International audienceAnthropogenic noise, cost and logistical constrains generaly limit to the use of land CSEM to a few transmiter positions for the deep imaging of the electrical conductivity. The 3D inversion of CSEM data in the near field using a single transmiter position suffers from critical sensitivity singularities. We proposed a robust inversion framework adapted to this ill-conditioned inversion problem. The framework relies specificaly on a robust Gauss-Newton solver, model parameter transformations to compensate the heterogeneous sensitivies, and on the reformulation of the near field CSEM data under the form of a pseudo-MT tensor. We describe the approach used for modeling and inversion implemented in our code POLYEM3D and show the advantages of pseudo-MT tensor formulation. The strategy have been tested on a pathologic synthetic case inspired from grayver et al (2013), and then was successfully applied to a real CSEM dataset acquired in the context of thermal water prospection in a noisy environnement

Bretaudeau, François

Coppo, Nicolas

Darnet, Mathieu

Penz, Sebastien

Wawrzyniak, Pierre

English

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HAL Id: hal-01458151
https://hal-brgm.archives-ouvertes.fr/hal-01458151
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3D land CSEM inversion in noisy environment with a
single transmiter: inversion approach and application for
geothermal water prospection
François Bretaudeau, Sebastien Penz, Nicolas Coppo, Pierre Wawrzyniak,
Mathieu Darnet
To cite this version:
François Bretaudeau, Sebastien Penz, Nicolas Coppo, Pierre Wawrzyniak, Mathieu Darnet. 3D land
CSEM inversion in noisy environment with a single transmiter: inversion approach and application
for geothermal water prospection. International Symposium in Three-Dimensional Electromagnetics
(3DEM), Gerald W Hohmann Memorial Trust, Mar 2017, Berkeley, United States. ￿hal-01458151￿
6th International Symposium on Three-Dimensional Electromagnetics
Berkeley, California, March 28–30, 2017
3D land CSEM inversion in noisy environment with a single transmiter: inversion
approach and application for geothermal water prospection
F. Bretaudeau1, S. Penz1, N. Coppo1, P. Wawrzyniak1, and M. Darnet1
1BRGM (French Geological Survey)
Summary
Anthropogenic noise, cost and logistical constrains generaly limit to the use of land CSEM to a few transmiter
positions for the deep imaging of the electrical conductivity. The 3D inversion of CSEM data in the near field
using a single transmiter position suffers from critical sensitivity singularities. We proposed a robust inver-
sion framework adapted to this ill-conditioned inversion problem. The framework relies specificaly on a robust
Gauss-Newton solver, model parameter transformations to compensate the heterogeneous sensitivies, and on
the reformulation of the near field CSEM data under the form of a pseudo-MT tensor. We describe the approach
used for modeling and inversion implemented in our code POLYEM3D and show the advantages of pseudo-MT
tensor formulation. The strategy have been tested on a pathologic synthetic case inspired from grayver et al
(2013), and then was successfully applied to a real CSEM dataset acquired in the context of thermal water
prospection in a noisy environnement.
Keywords: 3D inversion, land CSEM, noisy environment, single transmiter, sensitivity singularities, thermal
water prospection.
Introduction
EM prospection is a method of choice for many appli-
cations such as deep water or geothermal prospection.
However, the investigated areas are usually urbanised
so high level of cultural noise prevents from the use of
MT. Land CSEM is an alternative. But cost and lo-
gistical constrains generaly limits to the use of a small
number of transmiter positions, most of the time only
one. The inversion of CSEM data in the near field
using a single transmiter position suffers from critical
sensitivity singularities due to the unsymmetric illu-
mination. To overcome this problem we proposed an
inversion framework adapted to this ill-conditioned
inversion problem. The framework relies specificaly
on a robust Gauss-Newton solver, on model parame-
ter transformations and data reformulation under the
form of pseudo-MT tensors. We describe here the
approach implemented in our code POLYEM3D and
investigate the effect of the pseudo-MT tensor for-
mulation. We illustrate its application on a patho-
logic synthetic case inspired from (Grayver, Streich,
& Ritter, 2013) and then show the application of the
process to a real CSEM dataset acquired for thermal
water prospection at a few kilometer from a nuclear
power plant in France.
Method and/or Theory
The POLYEM3D code used in this study relies on
an hybrid semi-analytical/finite-volume modeling on
irregular cartesian grid (Streich, 2009). The FV for-
mulation provides a linear system:
A(ρ, ω)E = b. (1)
where A is the finite-volume operator matrix, ρ a 3D
resistivity distribution, E the 3D electric field and b
the source term.
The computed data dcs,r (component c of the electric
and/or magnetic field at each receiver r generated by
the source s) can be expressed as:
dcs,r = ℘
c
r Es (2)
where ℘cr is a restriction operator that extract the
value of the component of the field from the 3D elec-
tric field computed on the whole grid. It contains
interpolation operators and curl operator for mag-
netic field.
Inversion of EM fields is achieved by minimising the
misfit function:
Φ = δd†Wd
†Wdδd (3)
with δd = dobs − dcal the data residual vector.
In CSEM inversion the data vectors usually contains
each component of the electric and/or magnetic fields
for each station, source and frequencies. However,
other kind of observables can be used to build the
data vector. In the framework of local linear in-
version, we want at each iteration to determine the
model update δm solution of the Gauss-Newton equa-
tion:
<(J†J)δm = −<(J†Wdδd) (4)
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Bretaudeau, F. et al., 2007, 3D land CSEM inversion in noisy environment with a single transmiter
where J is the sensitivity matrix.
Reparameterization of the problem
The sensitiviy J decreases rapidly with the distance
from the source, resulting in a very poorly condi-
tioned linear system to be solved. In POLYEM3D,
this linear system is solved with LSQR that is known
to be efficient for poorly conditioned linear systems.
Preconditionning is also applied by model reparam-
eterization. Instead of performing inversion of ρ, we
can inverse m:
m = G−1D−1 C(ρ) (5)
with C a change of variable (such as logarithm), D an
arbitrary linear operator that rescale the sensitivity
loss with depth (as for instance in (Plessix & Mulder,
2008)), and G a linear operator that change the basis
of description of the model (for instance a basis of
splines described on a coarse grid). Each line of the
sensitivity matrix thus can be written:
Jcs,r = G
tDt
1
C ′(ρ)
Es
∂A
∂ρ
A−1℘cr
t (6)
A pseudo-MT formulation
The reparameterization allows to perform efficient 3D
inversion for MT or multiple source CSEM. However
it is still not enough to inverse CSEM data when a
single source is used, as the sensitivity singularity at
the source cumulates over each line of J. We found
that recasting the data acquired with two different
transmiters using a MT tensor formulation mitigates
the singularity due to the transmiter both in the data
and in the sensitivities. Taking for a station the def-
inition of a Z tensor as a transfer function:(
Ex
Ey
)
=
[
Zxx Zxy
Zyx Zyy
] (
Hx
Hy
)
, (7)
and considering two different sources (it can be typ-
ically two polarization of a single transmiter), we
can obtain for each station the 4 components of this
pseudo-MT tensor by a combination of the 8 electric
and magnetic fields generated by those two sources:
Zij = f(E
c
s , H
c
s). (8)
Recasting the CSEM data under this form reduce the
number of data by 2 and results in a sensitivity matrix
that is a linear combination of the common CSEM
sensitivities weighted by the values of the fields:
JZij = f(JEcs , JHcs , E
c
s , E
c
s) (9)
The pseudo-MT tensor is not to be linked to an appar-
ent resistivity or a MT tensor because depending on
the frequency and the source-receiver distance consid-
ered, the far field condition is not always respected. It
is however a well balanced observable that can be in-
verted if an accurate modeling of the real transmiters
is considered.
Validation on a synthetic case
We illustrate the behavior of the new formulation on
a 3D synthetic resistivity inspired from the model
of (Grayver et al., 2013). The survey is composed of
100 stations over a 5Ω.m medium with 3 anomalies at
1Ω.m, 50Ω.m et 100Ω.m. We consider the inversion
of MT data (far field), and inversion of CSEM data
generated with two orthogonal polarization located at
2km from the closest station, and 5 frequencies from
32s to 16Hz. The CSEM data are inverted first using
normalized electric fields and with pseudo-MTtensor
formulation.
The footprint of the transmiter in the sensitivity is
not completly removed but is reduced enough to al-
low convergence of the inversion. We show in figures
1 to 4 the inversion result obtained for MT data (far
field), normalized CSEM data and pseudo-MT tensor
formulation using 5 frequencies (32s, 8s, 1Hz, 4Hz
and 16Hz). For the CSEM data, the station array is
in far field condition for the highest frequencies and
in near field for the lowest. Sharper results should be
obtained with more efficient regularization but the
conclusions should not differ. Even though the deep
resistive anomaly is underestimated and a few arte-
facts appear around the shallow anomaly, the MT
data inversion reconstructs quite well the 3 anoma-
lies in very few iterations (< 15 iterations). The in-
version of CSEM weighted data fails to converge. It
gets stuck in a local minimum after the 1st iteration.
We clearly see in the inverted model the footprint of
the transmiter sensitivity anomaly which affect the
reconstruction. The deep anomalies are shifted and
smoothed along the wavepath between the transmiter
and the stations. The shallow anomaly is not recon-
structed, and several artefacts appear close to the
surface. Using the pseudo-MT tensor formulation,
the footprint of the transmiter in the sensitivity is re-
duced. Artefacts are still visible under the transmiter,
but the deep anomalies are better reconstructed and
the shallow anomaly is well imaged. Convergence is
also better (15 iterations).
2/4
Bretaudeau, F. et al., 2007, 3D land CSEM inversion in noisy environment with a single transmiter
Figure 1: Exact resistivity model (a) YZ plane
(b) XY plane at z =280m (c) XY plane at
z =1300m.
Figure 2: Final inverted model for the MT data - 4
components of the complex MT tensor
Figure 3: Final inverted model for the CSEM data
- both components of the complex electric and
magnetic fields normalized by a the modulus of
a reference field E0
Figure 4: Final inverted model for the CSEM data -
4 components of the complex pseudo-MT tensor
Real data example
The methodology has been applied to a land CSEM
survey acquired with a single transmiter position and
2 polarizations in an area where the geology is quite
complex with faults and strong 3D effects. The ac-
quisition was performed using 60 stations around the
village of Givet in France, close from the Belgium
border. The survey is located at 5 km from a nuclear
power plant, and high level of cultural noise clearly
prevent from the use of MT. The target was the in-
tersection of the top of a deeping limestone layer with
a regional fault zone at an expected depth of about
800m. Robust processing have been used to estim-
age transfer functions and provide noise estimation
for both component of electric and magnetic field.
We used for the inversion both electric and magnetic
fields recorded from 0.125Hz to 1024Hz. In this con-
figuration, even with appropriate preconditionning
and scaling, inversion of the electric and magnetic
fields could not converge and provide a consistent 3D
resistivity model. The inverted model was dominated
by the footprint of the sensitivity singularity of the
transmiter. Inversion of pseudo-MT tensors allowed
to build a 3D model consistent with geology. Figure
5 shows slices at different depths. The image is in
good accordance with geological knowledges of the
area. The footprint of the transmiter is no more vis-
ible. The fault limits are well imaged at the surface
as well as in depth where 2 different geological units
are clearly identifed of for side of the fault, and the
targeted layer appear shallower than expected. The
deep structure is also confirmed by regional grav-
ity map (figure 5). Furthermore, a long DC electric
profile have been acquired in the same area. The
comparison of this profile with a slice extracted from
the 3D model is displayed figure 6, and show very
similar features.
Figure 5: Slices of the 3D resistivity model and (f)
gravity map, with contours from the geological
map.
3/4
Bretaudeau, F. et al., 2007, 3D land CSEM inversion in noisy environment with a single transmiter
Figure 6: Cross section extracted from the 3D resis-
tivity model and 2D long DC resistivity profile.
Conclusions and discussion
We proposed an alternative formulation of the CSEM
inversion problem by recasting data as a pseudo-MT
tensor. We show on a synthetic case that this for-
mulation, when used with an accurate Gauss-Newton
inversion and an efficient reparameterization allows
to perform 3D inversion of CSEM land data using a
single transmiter where common field inversion fails.
The strategy show its effeciency on both synthetic
and real data. It could be also extended to multiple
transmiter CSEM survey, using multiple pseudo-MT
tensors for each station. However, it requires to al-
ways record high quality magnetic data, otherwise
the whole station can’t be used. Furthermore, there
is still acquisition configurations where the benefit of
this approach is not so evident. The behavior of the
formulation in different contexts should be investi-
gated more in depth.
Acknowledgements
The research leading to these results has received
funding from the EC Seventh Framework Program
under agreement No. 608553 (IMAGE).
Large scale modeling and inversion was performed
on the SRV185 BRGM supercomputer and thanks to
GENCI (Grand Equipement National de Calcul In-
tensif) and CINES (Centre Informatique National de
lâEnseignement Supérieur) supercomputing facilities.
All modelisations and inversions were performed us-
ing the POLYEM3D software developped at BRGM
in the framework of the IMAGE project.
REFERENCES
Grayver, A., Streich, R., & Ritter, O. (2013). Three-
dimensional parallel distributed inversion of
csem data using a direct forward solver. Geo-
physical Journal International, 193, 1432-1446.
Plessix, R., & Mulder, W. (2008). Resistivity
imaging with controlled-source electromagnetic
data: depth and data weigthing. 24, 034012.
Streich, R. (2009). 3d finite-difference frequency-
domain modeling of controlled-source electro-
magnetic data: Direct solution and optimiza-
tionfor high accuracy. Geophysics, 74 (5), F95-
F105.
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3D land CSEM inversion in noisy environment with a single transmiter: inversion approach and application for geothermal water prospection

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3D land CSEM inversion in noisy environment with a single transmiter: inversion approach and application for geothermal water prospection

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