Characterization of Lithostratigraphic Units using Neuro Fuzzy System

nalyses Applied to Rock Magnetic Data

Nuri Hurtado

, Vincenzo Costanzo-

Alvarez

, Diego L´opez-Rodr´ıguez

, Milagrosa Aldana

and Germ´an Bayona

Laboratorio de F´ısica Te´orica del S´olido, Escuela de F´ısica, Universidad Central de Venezuela, Caracas, Venezuela

Departamento de Ciencias de la Tierra, Universidad Sim´on Bol´ıvar, Caracas, Venezuela

Corporaci´on Geol´ogica Ares, Bogot´a, Colombia

Keywords:

euro Fuzzy System, Lithostratigraphic Units, Pattern Recognition.

Abstract:

In this work we employ the Neuro Fuzzy System hybrid algorithm to infer S− ratio through the experimental

magnetic susceptibility (χ) data measured in 90 samples, from a 670 meters - thick sedimentary sequence, at

the stratigraphic well Saltarin 1A (Colombia). The method is applied here as a means for pattern recognition

of the major lithostratigraphic units encompassed by this well (i.e. Guayabo, Len and Cabonera Miocene

Formations). The sets of fuzzy rules obtained work well only when used to infer S− ratios within the same

Formation from which they were derived. This is particularly noticeable in Guayabo, with lithological char-

acteristics different to those of Len and Carbonera. The contrasts between these three Formations seem to be

responsible for the inability of ﬁnding a unique set of fuzzy rules that could properly infer S− ratio over the

whole well using χ data only as the input variable.

1 INTRODUCTION

Geophysical and geological problems commonly in-

volve systems with a large number of parameters in-

teracting in a complex way. These interactions are

mostly non-linear and non-random resulting in an in-

creasing scatter of experimental data points that blurs

up any likely associative trend among them. The

Neuro Fuzzy Systems is a hybrid algorithm that com-

bines fuzzy logic with neural networks, The hybrid

describes these variables in natural and rigorous way.

Based on an automatic pattern recognition technique,

the fuzzy logic method searches for the different sets

of data involved in a complex system and for the em-

pirical relationships between them.

The Neuro Fuzzy Logic (NFL) method, a hybrid

algorithm that combines fuzzy logic with neural net-

works, has been previously used in the prediction of

complex petrophysical (Hurtado et al., 2009) and in

paleoclimatic (Da-Silva et al., 2010) parameters. In

most situations the results obtained have given rise to

a set of numerical connections between the different

variables involved as well as additional lithological

information about an area of particular interest (Finol

et al., 2001).

The S− ratio, a rock magnetic index that accounts

for the relative contributions of low and high coerciv-

ity material to the total saturation isothermal rema-

nent magnetization in a sample, has been determined

here according to the deﬁnition (Bloemendal et al.,

1992). By obtaining empirical relationships that cor-

relate S − ratio with magnetic susceptibility we are

actually exploring howthis magnetic parameter is tied

up to the concentration of ferromagnetic minerals in

the different strata analyzed. Our goal is to apply the

Neuro Fuzzy logic technique as a unbiased quantita-

tive tool for pattern recognition of the major strati-

graphic units involved. The Saltar´ın 1A seems to be

an ideal natural scenario for such a purpose since it

shows numerous lithological contrasts that give rise

to a complex geological system (Bayona et al., 2008).

In this work we have used the Neuro Fuzzy

logic technique to infer S − ratio from magnetic

susceptibility (χ) data from 90 different depth levels

(670 meters) of the stratigraphic well Saltar´ın 1A

(Colombian Llanos foreland basin, ﬁg.1). We employ

this technique to ﬁnd a set of fuzzy patches, with their

corresponding mathematical relationships, that come

close to the possible connections between S − ratios

and χ for the major geological units encompassed by

the well.

686

Hurtado N., Costanzo-Álvarez V., López-Rodríguez D., Aldana M. and Bayona G..

Characterization of Lithostratigraphic Units using Neuro Fuzzy System Analyses Applied to Rock Magnetic Data.

DOI: 10.5220/0004377706860689

In Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods (PRG-2013), pages 686-689

ISBN: 978-989-8565-41-9

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Geographical setting of the stratigraphic well

Saltar´ın 1A in Colombia (Llanos Foreland Basin)

2 STRATIGRAPHIC SETTING

The deepest formation studied in stratigraphic well

Saltar´ın 1A is Carbonera that includes a lower sand-

stone unit (654.6 to 670 m) accumulated in a ﬂu-

vial system, a middle mudstone unit accumulated in

a lacustrine system (608.2 to 654.6 m), and an upper

sandstone unit that records sedimentation in a ﬂuvial-

deltaic system (546.9 to 608.2 m). Overlying Car-

bonera is the Le´on Formation (441.8 to 546.9 m), a

muddy sequence of sediments from a fresh-water la-

custrine system.

On top of Le´on lies the Guayabo formation that

was divided in 6 lithological units (Bayona et al.,

2008): G1 (388 to 441.8 m) and G2 (312.9 to 388

m), the two lower units, consist of green-colored lam-

inated mudstones grading to sandstones interbedded

with light-colored massive mudstones with ferrugi-

nous nodules. These lithologies were interpreted as

the sedimentation from a ﬂuvio-deltaic system chang-

ing to more continental sediment accumulation in ﬂu-

vial ﬂoodplains. G3 (271.5 to 312.9 m) and G4

(205.5 to 271.5 m), the overlying units, are domi-

nantly mudstones and siltstones that accumulated in

ﬂuvial ﬂood plains. The unit G3 has more evidence

of subaerial exposure (light-colored mudstones, for-

mation of ferruginous nodules), whereas preservation

of coal beds and laminated mudstones in unit G4 in-

dicates less subaerial exposure of the ﬂood plains. G5

(81.6 to 205.5 m) consists of feldspar-rich sandstones

that record the ﬁlling of ﬂuvial channels. G6 (0 to

81.6 m), the uppermost unit of the Guayabo forma-

tion, records a change to ﬂoodplain with evidence of

subaerial exposure.

3 METHODS

For the characterization of the different lithostrati-

graphic units, through the inference of S − ratio,

we used a hybrid Adaptive Neuro Fuzzy Inference

System (ANFIS) with ﬁve layers that can be in-

terpreted as a neural network with fuzzy parame-

ters. ANFIS is equivalent, under some constrains,

to a Takagi, Sugeno, Kang (TSK) model (Finol and

Jing, 2002). To train our ANFIS we used S − ratio

(IRM

−0.03T

/SIRM

+3T

), as output and χ as input vari-

able.

We introduced the χ training data in either

semilogarithmic or direct form (i.e. log(χ) or χ re-

spectively). Tests were also carried out using different

combinations and numbers of fuzzy rules. Member-

ship functions employed in all the trials were either

linear, triangular, bell, pi, or gaussian. In each case

inferred S− ratio values were compared with their ex-

perimental counterparts. To quantify the performance

of the inference, we applied the R

between inferred

and experimental S − ratio data, and the Root Mean-

Square Error (RMSE) values.

4 RESULTS

For to ANFIS training we use a Gaussian membership

function, the fuzzy rules was adjusted from 2 to 4, in

order to monitor a possible improvement of the in-

ference. Also we pruve that non-linear mathematical

form of the function that relates the value of S-ratio

to the magnetite weight percentage for a array of syn-

thetic samples systematically mixed from magnetite

and hematite (Heslop, 2009; Frank and Nowaczyk,

2008).

We trained the ANFIS separately with the χ and

S− ratio experimental values from Guayabo, Len and

Carbonera and assessed the set of fuzzy rules obtained

in each case in all the three formations involved (see

Table 1). The ﬁgure 2 shows the results of some of

these inferences, for the ﬁrst case in which the AN-

FIS was trained using the experimental data from the

Guayabo sandstones only. The qualitative examina-

tion of ﬁgure 2a shows that the fuzzy rules, obtained

by training the ANFIS with Guayabo’s data, give a

reasonably good inference upon this Formation itself.

However, that is not true when these same rules are

applied to Le´on and Carbonera (ﬁgures 2b and c re-

spectively). The RMSE and R

values (Table 2) con-

ﬁrm this observation.

Similar tests were repeated by training the net only

with experimental data from the mudstones of Le´on

and Carbonera .These results are summarized in Ta-

CharacterizationofLithostratigraphicUnitsusingNeuroFuzzySystemAnalysesAppliedtoRockMagneticData

687

Table 1: Parameters of the Gaussian membership functions

and fuzzy rules obtained by training the Neuro Fuzzy net

using S− ratio and χ data from the three Formations.

With data from Fuzzy rules

and Range

Guayabo (G)

[16.80 −40.19] S− ratio = −1.63χ− 0.82

[65.35 +89.57] S− ratio = 0.0013χ+ 0.82

Le´on (L)

[05.46 −17.26] S− ratio = 0.0067χ+ 0.84

[01.47 +30.52] S− ratio = 0.002χ+ 0.87

Carbonera (C)

[02.21 −07.99] S− ratio = −0.027χ+ 0.93

[01.27 +10.68] S− ratio = 0.0016χ+ 0.95

Table 2: The RMSE and R

values obtained after applying,

in each case, the fuzzy rules to their own data and to those

from the other two Formations.

Evaluated RMSE / R

data from

G 0.17 / 0.33

L 0.01 / 0.54

C 0.03 / 0.80

G 0.56 / 0.04

L 0.07 / 0.13

C 0.32 / 0.10

G 0.50 / 0.06

L 0.22 / 0.00

C 0.07 / 0.27

bles 1 and 2. Once more, the minimum number of

fuzzy rules obtained from either Le´on or Carbonera,

allows a reasonably good inference over each of these

Formations themselves but it does not seem to provide

a good inference when applied to the other two.

5 CONCLUSIONS

In this work we have used the Neuro Fuzzy logic tech-

nique to infer S − ratio from magnetic susceptibility

(χ) data from 90 different depth levels (670 meters) of

the stratigraphic well Saltar´ın 1A, Colombian Llanos

foreland basin.

Training the ANFIS with only experimental χ and

S− ratio values implies the assumption that magnetic

susceptibility by itself can identify all the behavioral

Figure 2: S − ratio inference using an adaptative neuro

fuzzy inference system (ANFIS), training the network with

the S − ratio and χ data of the Guayabo Formation only,

and two fuzzy rules. Solid lines stand for the inferred data

whereas the crosses and dashed lines represent the experi-

mental data. Results of the inference are shown for the three

Formations involved: a) inference for Guayabo Formation

itself b) inference for Le´on Formation c) inference for Car-

bonera Formation (Table 2)

patterns of the S − ratios contained in a set of data.

Namely it should be a univocal correlation between

these two parameter, and equal χ values could not be

linked to different S − ratios. However, although it

is particularly noticeable the ability of the ANFIS to

infer for the major changes of S− ratio values within

the ﬁrst 300 meters of this well, beyond such a depth

level the fuzzy rules seem to be less sensitive to pre-

dict S− ratio changes.

This depth coincides with the transition zone from

alluvial plains sediments deposited in a reducing envi-

ronment, and oxidized paleosols, to lacustrine settings

where other magnetic minerals (i.e. Fe sulphides and

hematite) appear to be as important mineral phases.

Thus, we argue that an improvement of the infer-

ence beyond 300 meters would be only possible by

using, as input experimental data, not only χ values,

but also other magnetic and non magnetic parameters

that could account for all sorts of lithological changes

throughout the whole well. Such parameters should

provide information not only for the different types

of mineral assemblages, but also for changes in grain

size distributions and variable fractions of paramag-

netic minerals.

ACKNOWLEDGEMENTS

We would like to thank the CDCH-UCV for technical

support (Group Project PG-03-8269-2011).

ICPRAM2013-InternationalConferenceonPatternRecognitionApplicationsandMethods

688

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CharacterizationofLithostratigraphicUnitsusingNeuroFuzzySystemAnalysesAppliedtoRockMagneticData

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