Inversion comparison study in the cases of different

IAGA WG 1.2 on Electromagnetic Induction in the Earth Extended Abstract 19th Workshop Beijing, China, October 23-29, 2008

Inversion comparison study in the cases of different array configuration and inversion method Dahai Zhang1,2, Torleif Dahlin1, Roger Wisén1 1 2

Department of Engineering Geology, Lund University, Sweden

Shanghai Offshore Oil&Gas Company, SINOPEC, Shanghai, China

SUMMARY By inversion comparison study in the cases of different arrays (WN, SH, PP, DD, PD, GN) and inversion methods, 3-D effects on 2-D resistivity imaging were showed via numerical simulation of synthetic models and subsequent inversion of synthetic datasets and field datasets. Inversion was executed using 2-D and 3-D inversion software. 3-D finite difference forward modeling was carried out, and datasets were extracted as 2-D pseudosection along parallel profiles in one direction of the models. These datasets were inverted individually using a 2-D inversion algorithm and combined using a 3-D algorithm. In both cases inversions were carried out with L1-norm (robust) inversion as well as L2-norm (least-square) inversion. Keywords: DC, 3-D inversion, quasi-3D, array configuration, inversion parameter. effects in 2-D surveying are much smaller than

INTRODUCTION

2-D effects in 1-D surveying (Dahlin and Loke, Today 2-D resistivity surveying plays an

1997). The results presented here show that,

important

area

nevertheless, there is an advantage in performing

investigations. DC resistivity imaging is applied

3-D inversion compared to 2-D inversion. Of

broadly in the fields of engineering and

course, this also takes into consideration the

environmental surveying. We show that where a

extraordinary development of computers since

3-D environment is evident, the 3-D resistivity

the former studies.

role

in

many

large-scale

survey, as presented here, with subsequent 3-D inversion can give a much increased detail and

For the results presented here more tests, using

accuracy of the resulting resistivity model than

more experimental factors than for the earlier

the 2D inversion. In many cases this will most

studies (model parameters, array configurations,

likely be motivated by the aim and against the

inversion parameters, etc.), have been made.

additional costs.

Numerical simulation has been made for several resistivity models. Results from one of these

One of the most important short-comings for

models, that are representative for the entire

3-D inversion is that it is time-consuming and

study, are presented here. Also, a field example

computer exhaustive. The existence of 2-D

that clearly show the advantage of 3-D inversion

effects on 1-D resistivity modeling is a well

are presented.

known problem(e.g. Dahlin and Loke,1998). Former studies of 3-D effects on 2-D inversion,

METHOD

utilizing numerical simulation, show that 3-D

19th IAGA WG 1.2 Workshop on Electromagnetic Induction in the Earth Beijing, China, October 23-29, 2008

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ZHANG, et al, 2008, Inversion Comparison Study

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Techniques for acquisition and methods for

order to better understand the differences

interpretation of resistivity measurements have

between 2-D and 3-D inversion. Synthetic data

been

used

for different array configurations have been

extensively for several decades. Continuous

inverted using 2-D inversion with L1 and L2

profiling has been used to obtain a 2D image of

norm and 3-D inversion with L1 norm.

the

continuously

subsurface

developed

resistivity

and

and

is

a

well-documented method (Griffiths and Turnbull,

In the field examples, resistivity data was

1985; Overmeeren and Ritsema, 1988; Dahlin

collected as CVES data with different versions

1993; Griffiths and Barker 1993; Dahlin 2001).

of the ABEM Lund Imaging System (Dahlin, 1996). This CVES system allows for very

The

pole-pole

pole-dipole

(PP),

(PD),

dipole-dipole Wenner

(DD),

(WN)

and

flexible data collection. Based on the target and the

actual

geophysical

configuration

known

programmed and, if desirable, altered during the

described

in

any

standard

geophysical textbook (e.g. Sharma, 1997). The

data

density

can

any

Schlumberger (SH) configurations are well and

and

problem,

be

measurement sequence.

depth of investigation and sensitivity problems of different arrays are discussed by many authors (e.g.

Edwards,

1977;

Loke,

2002).

SYNTHETIC RESULTS

The

application of the multiple gradient (GD) array

The synthetic models are constructed in 6 layer

(Figure 1) for multi-channel measurement

slices, with a 41 by 21 electrode grid as shown in

systems was introduced by Dahlin and Zhou

2. The layer depths are 0.3, 0.7, 1.5, 2.4, 3.5 and

(2004). They show that this array has a high

4.7 m respectively. This model is a little bit

signal to noise ratio and at the same time a good

complex and can be regarded as a horst structure

distribution of the sensitivity. In this study we

with a contact between two rock units with

tested these six different array configurations.

different resistivity, 1000 Ωm and 300 Ωm respectively. The horst structure is overlain by a layer of 70 Ωm resistivity, representing a soil




layer. This layer also contain two smaller bodies

a A

M na

of low (30 Ωm) and high (1000 Ωm) resistivity.

B

N ma

Within the high resistive rock unit there is a low

sa

resistive structure (10 Ωm) representing a weathered fracture zone in the hard rock. Figure 1. Sketch

of

gradient

array

layout

showing the position of the electrodes for a

The 2D robust inversion result with WN, SH,

measurement

PD, and PP arrays are showed in Figure 3.

with separation factor

s = 7,

n-factor 2 and midpoint factor m = -2. The n-factor is here defined as the relative spacing

The location and geometry of the anomaly body

between the potential dipole and the closest

were showed from the slice map in different

current electrode.

array configurations, but the shape of anomaly body was distorted severely in the lower part for

The numerical simulations were carried out in

PD arrays, and for PP arrays it shows blur

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ZHANG, et al, 2008, Inversion Comparison Study

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anomaly boundary in the shallow part. Generally

depth of 4.3 meter, but the resistivity of

speaking, inversion result with WN arrays shows

surrounding media is a bit lower than true one,

the higher resolution compared to synthetic

even in 3-D inversion this problem still can be

model in the lower or shallow part.

found. Anyway, Wenner and gradient arrays inversion show the best representation ability in the

description

of

underground

electrical

property distribution among 6 different kinds of array configurations in the synthetic model experiment. FIELD DATASET Recently we made another field electrical resistivity measurement in Mörrum, South Sweden. The measurement net parameters are: seven 160m-long profiles, 5m electrode spacing, and 10m line spacing. The whole profile is west-eastward, and a weathering outcrop of blocky rock with slight topographic uphill is Figure 2. The depth slice map of conductive horst model with noisy surface model.

included in our work area, and gradient array was employed in this survey. Figure 24 shows the depth slice map of 2-D robust inversion and 3-D inversion results. From the 2D result, it is

Simultaneously we showed the inversion results

very obviously that a high resistivity (~ 10000

in general gradient array (Fig. 4). First, let’s

Ohm m) anomaly blocky body is located in the

have a quick look for 2-D inversion result slice

south part of the work area, extends to the deep

maps. In the shallow part, a conductive and

and disappeared at ~20m; about the same depth

resistive rectangle anomaly body is showed

place another high resistivity region emerges at

clearly in 2-D LS inversion, and horst structure

the northeast corner of work area; based on

in lower part is also represented as a stable and

above-discussed

continuous conductive anomaly extended to the

resistive anomaly body emerged on the surface

deeper; and better effect could obtain in 2-D

with conductive surrounding layer stems from

robust inversion, more strictly constrained

lower high resistivity basement located at the

condition made the border of anomaly body

northeastward depth of 20~30m, that is to say,

more clear and improve the inversion quality,

the whole high-resistive structure body obtruded

but which has the influence on the inversion

and exposed to the surface from lower northeast

effect on near-surface. Gradient arrays result

direction. At the same time we processed the

show better ability of survey depth than Wenner

datasets by 3-D robust inversion (see right map

arrays, even in the case of 2-D robust inversion,

in Fig. 24). The 3D result shows the similar

we still can distinguish the geometry shape,

electrical property distribution with 2D inversion

position and resistivity of conductive body in the

but higher resolution in lower part, it is the

19th IAGA WG 1.2 Workshop on Electromagnetic Induction in the Earth Beijing, China, October 23-29, 2008

we can deduce that the high

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ZHANG, et al, 2008, Inversion Comparison Study

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reason that 2-D inversion got the fewer data

electrode arrays, Geophysical Prospecting, 52,

points than 3-D. But the 3-D result supplies the

379-398.

further clearer testimony to abovementioned deduction.

Dahlin, T., Loke, M. H., 1997, Quasi-3D resistivity

CONCLUSION AND DISCUSSION

imaging

–

mapping

of

three

dimensional structures using two dimensional DC resistivity techniques, Procs. 3rd meeting of

By lots of synthetic geological modeling and

Environmental and Engineering Geophysics

field

Society, Denmark, 143-146.

datasets

inversion,

the

research

consequences show 3-D effects exists in the 2-D surveying, but it is much less than 2-D effects in

Edwards, L. S., 1977, A modified pseudosection

the 1-D surveying. To decrease 3-D effect as

for

possible as we can, the choice of the array

Geophysics, 42, 1020-1036.

resistivity

and

induced-polarization,

configurations and inversion parameter have a important role in the inversion results, Wenner

Griffiths,

D.H.

and

Barker,

and Gradient arrays inversion show the best

Two-dimensional

resolution to the resistivity anomaly structure,

modeling in areas of complex geology, Journal of

and dipole-dipole array gets the worst. 3-D

Applied Geophysics, 29, 211-226.

resistivity

R.D., imaging

1993, and

inversion is sensitive to large-scale resistivity structure than 2-D inversion, and 2-D L1-norm

Griffiths, D.H. and Turnbull, J., 1985, A

inversion also presents the robust advantages in

multi-electrode array for resistivity surveying,

depth and anomaly body border. Combining 2-D

First Break, 3(7), 16-20.

and 3-D advantages, prudent selection of array type and inversion are helpful for improving the

Loke, M. H., 2002, Tutorial: 2D and 3D electrical

final geological model.

imaging surveys. Overmeeren, R.A. van and Ritsema, I.L., 1988,

REFERENCE

“Continuous vertical electrical sounding,.” First Dahlin, T., 1993, On the Automation of 2D

Break, 6(10), 313-324.

Resistivity Surveying for Engineering and Environmental Applications, Dr.Thesis, ISRN

Sharma,

LUTVDG/TVDG--1007--SE,

engineering geophysics, ISBN 0-521-57632-6,

ISBN

91-628-1032-4, Lund University, 187p.

P.V.,

1997,

Environmental

and

Cambridge University Press, UK.

Dahlin, T., 2001, The development of electrical imaging techniques, Computers and Geosciences, 27(9), 1019-1029. Dahlin, T and Zhou, B., 2004, A numerical comparison of 2D resistivity imaging with ten

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Figure 3. Horst model inversion slice map in WN, SH, PP, PD array configuration, respectively.

2-D inversion (L2-norm)

2-D inversion (L1-norm)

3-D inversion (L1-norm)

Figure 4. Horst model inversion slice map in gradient array configuration.

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Figure 5. 2-D (Left) and 3-D (Right) inversion result slice map of gradient field dataset in Mörrum, Sweden.

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