Introduction
Traditional Methods for
WellWell-toto-Well Correlation
Authors
Piotr W. Mirowski
Formerly Schlumberger-Doll Research
Now Ph.D candidate,
Courant Institute, New York University, NY
piotr.mirowski@computer.org
Michael Herron
Schlumberger-Doll Research, Ridgefield, CT
MHerron@ridgefield.oilfield.slb.com
Nikita Seleznev
Schlumberger-Doll Research, Ridgefield, CT
Nseleznev@ridgefield.oilfield.slb.com
Samuel D. Fluckiger,
Schlumberger, Doha, Qatar
sfluckiger@doha.oilfield.slb.com
Manual correlation on gamma ray and resistivity logs
Well-to-well correlation is an inexact
art form. Correlations typically use
only total gamma ray and resistivity.
While lines are drawn connecting
wells, the reasoning process for
selecting the correlation points is
usually unexplained. In the best
case, the shapes of the curves are
used for matching, but the absolute
values are commonly not considered.
David S. McCormick
Schlumberger-Doll Research, Cambridge, MA
DMcCormick@boston.oilfield.slb.com
Abstract
New Software For Well-To-Well Correlation Of Spectroscopy Logs
This figure shows an example of
intrareservoir correlation based on
electric logs and part of a complex
study with a biostratigraphic
approach in Venezuela (Rull, 1994).
We have developed a research prototype PC application, Well2Well, which enables improved well-to-well
correlation, especially when coupled with spectroscopy log data.
The advantage of using spectroscopic log data is the absolute values of the chemical concentrations of the
most important rock-forming chemical elements. The full list available includes elements from the
Elemental Capture Spectroscopy (ECS) and Natural Gamma Ray Spectroscopy (NGS, HNGS) sondes. This is
in contrast to the traditional use of gamma ray/spontaneous potential and resistivity data, which are at
least as sensitive to the fluids as to the rock. Elements that are believed to be more geologically important
can be included in the analysis and weighted according to the user’s preference, while less important
trace elements such as thorium and uranium, which are major components of the gamma ray, may be
excluded. The input logs can be preprocessed and smoothed with edge-preserving algorithms to make the
correlation results more stable.
Automated wellwell-toto-well correlation on gamma ray logs
These well-to-well depth correlations rely on the Dynamic Programming algorithm, inspired by the genematching algorithms used in biology, which computes a log signature mismatch matrix between a pair of
wells and then finds the best correlation path thanks to an optimal path search through that matrix.
No commercial plans are yet made for this software. However, tests on multiple datasets from North
America demonstrate high-fidelity well-to-well correlations on wells separated by several hundred meters,
suggesting making our research prototype software is a very promising geological characterization tool.
Spectroscopy logs
Elemental concentration logs were obtained from the
Elemental Capture Spectroscopy (ECS*) sonde.
The ECS* sonde uses a standard 16-Ci [59.2 ¥ 1010-Bq]
americium beryllium (AmBe) neutron source and a
large bismuth germanate (BGO) detector to measure
relative elemental yields based on neutron-induced
capture gamma ray spectroscopy. The primary
elements measured in both open and cased holes are
for the formation elements silicon (Si), iron (Fe), calcium
(Ca), sulfur (S), titanium (Ti), and gadolinium (Gd),
chlorine (Cl), barium (Ba), and hydrogen (H).
Wellsite processing uses the 254-channel gamma ray
energy spectrum to produce dry-weight elements,
lithology, and matrix properties. The first step involves
spectral deconvolution of the composite gamma ray
energy spectrum by using a set of elemental standards
to produce relative elemental yields. The relative yields
are then converted to dry-weight elemental
concentration logs for the elements Si, Fe, Ca, S, Ti, and
Gd using an oxides closure method. Matrix properties
and quantitative dry-weight lithologies are then
calculated from the dry-weight elemental fractions
using empirical relationships derived from an extensive
core chemistry and mineralogy database, and a realtime petrophysical analysis program.
The algorithm presented here has already been applied for the well-to-well correlation of Gamma Ray,
Neutron Porosity, Density, Spontaneous Potential, Spherically Focused Laterolog and Induction Log
Medium logs (Le Nir et al., 1998, illustrated on the figure above).
NPLC
Detector
Acquisition
Cartridge
AmBe Source
BGO Crystal
And PMT
Boron Sleeve
Electronics
Heat Sink
Dewar Flask
Spectroscopy sonde
* Mark of Schlumberger
However, this algorithm
has not been used with
spectroscopy logs such
as the dry weight
percentage channel logs
of Si, Ca, Fe, S, Ti, Gd or
Al elements.
The figure on the right
illustrates the interface of
our prototype software
for applied to well-to-well
correlation of standard
gamma ray logs. As we
will see in our poster,
these results can be
significantly improved.
New Software for Well-to-Well Correlation
of Spectroscopy Logs
Piotr Mirowski, Michael Herron, Nikita Seleznev, Samuel Fluckiger, David McCormick
WellWell-toto-well correlation algorithm
To automate the process of determining correlations between pairs of wells, we employ the technique of
dynamic programming (Lineman et al., 1987; Doveton, 1994; Le Nir et al., 1998), inspired by the gene-matching
algorithms used in biology. This technique consists of computing a mismatch matrix between log values in a
pair of wells and then finding the best connection path through that matrix using an optimal path search.
Mismatch matrix
The mismatch matrix is a two-dimensional
representation of the difference between chemical
signatures (i.e. log values) measured in two
different wells. For each possible pair of depth
values, it shows where the chemical signatures in
both wells are similar (low value) or dissimilar (high
value). The optimal path appears as a “valley” of
low values (of mismatch) through the pairwise map.
The mismatch can be defined as a “distance”
between log values. For a single log channel, we
compute a rectangular mismatch matrix, Mij, using
differences between absolute log values l1(di) in
well 1 at depth index i, and l2(dj) in well 2 at depth
index j. Low and high values of Mij respectively
correspond to strong and weak connections for a
particular couple of samples.
M ij = l1 ( d i ) − l 2 ( d j )
Optimal Path Search Algorithm
cost (1,1) = WM 11
The Dynamic Programming algorithm is an optimal
path search through the weighted mismatch matrix.
It relies on a cumulative cost matrix cost that is, for
a given pair (i, j), the cumulative sum of mismatches
on a path going from (1, 1) to (i, j), and on a
“direction” matrix dir.
cost ( i,1) = cost ( i − 1,1) + WM i1
∀i ∈ [ 2, M ] 
 dir ( i,1) = 1

c1 = cost ( i − 1, j )
c = cost i − 1, j − 1
(
)
2

∀i ∈ [ 2, M ] 
c3 = cost ( i, j − 1)
∀j ∈ [ 2, N ] 
cost ( i, j ) = min ( c1 , c2 , c3 ) + WM ij
dir ( i, j ) = arg min ( c , c , c )
1 2
3

1,2,3
{ }
To start the process it is necessary to assign initial
column and row values of the matrix: cost(1, 1),
cost(1, j) and cost(i, 1), as well as the directions
dir(1, 1), dir(1, j) and dir(i, 1).
dir (1,1) = 2
cost (1, j ) = cost (1, j − 1) + WM 1 j
∀j ∈ [ 2, N ] 
 dir (1, j ) = 3
Good
Good
Mediocre
Mediocre
Bad
Bad
Bad
Bad
A perfect well-towell correlation
corresponds to a
straight optimal
path
on
the
mismatch matrix,
joining the Top
and
Bottom
markers.
The
correlation strata
are then parallel.
2170
Well A
Log curve filtering
To facilitate the connection of wells on their log
values, it can be useful to smooth the log values so
as to soften the apparently “noisy” aspect of logs
and provide a better continuity on adjacent depth
samples.
Optimal path
1880
ll A
We
1680
1540
1710
lB
l
e
W
2160
1840
Well B
In this example we show the mismatch matrix computed on Si dry weight channels from two wells A and B.
Columns of the matrix correspond to depths indexes of well B, and rows to those of well A. Dark values
correspond to a high “mismatch” or “distance” between the log values, whereas light values correspond to
a good “match”. On the 3D rendering of the region bounded by the green rectangle, mismatches appear as
plateaus and good correlations as valleys. The optimal path is highlighted with dots.
Weighted mismatch matrix
The weighted mismatch matrix is a linear
combination of mismatch matrices for the different
available log channels, each log cannel given a
weight between 0 and 1 that is proportional to its
user-assigned relative importance.
+ 1x
Silicon
This weighted mismatch matrix defines a multi-log
metric of well-to-well connection and hence
enables a multi-dimensional search of optimal path
in the well-to-well log distance space.
WM ij = ∑ wk l1,k (d i ) − l2,k ( d j )
+ 0.5x
Calcium
Unfiltered
Filtered
Test software prototype implemented
k
0.5x
The filters we have used in our study include the
Mathematical Morphology filter (Serra, 1986, see
the figure on the right), median filter, and the
Gaussian filter. We tend to prefer edge-preserving
filters such as the latter, because they do not
“smear out” spikes and important changes in log
curves that can correspond to geological events.
These filters are local, i.e., for a given depth, the
new value of the log curve is computed as a
function of the log values of a small set of depth
samples above and below.
=
Aluminum
Weighted
Mismatch
Matrix
Illustration of the concept of weighted mismatch matrix, where the mismatch matrices for Silicon and
Aluminum dry weight channel logs have weights of 0.5, and the mismatch matrix for Calcium has a weight 1.
Spectroscopy
Well-to-well
Well
log
displays
We developed a program with a user-friendly
log channel selection
correlation display
interface. The program allows us to import well log
data (including spectroscopy dry weight percentage
channels), to specify for each well start and end
markers for the well-to-well correlation interval,
select and assign user-specified weights to log
channels according to their interpreted geological
importance, apply filters to log curves, visualize
mismatch matrices and well-to-well correlation
results, and export the results as text files.
Running on Windows platform, it took a few
seconds for our software to compute well-to-well
correlations in a dataset of 2,500 feet of multichannel logs sampled at 0.5 foot intervals. Such a
good performance makes this technique a
promising tool for geoscientists.
Mismatch matrix display
Spectroscopy logs carry
complementary information
MultiMulti-log multimulti-well correlation
Perfect correlation between wells 1 and 2…
Silicon
SingleSingle-log correlation…
Very good
correlation
points
on Si and Ca
Good
overall
correlation
with Ca
Isolated
event
on Si
Silicon
Isolated
events
Ti and Gd
are trace
elements
in wells
A and B
Iron
Geological event
Sulfur
Parallel
marker
beds
Very good
correlation
points on Al
Isolated
events
Gadolinium
Optimal path
=
straight line through
mismatch matrix
Aluminum
Gamma Ray
Intervals
between
markers
are
heteroheterogeneous
Silicon
Sulfur
Sand bed
… vs. MultiMulti-log correlation
Perfect wellwell-toto-well
correlation
when using a
weighted mismatch
matrix
Unconformity
minimized
on Si
Unconformity
minimized
on Al
+
1 x Calcium
+
0.5 x Aluminum
Contributions
of Sulfur logs
Contributions
of Silicon logs
Correlation results between siliclastic wells A and B obtained for a weighted set of Silicon, Calcium
and Aluminum dry weight channel logs. Si and Al logs were given a weight of 0.5, whereas Ca logs
were given a weight 1. Unlike the single-channel correlation, the multi-log correlation reveals a very
similar sequence stratigraphy in both wells, yet horizontally distant by a distance of a few hundred
meters.
Silicon (in green) and Sulfur (in red)
dry weight percentages channel logs
vehicle complementary information for
the correlation of these two wells from
a dataset from North America.
These
are
carbonate/evaporite
sequences and the silicon represents
sand, mainly quartz, and some clay. In
this environment, the sulfur is due to
anhydrite, and many anhydrite beds
are chronostratigraphic as well as
lithostratigraphic surfaces.
Silicon
Sulfur
There is a similarly good
correlation
between
Well_3 and Well_4, from
the
same
carbonate/
evaporate dataset from
North America. A sand bed
that did not exist in wells 1
and 2 appears at an
approximate depth 4800ft,
and is visible on the Silicon
dry weight percentage
channel logs.
… appearance of a sand bed between wells 1 and 3
Poor correlation results between two siliclastic wells A and B from a dataset from North America
containing shale, sandstone and thin marine limestone horizons. One single mismatch matrix, derived
from one single log, was used at a time. Equally poor results were obtained with Gamma Ray logs only.
0.5 x Silicon
Two wells, Well_1 and
Well_2, from a dataset
from carbonate/evaporate
dataset in North America,
showing a very good
correlation of sequence
stratigraphy despite being
distant of 100 meters. We
filtered the logs before
well-to-well correlation in
order to provide with a
better
continuity
on
adjacent depth samples of
log curves.
… very good correlation between wells 3 and 4…
Fe and S
bad correlation
channels
Calcium
Titanium
Parallel
correlation strata
Sulfur
Silicon
Sulfur
Well_1 and Well_3 have a
different sequence stratigraphy. There is a missing
sand bed in well 1. It has to
be noted that the sand bed
appears only on the Silicon
dry weight channel logs.
The correlation strata
above the sand bed are
leveled out by the Top
correlation marker. The
optimal path search is
indeed done only between
Top and Bottom markers.
References
Conclusions
Doveton, J.H., “Lateral Correlation and Interpolation of Logs”,
Geologic Log Analysis Using Computer Methods, AAPG
Computer Applications in Geology No. 2, 1994, AAPG, Tulsa,
pp.127-150.
No commercial plans are yet made for this
software.
However, tests on multi-channel
geochemical log datasets from North America
demonstrate precise, consistent well-to-well
correlations on wells separated by several
hundred meters, suggesting that this prototype
software using multiple geochemical logs is a
very promising geological characterization and
interpretation tool.
LeNir I., Van Gysel N., Rossi D., “Cross-Section Construction
From Automated Well Log Correlation: A Dynamic Programming
Approach Using Multiple Well Logs”, SPWLA 39th Annual
Logging Symposium, May 26-29, 1998.
Lineman D.J., Mendelson J.D., Toksos M.N., “Well To Well Log
Correlation Using Knowledge-Based Systems and Dynamic
Depth Warping”, SPWLA 28th Annual Logging Symposium, June
29-July 2, 1987.
Rull,
V.
“High-Impact
Palynology
in
Petroleum
Geology:
Applications from Venezuela (Northern South
America)”, AAPG Bulletin, v. 86, no. 2, February 2002, pp.279-300.
Herron S., Herron M., “Application of Nuclear Spectroscopy
Logs to the Derivation of Formation Matrix Density”, SPWLA 41st
Annual Logging Symposium, June 4-7, 2000.
Serra J., "Introduction to mathematical morphology", Computer
Vision, Graphics, and Image Processing, Volume 35 , Issue 3,
September 1986, pp.283-305.
Acknowledgements
We would like to thank Rick Kear, Philippe Marza
and Romain Prioul for useful suggestions on the
software usability. Mohamed Aly, Jim Bristow,
Alexis Carrillat, Selim Djandji, Roy Dove, Tamir ElHalawani, Ahmed Elsherif, Sherif Farag, Melissa
Johansson, Lucian Johnston, Rick Lewis, Richard
Netherwood, John Philips, Raghu Ramamoorthy,
Frank Shray, Nneka Williams, Michael Wilson,
Rachel Wood, and Meretta Qleibo helped test the
software.