737–749, doi:10.1111/j.1365-2478.2008.00695.x. Choudhury K, Saha DK, Chakraborty P (2001) Geophysical study for saline water intrusion in a coastal alluvial terrain. Journal of Applied

Geophysics, 46(3), 189-200. doi:10.1016/S0926-9851(01)00038-6 Gallardo LA, Meju MA (2003) Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data.

Geophysical Research Letters, 30(13), 1658–1661, doi: 10.1029/2003GL017370. Gallardo LA, Fontes SL, Meju MA, Buonora MP, de Lugao PP (2012) Robust geophysical integration through structure-coupled joint inversion and

multispectral fusion of seismic reflection, magnetotelluric, magnetic, and gravity images: Example from Santos Basin, offshore Brazil. Geophysics,77(5), B237-B251. doi: 10.1190/geo2011-0394.1

Haber E, Oldenburg D (1997) Joint inversion: A structural approach. Inverse Problems, 13(1), 63–77, doi: 10.1088/0266-5611/13/1/006. Lochbühler T, Doetsch J, Brauchler R, Linde N (2013) Structure-coupled joint inversion of geophysical and hydrological data. Geophysics,78(3), ID1-

ID14. doi: 10.1190/geo2012-0460.1

1 1 1( ) ( )T T T T i

x x x x dx dx x x x dx dx x x x T Tm G g A W W A C C A W W d C Cm

1

1 1 1 1

1 1( )T T

i i

m G g G B BG B BG g B m m

max( , , )1 1x DC RMT Sdx x

jx x jx

a N N Nk diag diag

N

W

Fig-1:a1-b1-c1) Synthetic test models (Gallardo and Meju, 2004), a2-b2-c2) Individual inversion results, a3-b3-c3) Joint inversion results with standard data weight, a4-b4-c4) Joint inversion results of proposed weighting operator for SR, DCR and RMT methods, respectively.

7 REFERENCES