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Joint Inversion of EM and Seismic Data

Application on two synthetic reservoirs

Carvalho, Carolina; Azevedo, Leonardo

Email addresses: Carolina.carvalho58@hotmail.com; leonardo.azevedo@tecnico.ulisboa.pt

Centre for Petroleum Reservoir Modelling

Instituto Superior Técnico

Avenida Rovisco Pais, 1

1049-001 Lisboa

Abstract – This work aims to implement a new

algorithm to jointly invert seismic and

electromagnetic data in two synthetic reservoirs

with different characteristics.

The proposed technique is an iterative

geostatistical methodology to jointly invert EM

and seismic reflection data directly for acoustic

impedance, porosity and water saturation. The

model parameter space is perturbed

sequentially recurring to sequential simulation

and co-simulation while the convergence of the

inverse procedure is ensured by a genetic

algorithm that acts as a global optimizer. A

consistent link between the petrophysical and

elastic domains is ensured by the use of a

calibrated rock physics model.

Keywords: joint inversion, EM, seismic, GSI

1. Introduction

Seismic inversion is a common and imperative

tool in the gas and oil industry. It allows the

inference the main elastic properties of the

subsurface.

The acquisition of electromagnetic data and its

inversion allows us to map the electrical

resistivity contrasts in the subsurface. This

method is mainly utilized in offshore and, can be

magnetotellurics (MT) or controlled source

electromagnetics (CSEM), the last one is the

focus of this work.

Electromagnetic (EM) data allows to map the

resistivity of the subsurface. This is very

important in the gas and oil industry, since it

allows distinguishing between different fluids,

allowing to visualize targets to drill without an

evasive method and reduce the costs of

operations. EM data helps to achieve that goal

by allowing to map the resistivity and determine

areas more resistive.

By itself, the EM data is very helpful in the

characterization of the subsurface, but that are

factors that can compromise this data, such as

evaporites, volcanic rocks, salt, etc, because of

the high resistivity of this lithologies.

The conjugation of EM and seismic data is a logic

step, while EM data give us the areas with higher

resistivity, the seismic data allow us to infer the

main structures of the subsurface and its elastic

properties through seismic inversion.

The method applied in this work performs the

joint inversion of this two types of geophysical

data and it was applied to two different

synthetic reservoir.

2. Geostatistical Joint Inversion of EM and

seismic data

This new methodology was developed recently

[1] and it is a global iterative methodology that

invert seismic and EM data for porosity, water

saturation acoustic impedance and resistivity.

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While the perturbation of the model is

performed recurring to sequential simulation

and co-simulation, the convergence is ensured

by a genetic algorithm, based on the cross-over

principle, works as a global optimizer to

simultaneously converge the synthetic data into

the real data.

The geostatistical joint inversion of seismic and

EM data can be summarized in the following

sequence of steps (Fig. 1; Azevedo and Soares,

2014):

1) Simulation of Ns models of water

saturation (Sw) recurring to stochastic

sequential simulation DSS (Soares,

2001) and using the available Sw-log

data as experimental data for the

simulation procedure;

2) Co-simulation of Ns porosity models

using DSS with joint probability

distributions (Horta and Soares, 2010),

the available porosity well-log data as

experimental data and each Sw model

simulated in the previous step as

secondary variable;

3) Following Archie’s Law (Archie, 1942),

calculate Ns synthetic resistivity

responses for each pair of Sw and

porosity models simulated and co-

simulated in the previous steps;

4) Following a pre-calibrated rock physics

model at the wells locations, and for

each porosity model generated in 2),

derive Ns acoustic impedance (AI)

models and compute the

corresponding normal incidence

synthetic seismic response;

5) Compute, in a trace-by-trace basis, the

correlation coefficient between

synthetic and real resistivity and

seismic responses;

6) Selection of the petro-elastic traces

that simultaneously ensure the

maximum correlation coefficient

between the recorded and the

synthetic seismic data computed in the

previous step. The individual

correlation coefficients are weighted

averaged depending on the quality of

the input geophysical data. Save these

elastic traces as the best joint

saturation and porosity volumes

among with the corresponding

correlation coefficients;

7) Co-simulation of a new set of Sw and

porosity models recurring to co-DSS

and using the best joint saturation and

porosity models as secondary variables

along with the available well-log data;

8) Iterate and return to 2) until a given

global correlation coefficient between

synthetic and real resistivity and

seismic data is reached.

The convergence of the procedure is ensured by

a genetic algorithm that works as a global

optimizer to converge synthetic with real data.

In this case is ensured by a weighted mean of the

individual trace-by-trace correlation coefficient

(Eq. 1).

𝐶𝐶𝑡𝑟𝑎𝑐𝑒 = 𝑤1 × 𝐶𝐶𝑠𝑒𝑖𝑠𝑚𝑖𝑐 +𝑤2 × 𝐶𝐶𝐸𝑀

Fig. 1 Schematic representation of the geostatistical Joint EM and seismic reflection data inversion workflow in Azevedo, L. and Soares, A. (2014)

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Where CCtrace is the joint trace-by-trace

correlation coefficient between real and

synthetic seismic and resistivity data, w1 is the

weight associated with the individual correlation

coefficient between seismic traces (CCseismic) and

w2 is the weight associated with the individual

correlation coefficient between EM traces

(CCEM).

The weights regulate the influence of each type

of geophysical data within the inversion and, can

be altered depending on the noise level of the

recorded data.

The selection of the best pair of models that

produce simultaneously the highest correlation

between real and synthetic seismic and EM data

is not trivial. We use an approach based on the

interpolation of correlation coefficient between

each individual synthetic and real seismic and

EM trace. We select the petro-elastic models

that ensure the flattest interpolation line, with

higher intersect and lower deviations between

the points and the interpolation. In scenarios 1

and 2 the interpolation was made according to

the previous stated, contrary to scenario 3,

when the order of seismic and EM was inverted

in order to give more importance to EM data.

3. Stanford VI-E

The Stanford VI-E reservoir was developed by [3]

with the proposed of testing algorithms. The

structure of the reservoir is an asymmetric

anticline with N15Eº axis and presents a regular

grid (150x200x200 cells). The reservoir size is

3750 by 5000m and 120m of thickness, each cell

presents x and y=25m, and z=1m.

In terms of the stratigraphy it presents three

layers that corresponds to a fluvial channel

system prograding into the basin.

Regarding this work, it was only used the two

first layers (Fig. 2). Layer 1 is composed by a

fluvial channel system and layer 2 by sinuous

channels.

Therefore, we only use 150x200x120 cell which

gave us a dimension of 3750 by 5000m with a

120m thickness.

The rock physics model used in the inversion

procedure was based on the parameters of the

channel facies (Tab. 1).

Fraction K

(GPa) G(GPa)

Density

(g/cc)

Quartz 0.65 36.6 44 2.65

Feldspar 0.2 75.6 25.6 2.63

Calcite 0.15 80 20 2.7

Tab. 1 Rock Physics model parameters corresponding

to channel facies used in the inversion procedure

As experimental data it was used 18 wells from

the 32 available. Original seismic model and

resistivity can be visualized in Fig. 3 e Fig. 4,

respectively.

Fig. 2 Stratigraphic map of layer 1 and layer 2 of SVI-E (adapted from Lee and Mukerji (2013)).

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Fig. 3 Horizontal slice from real seismic map z=96.

Fig. 4 Horizontal slice from real resistivity map z=96.

3.1. Results

After the 6 iterations, which with 32 simulation,

the seismic inverted models converge with an

average correlation coefficient above 0, 7 for all

the scenarios.

For Stanford VI-E the models that show a good

correlation with the real data and the

reproduced the morphology of the main

channel, as well as the continuity and spatial

distribution of the properties result from the last

scenario, when increasing the importance of

EM, as can be seen in Fig. 5.

Fig. 5 Horizontal slice resulting from the average mean of the scenario 3 for seismic model.

In terms of the resistivity models (Fig. 6)

resulting the structure and spatial distributions

of the property and the channel were insured.

Nevertheless, the values for the property is

underestimated comparing to the real data.

Fig. 6 Horizontal slice resulting from the average

mean of the scenario 3 for resistivity model.

For the models retrieved regarding water

saturation the stated for the resistivity models it

is also applied, nevertheless in this case the

values are overestimated (Fig. 7).

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Fig. 7 Horizontal slice resulting from the average mean of the scenario 3 for water saturation model.

In terms of the acoustic impedance models

resulting from GSI (Fig. 8) the procedure struggle

to reproduce the non-stationarity of the data

and the structure and continuity of the property

and main channel are not well reproduced. In

the model retrieved from the joint inversion the

correlation with the real data is very good and

the structure of the main channel is well defined

(Fig. 9).

Fig. 8 Horizontal slice resulting from the average

mean model for acoustic impedance resulting from

GSI.

Fig. 9 Horizontal slice resulting from the average mean model for acoustic impedance resulting from scenario 3.

4. CERENA-I

CERENA-I (Fig. 10) it’s a synthetic reservoir

developed by Pinto (2014) to recreate a Brazilian

pre-salt carbonate reservoir and presents a

point grid (161x161x300). Each cell has

25x25x1m of spacing. In this reservoir it was only

used a sectorial model with 45x42x300 cells,

which give a reservoir dimension of 1125 by

1050m and 300m of thickness.

Stratigraphically, this reservoir is composed

three units composed by two different facies:

reservoir facies (microbiolites) and non-

reservoir facies (mudstones).

The rock physics model used in the inversion

procedure was based on the parameters of the

reservoir facies (Tab. 2).

Fraction K

(GPa) G(GPa)

Density

(g/cc)

Quartz 0.1 37 44 2.65

Aragonite 0.05 44.8 38.8 2.9

Calcite 0.85 76.8 32 2.7

Tab. 2 Rock Physics model parameters corresponding

to reservoir facies used in the inversion procedure

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The real seismic model and resistivity model can

be visualized in Fig. 10 and Fig. 11, respectively.

Fig. 10 Vertical slice from real seismic

Fig. 11 Vertical slice from real resistivity model.

4.1. Results

The results retrieved from the joint inversion for

CERENA-I reservoir were not as clear as the ones

resulting from the Stanford VI-E. Instead, for this

reservoir the models resulting from scenario 2

(more importance on seismic data) show a

better correlation with the original data.

In terms of seismic all the scenario have a good

correlation with the real data with very similar

results between then.

Regarding the resistivity models, the models

more similarity with the real data were resulting

from scenario 2. In Fig. 11 can be visualized the

reproduction of the value on the main reservoir

body.

Fig. 12 Vertical slice resulting from the average mean model for resistivity - scenario 2.

For water saturation results the models

resulting from scenario 2 were better comparing

to the other two scenario. In this models, the

structure of the main reservoir body can be

visualized (Fig. 12) and the values are similar to

the real ones.

Fig. 13 Vertical slice resulting from the average mean model for resistivity - scenario 2.

For acoustic impedance models were verified

that the procedure struggle to reproduce the

non-stationarity of the reservoir as well as for

the Stanford VI-E reservoir, and the model that

better reproduce the original data were

resulting from scenario 2.

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5. Conclusions

The main objective of this thesis was the

implementation of a new iterative joint

geostatistical seismic and EM inversion

methodology to two different case studies and

comparing the resulting models with a

conventional seismic inversion methodology.

There was an improvement of the inverted

properties, with more accurate acoustic

impedance models for both reservoirs. In

addition, we are able not only to derive acoustic

impedance but also petrophysical properties of

interest such as water saturation and porosity.

On order hand, comparing the results from the

different scenarios of the new iterative

geostatistical inversion methodology for joint

inversion of EM and seismic data, for both

reservoirs the main lithological structures were

reproduced, despite the spatial discontinuity

inside the meandering channels (SVI-E) and the

microbiolites (CERENA-I).

The inverted models resulting from the joint

inversion for petro-elastic properties showed a

good matched with the real data. For SVI-E the

best inferred models were resulting from

scenario 3 and for CERENA-I the models from

scenario 2, despite in the last synthetic reservoir

the results were very similar for the two

scenarios. In terms of water saturation models

the algorithm struggles to converge to the

solution. For both reservoirs, outside the

reservoir facies, the data shows a mismatch with

the real ones. This mismatch may be explained

by the use of Archie’s law and Waxman and

Smit’s equation in different lithologies than the

clastic ones, for water saturation and resistivity

calculation; and the simplifications on the rock

physics models for the petro-elastic properties.

The other inverted models have more defined

and with the conjugation of the resistivity,

porosity and water saturation, one can infer if

the areas has a hydrocarbon reservoir.

In terms of further recommendations, is very

important to test the performance of this

algorithm in real seismic and EM data. Also,

there is the need to improve the resistivity

forward modelling in order to deal with more

complex geological settings. It is clear that such

approximation with Archie’s law and Waxman

and Smit’s equation may not be enough. This is

a direct conclusion from the second case study.

6. References

[1] Azevedo, L. and A. Soares (2014).

"Geostatistical joint inversion of seismic and

electromagnetic data."

[2] Horta, A. and A. Soares (2010). "Direct

Sequential Co-simulation with Joint Probability

Distribution."

[3] Lee, J. and T. Mukerji The Stanford VI-E

Reservoir: A Synthetic Data Set for Joint Seismic-

EM Time-lapse Monitoring Algorithms, Stanford

University.

[4] Pinto, P. (2014). Dynamic simulation on the

synthetic reservoir CERENA I.