Sismik Hız ve Rezistivite Karşılaştırılması

1. ORIGINAL ARTICLE
Geostatistical integration of seismic velocity and resistivity data
for probabilistic evaluation of rock quality
Seokhoon Oh
Received: 13 June 2011 / Accepted: 1 September 2012 / Published online: 12 September 2012
Ó Springer-Verlag 2012
Abstract This study applied a geostatistical approach to
integrate various geophysical results for the probabilistic
evaluation of rock quality designation (RQD) in regions
between boreholes. Two of the geophysical survey results,
electrical resistivity and seismic velocity, were transformed
into a probabilistic distribution with the directly observed
RQD values at the boreholes using an indicator value
method. The initial spatial distribution of RQD, inferred
from indicator kriging of observations from the boreholes,
was improved by support of the geophysical results based
on the integration by a permanence ratio. The integration
was good enough to produce results that compensated for
the defection of each exploration method. Also, the prob-
abilistic feature of the final product of the RQD distribution
made it possible to assess a more quantitative rock quality
evaluation and better decision making for safety design.
Keywords Geostatistics Á RQD Á Permanence ratio Á
Integration Á Decision making
Introduction
Rock quality designation (RQD) represents the degree of
jointing or fracture in a rock mass measured as a percent-
age of the drill core in lengths of 10 cm or more. It is
generally known that high-quality rock has an RQD of
more than 75 %, and low-quality rock has less than 50 %.
RQD has considerable value for estimating the support of
rock tunnels, and it forms a basic element value of the
major mass classification systems. In general, RQD is
decided only at boreholes.
In regions between boreholes, RQD should be decided
indirectly; one of the simplest ways to do this is to interpolate
the observed RQD values into the rest of the region with no
borehole. This method may be suitable for a site with densely
distributed boreholes; however, in most cases, it is not valid.
This kind of problem coincides with the geostatistical solu-
tion, where expensive and exact primary data (RQD) are
estimated based on inexpensive and easily obtained data that
are approximate and secondary. The secondary information
used in this study is the result of geophysical exploration.
Geophysical data support the determination of the physical
property of subsurface structure indirectly; and this feature is
very suitable as the secondary information that compensates
the borehole data of hard type information. Traditionally,
geostatistics has played an important role in integrating
various sources of information (Haas and Olivier 1994;
Torres-Verdin et al. 1999; Oh and Kwon 2001; Oh et al.
2004). The major advantage of geostatistics is that it provides
a newly integrated product that reflects the common element
of each source from the analysis of spatial relations. In the
process, uncertainty analyses from probabilistic approaches
provide decision makers with a degree of confidence for their
final products. Of the various geostatistical processes, the
one used for the interpretation of geophysical exploration is
the most important. Geophysical exploration has become
increasingly integrated (i.e., two or more explorations are
applied together) over the years (Chakravarthi et al. 2007;
Fregoso and Gallardo 2009; Lawton and Isaac 2007). This
tendency has arisen because the results of exploration require
that the risks arising from the uncertainty of interpretation be
minimized; therefore, integration enhances the decision
maker’s confidence level.
S. Oh (&)
Department of Energy and Resources Engineering,
Kangwon National University, 192-1 Hyoja 2-dong,
Chuncheon, Kangwon 200-701, South Korea
e-mail: gimul@kangwon.ac.kr
123
Environ Earth Sci (2013) 69:939–945
DOI 10.1007/s12665-012-1978-3

2. Inthisstudy,electricalresistivityandseismicvelocitywere
integrated to produce a RQD distribution in a probabilistic
way. One of the difficult aspects of dealing with geophysical
data in a probabilistic way is how to describe the geophysical
result with probability (Oh and Kwon 2001). This problem is
solved by adopting geostatistical indicator kriging and the soft
indicator value (Deutsch and Journel 1997).
A previous study (Barton 2006) stated that seismic
velocity and RQD may have a correlation; however, there are
also large variations in correlation according to the location
and class of rocks. For example, the correlation between two
physical properties is generally strong in gneiss regions, but
the pattern changes sharply in sedimentary regions,
depending on the degree of porosity and cementation. Seis-
mic velocities depend on a variety of parameters: first, the
composition, and the type of rock. Not only larger cracks or
fractures lower the P-wave velocities but also microcracks as
a result from weathering have a significant effect on the
seismic velocity, Vp. However, microcracks might have a
lower effect on RQD, thus resulting in high-quality rock.
This peculiar characteristic makes it difficult to decide the
classification of rock quality by depending on seismic
velocity exclusively. Nevertheless, seismic velocity is
believed to accurately represent the stiffness of rock, con-
sidering the propagation of seismic waves. In this study,
seismic velocity Vp is used to estimate the subsurface status.
Although Vs is known to be more correlated with the stiff-
ness of rock than Vp, practical aspects limit the use of Vs
survey in situ such as source generation, mode conversion,
late arrival, etc. Seismic velocity is still affected by a variety
of parameters except previous factors especially in micro
scale. These factors may be dealt with uncertainty, and
macroscopic approach will be more probable in this study.
Another way of estimating the RQD by geophysical
approach is electrical resistivity. The electrical resistivity of
rock is sensitive to porous media (Oh 2012), and it represents
the state of the rock, which is believed to depict its structural
characteristics. For example, a fracture zone along a fault line
orsheer zone ishighly probabletohaveporousmedium, and it
would indicate low resistivity value. However, electrical
resistivity also depends on a variety of parameters in the rock
such as fluid content and its resistivity; and it produces
sometimes obscure and uncertain results. Considering these
problems that may occur in the independent interpretation of
each method, a combination of the two different results can
improve RQD estimation by geostatistical processes.
Geostatistical data integration
Journel (2002) proved that the probability of estimating
event A based on information from B and C is given by
PðAjB; CÞ ¼
a
a þ bc
ð1Þ
where a, b, and c are, respectively,
a ¼
1 À PðAÞ
P(AÞ
; b ¼
1 À PðAjBÞ
P(AjBÞ
; c ¼
1 À PðAjCÞ
P(AjCÞ
:
ð2Þ
This formula was called the permanence ratio (Journel
2002), and it meant simply that the probability of event
A depending on the proof of B and C can be calculated
mathematically from the prior probability of the event itself
[P(A)], and the probability of event A based on proof
B [P(A|B)] and proof C [P(A|C)]. Actually, the permanence
ratio model originally proposed by Journel (2002) was
extended to the tau model by Krishnan et al. (2005). Unlike
the traditional Bayesian combination approach based on
the assumption of conditional independence, the logistic-
type ratio of the a priori and posteriori probabilities are
considered in the permanence ratio model. This model
conceptually takes into account data redundancy between
the data utilized. If one directly applies this model, the
equation is equivalent to combination under conditional
independence. Therefore, to account for data redundancy,
tau weight values should be considered (although the
derivation of the tau value is still very difficult). However,
this article aims to apply this approach to integration field,
and detailed description is omitted. When it comes to
geophysical data interpretation, event A might be an
estimation done by geophysical survey, for example, with
the probability of ground subsidence, the existence of a
subsurface cavity, or the probability of an RQD over 60 %.
The information of B and C might indicate the probability
of supporting data, such as a geophysical survey or a
borehole test. Therefore, probability P(A|B,C) indicates an
estimation of the primary parameter A, based on the
secondary information of B and C using the rule of
permanence ratio. According to Journel (2002), this rule
can be extended to cases dealing with three or more sources
of secondary information, and this necessitates the
integration of related information. In contrast to the
Bayesian integration, which requires terms of conditional
or perfect independence, this approach induces the
improvement of integrated information according to the
contribution of each source. This method provides a more
effective way of integrating information from different
sources.
In this study, event A is defined as the probability of
RQD over or under a specified value (e.g., an RQD over
60 % or under 30 %) at an arbitrary point, and event A is
estimated based on electrical resistivity [P(A|B)] and seis-
mic velocity [P(A|C)] using the permanence ratio.
940 Environ Earth Sci (2013) 69:939–945
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3. Probabilistic estimation of geophysical results
Many researchers have attempted to deal with the geo-
physical problem using the probabilistic approach; how-
ever, it is always difficult to describe geophysical results
probabilistically (Oh and Kwon 2001). This problem
mainly arises from the difficulty of estimating geophysical
results with frequency, which is the most general approach
used in other fields. The geostatistical approach solves this
problem impartially in a way that considers the correlation
between the spatial distribution of the data and the point to
be estimated. Although a final decision for the interpreta-
tion of data from different data may still depend on geo-
physicists with experience, this way of approach will also
provide the expert with some useful information.
Prior distribution P(A)
The RQD value is the set obtained at the boreholes as the
primary information to be estimated by geostatistical
integration. All of the drilling process for core acquisition
is conducted in NX size, and complete cores are only used
for RQD measurement. Except for only a small number of
cores obtained at near surface, most of the samples are
complete, and it is not difficult to measure RQD. In geol-
ogy, the study area is mainly composed of metamorphic
and volcanic rocks, except weathered sedimentary rocks at
the surface. The prior distribution for RQD, P(A), was
made by indicator kriging (Deutsch and Journel 1997),
based on the observed RQD at each borehole. Figure 1
shows the probability distribution estimated to have an
RQD values over 60 % from P(A), which indicates the
higher probability of an RQD over 60 % when the esti-
mated probability is larger. As can be seen, the spatial
variation of the distribution is limited to the area around the
boreholes, because of the lack of data support in the region
without boreholes. However, this distribution is solely
dependent on the direct observation of the primary value,
RQD, with no relation to the geophysical result. Therefore,
it can be selected as the prior information, P(A).
Secondary information: P(A|B) and P(A|C)
The supporting data, P(A|B) and P(A|C), were induced from
a geophysical survey of electrical resistivity and seismic
velocity. Figures 2 and 3 depict the survey results of the
electrical resistivity and seismic velocity, respectively,
including the location of the boreholes. Some zones that
seem to be weak in resistivity section are marked from A to
H to check the variation after the integration. This survey
project was originally planned to assess the rock quality
through a mountain. This information was needed to design
a tunnel project. The location of the projected tunnel is also
displayed in the figures. The survey result of electrical
resistivity in Fig. 2 was obtained by applying dipole–dipole
array and its 2D inversion. The survey was conducted using
SuperSting R8 from AGI, Inc., and totally 128 electrodes
of 20-m spacing were installed. Dipole–dipole array is
known to be sensitive to detect horizontal variation in
highly resistive area, and the section of seismic velocity in
Fig. 3 resulted from the survey of P-wave tomography. The
seismic survey was conducted using an explosive source to
clearly distinguish the first arrival from background noise.
Three profiles of 64 channels of geophone are folded to
cover the entire area, and five shots for each profile are
exploded. Investigating the survey results of electrical
resistivity, two representative zones believed to be weak
were noticed (a low resistivity value can indicate weak
rock properties). The two zones were located at the x-axis
of 20,100 (marked as A) and the axis of 20,900 (marked as
C). These values showed relatively low resistivity values.
In contrast, the seismic velocity section did not depict any
significantly isolated low anomaly zone. Only a gradual
change of seismic velocity appeared, having increased
velocity with increasing depth. These characteristics,
which were in each survey, clearly explain the tendency
mentioned earlier. The integrated results will be checked
later to see the contribution of each result.
To convert these geophysical results into a probabilistic
distribution reflecting the relation with primary informa-
tion, each geophysical result was compared with the
observed RQD values at the boreholes where the locations
of the geophysical and RQD data were shared. That is, the
threshold value was set for the parameter of the geophys-
ical results. Then the RQD values, which corresponded to
the same range of geophysical results is collected. The
collected RQD values for each threshold of the geophysical
result were used to make the secondary information appear
as a non-parametric cumulative density function (CDF)
from the cumulative frequency table. The bicalib routine of
Fig. 1 Prior probability distribution of RQD over 60 % from indicator kriging of direct observation at borehole
Environ Earth Sci (2013) 69:939–945 941
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4. GSLib (Deutsch and Journel 1997) aligns the group of RQD
values that belong to the given range of geophysical results to
the order ofindicator, which makesa probabilistic distribution
for the arbitrarythreshold. Therange ofthreshold is set to bein
steps of 0.04 from 2.3 to 2.82 in log value of resistivity. The
decision of range of threshold may importantly affect the final
result, i.e., the calibration results heavily depend on how to
group RQD values that belong to the given range of geo-
physical results. The probabilistic structure for the arbitrary
threshold of geophysical results was then expanded to the rest
of the region without boreholes. This process substitutes the
geophysical results with a probabilistic distribution supported
by the primary data. Figure 4 shows the procedure for making
secondary information from geophysical data with primary
data obtained at boreholes.
Figures 5 and 6 depict the secondary information made
from above process, where Zk represents the threshold
value of RQD. The probability was less than or equal to the
threshold value of RQD, Zk, at each location appears in the
figures. Considering the case of Zk = 20 in Fig. 6, the
probability that RQD is less than 20 is under 50 % in most
of the region, except near the surface. The near-surface
region had a high probability of having low values of RQD.
The opposite was the case for Zk = 70, shown in Fig. 6,
where most of the region had a high probability
(75–100 %) of having an RQD less than 70. However,
some regions may have had an RQD value higher than 70.
These two figures represent the most important procedure
for this kind of geostatistical integration approach, which
can be applied to a variety of other problems.
Application of permanence ratio to integration
Figures 5 and 6 explain the differences between the two
geophysical surveys. Electrical resistivity appears to have
been effective for detecting structural variations (such as
isolated low anomaly zones linked with locally weak
areas), whereas the seismic velocity describes well the
variations of physical properties with the change of stra-
tigraphy. The integrated result is expected to compensate
for the discrepancy of this tendency in the way of accepting
the part of information that is more accountable for the
primary data.
Figure 7 displays the integrated result for the RQD
estimation by the application of the permanence ratio to
electrical resistivity and seismic velocity, which demon-
strates an RQD probability over 60 %. The region with a
high probability of having an RQD value larger than 60 is
believed to be safe for geotechnical applications or tunnel
engineering. If an interpreter wants a more rigorous value
for RQD, then the threshold values may be changed to
reflect it. After the integration, zones B and D in Fig. 2 are
still showing low RQD values extended to a deep region.
For the comparison, Fig. 8 shows the probability map in
the case of an RQD under 30 %, which may be used to
distinguish a somewhat weak zone from the overall region.
As seen from the figure, the probability of having a low
RQD value is high in the near-surface region. A compari-
son of the integrated results with each independent source
of geophysical data indicates a noticeable improvement, as
expected.
Projected tunnel
100 300 500 700 Ohm-m
A
B
Fig. 2 The survey results of electrical resistivity, including the location of boreholes
Projected tunnel
1000 2000 3000 4500 m/s
Fig. 3 The survey results of seismic velocity, including the location of boreholes
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5. Confidence analysis of integration
The probabilistic analysis adopted in this study also pro-
vides an integrated estimation with a new approach to
confidence analysis. The confidence analysis provides the
opportunity to check the reliability of the obtained result,
and it helps us to infer the errors quantitatively embedded
in the estimation. This procedure provides the decision
maker with assistance criteria related to cost estimation
(Goovaerts 1997).
In Fig. 8, which shows the probability map of RQD
under 30 %, some regions with especially high probability
may be designated as unsafe. For example, the zone with a
probability higher than 60 % may be classified as hazard-
ous with confidence. Such a region can be defined as
follows:
Prob ZðuÞ zcjnf g [ pc ð3Þ
where Z(u) is the estimated value, Zc is the threshold value,
n is the number of supporting data, and pc is the prede-
termined probability. That is, if the probability that the
estimated value [Z(u)] that is less than the threshold (Zc) at
a certain point is higher than the predetermined probability
(pc), then the point is classified as hazardous. In Fig. 9, the
0.00
0.20
0.40
0.60
0.80
1.00
0 10 20 30 40 50 60 70 80 90 100
0.25 0.25 0.25 0.25 0.75 1.00 1.00 1.00 1.00 1.00 1.00
0.12 0.26 0.41 0.59 0.68 0.79 0.91 0.94 0.94 0.97 1.00
0.36 0.50 0.64 0.79 0.79 0.79 0.93 0.93 0.93 1.00 1.00
0.09 0.18 0.41 0.55 0.73 0.82 0.86 0.91 0.95 1.00 1.00
0.06 0.17 0.28 0.28 0.33 0.44 0.67 0.83 0.89 1.00 1.00
0.07 0.07 0.07 0.11 0.26 0.33 0.37 0.48 0.70 0.81 1.00
Cumulative frequency table
RQD vs. Resistivity(Log) scattergram
RQD
CDF
Resistivity map
Fig. 4 Making a probabilistic
distribution from supporting
secondary data. A group of
primary values (here, RQD)
within the predetermined range
of secondary data (electrical
resistivity) was collected to
make the cumulative frequency
table. The table was converted
to a non-parametric cumulative
distribution function for the
range, and it was substituted
with resistivity values at any
point corresponding to the range
Fig. 5 Cumulative distribution
of P(A|B) for each threshold
value Zk from electrical
resistivity
Environ Earth Sci (2013) 69:939–945 943
123

6. regions (except those colored as gray) indicate a hazardous
classification by the criterion with Zc = 30 and pc = 60 %.
However, this classification has another kind of uncer-
tainty: the possibility of incorrect classification. The fol-
lowing probabilistic formula defines such an incorrect
classification:
aðuÞ ¼ Prob ZðuÞ [ zcj½zÃ
LðuÞzcŠ; ðnÞ
È É
ð4Þ
where Z(u) is the real value at point u, and zÃ
L uð Þ is the
wrongly estimated value. This formula indicates a case
where even though the estimation was classified as
hazardous ð½zÃ
L uð ÞzcŠÞ, the real value was larger than the
threshold (Z uð Þ [ zc). This probability may be simply
calculated from Eq. (1) by subtraction, which is just a
complementary part of the inferred probability. The result
is given in Fig. 9, which shows that the value of aðuÞ is
very low in the near surface region, indicating a hazardous
zone with high confidence, whereas some regions appear to
have a relatively high aðuÞ value, which indicates that the
classification may be wrong. The information displayed in
Fig. 9 determines a very useful aspect of the probabilistic
approach.
Fig. 6 Cumulative distribution
of P(A|B) for each threshold
value Zk from seismic velocity
Fig. 7 The integrated result for RQD estimation by application of the permanence ratio to electrical resistivity and seismic velocity, which maps
the probability of RQD over 60 %
Fig. 8 The probability map for
RQD estimated under 30 %
evaluated from direct borehole,
resistivity, and seismic
tomography data
Fig. 9 Probability aðuÞ of wrong classification as hazardous for
Zc = 30 and pc = 60 %. The aðuÞ is very low in the near-surface
region, indicating a hazardous zone designation with high confidence,
whereas some regions appear to have relatively high aðuÞv values,
which indicates that the classification may be wrong
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123

7. Conclusion
An improved way of inferring physical properties in rela-
tion to geophysical surveys via geostatistical integration is
proposed. In this study, electrical resistivity, seismic
velocity, and the direct observation of RQD at boreholes
were used together to estimate RQD values at a region with
no boreholes by means of the probabilistic approach. To
deal with the geophysical data in a probabilistic way, a
special method was devised, and prior information was
obtained by indicator kriging of direct observations of
RQD. The secondary information, made from a comparison
between the geophysical results and the primary data,
described well the characteristics of each applied survey.
The integrated result seems to provide a useful way to
obtain information compared to the independent result of
geophysical survey, and the advantage of the probabilistic
approach appeared in various c analyses. Although the
search for an estimation of rock quality was only proposed
in this study, a wider application of this method is rec-
ommended for the integrated analysis of geophysical data,
likely in the cases of problems of cavity detection or
ground subsidence.
A good integration from various sources of information,
such as seismic velocity and electrical resistivity used in
this study, should explain the geology or geosciences.
Therefore, success or failure of good integration highly
depends on the preliminary detailed interpretation of each
physical property. Ignoring it, the result would be far from
true information, and even may fail in the final decision. A
statistical integration or interpretation is not magic, how-
ever, just an explanation method based on observed data.
Acknowledgments This study was funded by the Korea Meteoro-
logical Administration Research and Development Program under
Grant CATER 2012-8020.
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