AVO Inversion - HRS application

EMERGE
Multi-Attribute Analysis

April 2014 2
EMERGE Course Outline
EMERGE introduction
Exercise 1: Setting up an EMERGE Project
Seismic Attributes
Cross Plotting
Exercise 2: The Single-Attribute List
Multiple Attributes
Validation of Attributes
Exercise 3: The Multi-Attribute List
Using the Convolutional Operator
Exercise 4: The Convolutional Operator
Exercise 5: Processing the 3D Volume
Neural Networks in EMERGE
Exercise 6: Predicting Porosity Logs
Training the Neural Network
Exercise 7: Using Neural Networks
Case Study: Using Emerge to predict Vshale
PNN Classification
Exercise 8: Using Classification
S-wave Prediction
Exercise 9: Predicting Logs from Other Logs

April 2014 3
Introduction to EMERGE
The Objective of the EMERGE Program:
 EMERGE is a program that analyzes well log and seismic data at well
locations.
 It finds a relationship between the log and seismic data at the well
locations.
 It uses this relationship to “predict” or estimate a volume of the log
property at all the other locations of the seismic volume.

April 2014 4
The Data that EMERGE uses:
…
 A seismic volume (usually 3D).
 A series of wells which tie the volume.
 Each well contains a “target” log, such as porosity, which is to be
predicted.
 Each well also contains the information for converting from depth to time,
usually in the form of a check-shot corrected sonic log.
 (Optional) One or more “external” attributes in the form of seismic 3D
volumes. For example Impedance, Density, Vp/Vs.

April 2014 5
Theoretically, any type of log property may be used as a target for EMERGE.
…
Practically, the following types have been predicted successfully:
…
 P-wave velocity
 Porosity
 Density
 Gamma-ray
 Water saturation
 Lithology logs
…
The only requirement is that an example of the target log must exist within
each of the wells.
Since EMERGE assumes that the target log is noise-free, it is usually
important to edit the target logs before applying EMERGE.
Since EMERGE will be correlating the target logs with seismic data on a
sample by sample basis, the proper depth-to-time correlation is critical. For
this reason, check-shot corrections and manual correlation are usually
necessary.

April 2014 6
Inversion Emerge
Uses seismic and well log
data.
Uses seismic and well log
data.
Predicts a volume of
impedance (acoustic,
elastic, shear).
Predicts a volume of any
log property.
Uses the convolutional
model to relate logs with
seismic.
Does not use any a priori
model. Instead,
determines an arbitrary
relationship statistically.
Requires the extraction of
the wavelet.
Does not require wavelet
extraction. Effectively, the
wavelet is part of the
derived relationship.
Operates on pre-stack and
post-stack seismic data
using a deterministic
model (e.g. Aki-Richards).
Operates on seismic
attributes statistically,
including post-stack and
pre-stack attributes.
May be used with very few
wells – as few as one.
Requires sufficient well
control (at least 3 wells).
The result is validated by
creating a synthetic
seismic section which
matches the real data.
The result is validated by
“hiding” wells and
predicting them from other
wells.
The effective resolution is
limited by the seismic
bandwidth.
The resolution may be
enhanced by neural
network analysis.
EMERGE can be thought
of as an extension of
conventional post-stack
inversion:

7
9. Multi Attribute P-wave Log Predict
4 wells, only 2 of which contain P-wave
1. Set-Up P-wave Velocity
2. Single Attributes
3. Multi-Attributes
4. Convolutional Operator
5. Applying to a 3D volume
12 wells, check shot corrected
6. Multi Attributes for Porosity
7. PNN for Porosity
8. PNN for Classification
7 wells with P-wave, Density, Porosity
and Classes
April 2014
EMERGE Workshop Data
Numbers in red
refer to exercises
During this
workshop we will
use 3 different
pre-prepared well
datasets and 2
seismic volumes

April 2014 8
We are going to predict:
Volumes of log properties
Facies
Logs from other logs
P-wave by multi attribute regression
Porosity by multi attribute regression
Porosity by neural network
Porosity classes by neural network
Porosity classes/facies by neural network
Porosity classes/facies by neural network
Missing logs by multi attribute regression
The speed of EMERGE training and PNN has
benefitted from multi-threading in HRS-9.

EMERGE
….
Exercise 1: Project Set-Up for
Prediction of P-wave Velocity

April 2014 10
P-wave logs for 12 wells
(The Target)
Seismic and P-Impedance
3D volumes (The Attributes)
Wells correlated accurately to seismic
Exercise 1

April 2014 11
The objective of this analysis is to predict new P-wave logs for
the entire 3D survey. But with the corresponding Target log
types present and the appropriate 3D Attribute volumes, this
same technique could equally predict any log property.
Exercise 1

April 2014 12
Start the GEOVIEW program by double-
clicking the icon on your screen:
When you launch Geoview, the first
window that you see contains a list of
projects previously opened in Geoview.
For example, the figure below shows a
previous project, which could be opened
now. Your list may be blank if this is the
first time you are running Geoview.
Exercise 1

April 2014 13
For this tutorial, we will start a new
project. At the start of any project it
is helpful to set the default paths to
the location where the data is
stored. To do that, click the
Settings tab:
You can see a series of default locations for the Data Directory, Project
Directory, and Database Directory. We would like to change all of these to
point to the directory where the tutorial data is stored.
To change all of the directories to the same location, select the Settings tab
and click on the option Set all default directories to. Then click the button to
the right:
Exercise 1

April 2014 14
Then, in the File Selection Dialog,
select the folder which contains the
workshop data and click Ok:
After setting all three paths, the
Geoview window will now show
the selected directories (note
that yours may be different):
When you have finished setting all
the paths, click Apply to store these
paths:
Exercise 1

April 2014 15
Now select the Projects tab and
click the New Project button:
A dialog appears, where we set the project name. We will call it
Velocity Project, as shown below. Enter the project name and click
OK on that dialog:
Exercise 1

April 2014 16
Now a dialog appears, asking for the
name of the database to use for this
project:
The database stores all the wells used in this project. By default, Geoview
creates a new database, with the same name as the project and located in the
same directory. For example, this project is called Velocity Project.prj, so the
default database would be called Velocity Project.wdb.
But for this exercise, to save time, we have already created a database, which
has the wells already loaded.
Exercise 1
Do not click OK yet

April 2014 17
To use the pre-prepared database, click
Specify database:
On the pop-up dialog which appears,
select Open:
Then, select the database guide.wdb, as
shown, and click OK:
Exercise 1

April 2014 18
Now the previous dialog shows the selected
database and the new project name. Click
OK to accept this:
The Geoview Start Window
now looks like this:
Exercise 1

April 2014 19
One part of the Geoview window (called
the Project Manager) shows all the project
data so far. The tabs along the left side
select the type of project data. Right now,
the Well tab is selected and we can see
the 12 wells from the external data base.
Click the arrow sign near one of the wells
(01-17 is shown as an example), to see a
list of curves in that well:
To see more details about the wells, click
the Data Explorer tab to the right:
Exercise 1

April 2014 20
The Geoview window now
changes as shown:
Click the arrow next to any of the
wells (for example, well 01-17) to
see more information about the
curves in that well:
Exercise 1

April 2014 21
Finally, to see the most complete view of
the log curves within a well, go to the icon
for that well within the Project Data window
and double-click. In this case, we will
choose well 01-08:
This creates a new tab within
the main Geoview window,
called the Wells tab, which
displays the selected well
curves:
Exercise 1

April 2014 22
We have now loaded the wells which will be
used in the Emerge process. The next step
is to load the seismic volumes.
On the far left side of the Geoview
window, click the Seismic tab:
The window to the right of this tab
shows all seismic data loaded so far.
This is empty. Go to the bottom of the
window and click the Import Seismic
button:
Exercise 1

April 2014 23
On the pull-down menu, select
From SEG-Y File:
On the dialog that appears, we see
two seismic files in the Emerge data
directory. We will load them both.
Click the Select All button:
Click Next at the base of the dialog:
Exercise 1

April 2014 24
On the next page, we are
specifying two things.
First the files are 3D
geometry. Secondly,
these are two separate
files, which happen to
have the same geometry.
Click Next to accept
these defaults:
Exercise 1

April 2014 25
You can specify what
information can be found in
the trace headers. In our
case, we have both Inline &
Xline numbers and X & Y
coordinates in the headers.
Click Next:
Set the Amplitude Type for
the inversion volume as
impedance.
Exercise 1

April 2014 26
Now we see the SEG-Y Format page:
By default, this page assumes that the
seismic data is a SEG-Y file with all
header values filled in as per the
standard SEG-Y convention. If you
are not sure that is true, click Header
Editor to see what is in the trace
headers.
In this case, we believe the
format information is correct for
both files we are reading in. To
confirm that, click Apply Format
to all files:
Exercise 1

April 2014 27
Now click Next to move to the next page.
The following warning message appears
because the program is about to scan the
entire SEG-Y file:
Click Yes to begin the scanning process.
When the scanning has finished, the
Geometry Grid page appears:
Because we have read in the proper header
information, the geometry is correct. Click OK.
Exercise 1

April 2014 28
After building the geometry files, a new
window appears, showing how each of the
wells is mapped into this seismic volume:
In this case, all the wells are mapped to the
correct Inline / Xline locations because the X
and Y locations have been properly set within
the Geoview database. If this had not been
done previously, you would type in correct
values for the Inline and Xline numbers.
Click OK to accept the locations
shown on this window.
Now the seismic data at Inline 1
appears within the Geoview window:
Exercise 1

April 2014 29
By using the arrow
next to the well
icon, the display
can be jumped to a
well location.
In this case select
well 08-08.
Scroll down to the
bottom of the well.
Exercise 1

April 2014 30
To simultaneously show both the seismic and inversion volumes, click on the eye
for Window 2, then drag and drop the inversion volume into the new window.
Exercise 1

April 2014 31
We have now loaded all the data necessary.
This analysis takes place in two stages.
In the first, training, stage, Emerge analyzes
the target log and seismic data at the well
locations to derive a statistical relationship
between them.
In the second, application, stage, Emerge
applies the derived relationship to the entire
volume to create log values throughout that
volume.
Exercise 1

Click the arrow sign next to the Emerge
name to show the Emerge processes:
April 2014 32
To start the Emerge training, click on the
Processes tab. This shows a list of all processes
available in Geoview:
Finally, double-click Emerge Training.
Exercise 1

This causes the training
dialog to appear:
This dialog contains all the
information needed to set up
the training process. There
are a series of 4 tabs:
April 2014 33
Exercise 1

April 2014 34
On the first page, we are specifying
P-wave as the Target Log Type we
wish to predict.
In this exercise, we wish to predict P-
wave velocity throughout the seismic
volume, so select that from the pull-
down menu:
Exercise 1

April 2014 35
Also, we are specifying that, although the log is measured in depth, the analysis
(Processing Domain) will be done in Time. This is because the seismic data is
measured in time. The sample rate is needed so that Emerge can do the depth-
to-time conversion properly.
The left column lists all
the wells in the
database which
contain a P-wave
velocity log. Click
Select All to use all the
available wells.
Exercise 1
Click Next to see the
Volumes tab:

April 2014 36
The Volumes tab is now
activated:
We wish to use both of the
available seismic volumes, so
click Select All:
The lower part of the
Emerge Training dialog
shows the selected
seismic volumes and
allow us to specify
whether each volume is of
the type Seismic or type
External Attribute:
Click Next.
Exercise 1

April 2014 37
The third page of the
dialog now appears:
This page tells the program how to extract the trace at each well
location which is used in the training process. The default is to
extract a single trace that follows the trajectory of each of the
wells, whether vertical or deviated. Alternatively, you could
modify the Capture Option to “Distance”, which will average all
traces within a specified distance from each well.
We will use the Neighborhood radius value of 1, as shown. This
means that the composite trace will be the average of those
traces within 1 inline or xline of the well location. This is an
average of 9 traces. Click Next.
Exercise 1

April 2014 38
The Analysis Window tab specifies the analysis
window for training, in terms of tops that have
already been entered into the Geoview
database.
Select Top instead of Log Start and Log End:
Note that the analysis window can be changed later if desired.
Exercise 1
Click OK at the bottom of the dialog.

April 2014 39
The Emerge main window
shows the analysis data for
one well: the target log in
red, the single seismic trace
in black, and the external
attribute in blue.
Target
Log
Seismic
Trace
Inversion
Trace
Analysis
Window
Exercise 1
The yellow horizontal bars
indicate the analysis
window.

April 2014 40
Exercise 1
To display a different well or multiple
wells, you can select from the well list
drop down menu. Select Multiple
Wells to view all the wells:
Move the slide bar at
the bottom of the
window to view different
wells.

April 2014 41
Exercise 1
Right click on the log track and we
can see a series of display options.
Here we want to show the top
names, so click Show Top Names.
A top track is displayed with the top
names.

April 2014 42
A dialog appears that allows
you to set the analysis
windows for each well
individually.
Click on the log track, hold
the button and select a
range, i.e. from 900 ms to
1100 ms.
To examine (and possibly
change) the analysis window,
click Change Analysis Window
button in the tool bar:
Exercise 1

April 2014 43
Exercise 1
Click Apply to All to define the
same analysis window for all
wells.
We then see the table is updated
with the user defined data range
of analysis window.

April 2014 44
(End of Exercise 1)
Exercise 1
In the following exercises, we want
to use the tops to define the analysis
window. Fill in the parameters page
as shown and click Apply:

EMERGE
….
Attributes and Crossplotting with
the Target Log

April 2014 46
Seismic Attributes
Seismic attributes are transforms, generally non-linear, of a seismic
trace.
 There are two types of attributes:
 Sample-based: which are calculated from the trace on a
sample-by sample basis.
 Example: amplitude envelope.
 Horizon-based: calculated as averages within a window.
 Example: average porosity between two horizons.
 For EMERGE, all attributes must be sample-based.
 EMERGE has the ability to automatically calculate a set of ‘Internal’
attributes from the seismic trace

April 2014 47
EMERGE calculates the following internal attributes from Seismic :
1B. Combinations of Instantaneous
Amplitude Weighted Cosine Phase
Amplitude Weighted Frequency
Amplitude Weighted Phase
Cosine Instantaneous Phase
Apparent Polarity
1A. Instantaneous
Amplitude Envelope
Instantaneous Phase
Instantaneous Frequency
2. Windowed Frequency
Average Frequency
Dominant Frequency
4. Derivatives
Derivative
Derivative Instantaneous Amplitude
Second Derivative
Second Derivative Instantaneous Amplitude
5. Integrated
Integrate
Integrated Absolute Amplitude
6. Time
3. Filter Slices

April 2014 48
f(t)
Time
h(t)
s(t)
A(t)
Instantaneous Attributes
which is like a 90° phase shifted trace. Writing the complex trace in polar
form, as shown below, gives us the two basic attributes: the amplitude
envelope, A(t) and instantaneous phase, f(t). (Note that the term
instantaneous amplitude is used synonymously with amplitude envelope.)

















)
(
)
(
tan
)
(
:
and
)
(
)
(
)
(
1
:
where
)
(
sin
)
(
)
(
cos
)
(
))
(
exp(
)
(
)
(
)
(
)
(
1
2
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t
s
t
h
t
t
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t
s
t
A
i
t
t
iA
t
t
A
t
i
t
A
t
ih
t
s
t
C
f
f
f
f
Instantaneous
Amplitude Envelope
Instantaneous Phase
Instantaneous Attributes were first described in
the classic paper by Taner et al (Geophysics,
June, 1979). They are computed from the
complex trace, C(t), which is composed of the
seismic trace, s(t) and its Hilbert transform, h(t),

April 2014
49
Amplitude envelope of inline 95. Amplitude envelope at well 08-08.
With and without
color amplitude fill

April 2014 50
( )
( ) the instantaneous frequency
d t
t
dt
f
  
A third basic attribute is the instantaneous frequency, which is the time
derivative of the instantaneous phase. In equation form, we can write:
Instantaneous
Amplitude Envelope
Instantaneous Phase

April 2014 51
cos ( ) cosine instantaneous phase,
A(t)cos ( ) amplitude weighted cos phase,
A(t) ( ) amplitude weighted phase,
A(t) ( ) amplitude weighted frequency.
t
t
t
t
f
f
f





The other instantaneous attributes in
EMERGE are combinations of the three
basic attributes, as shown below:
The apparent polarity attribute is the amplitude envelope multiplied by the
sign of the seismic sample at its peak value, applied in a segment between
the troughs on either side of the peak.
Combinations of Instantaneous
Apparent Polarity

April 2014 52
Amplitude Weighted Phase of inline 95.
Combinations of Instantaneous
Apparent Polarity *

April 2014 53
Windowed Frequency Attributes
From this window, either the average
frequency amplitude or the dominant
frequency amplitude is chosen and
this value is placed at the center of
the window. A new window is then
chosen 32 samples later (the default)
and the new frequency attribute is
calculated and so on. Note that the
defaults can be changed in the
Attribute / Attribute Parameters
dialog, shown here.
A second set of attributes in EMERGE is based
on a windowed frequency analysis of the seismic
trace. In this process, the Fourier transform of
each seismic trace is taken over a 64 sample
window (the default).
Windowed Frequency
Average Frequency
Dominant Frequency

April 2014 54
Windowed Frequency
Average Frequency
Dominant Frequency
Average Frequency of inline 95.

April 2014 55
Filter Slice Attributes
A third set of attributes in
EMERGE is comprised of narrow
band filter slices of the seismic
traces. The following 6 slices
are used:
5/10 – 15/20 Hz
15/20 – 25/30 Hz
25/30 – 35/40 Hz
35/40 – 45/50 Hz
45/50 – 55/60 Hz
55/60 – 65/70 Hz
Filter Slices
Narrow Filter of inline 95.

April 2014 56
.
,
2
2
1
1
1
2
1
1
2
1
t
s
s
s
t
d
d
d
t
s
s
d
i
i
i
i
i
i
i
i
i














Derivative Attributes
A fourth set of attributes in EMERGE is based on the first or second
derivative of the seismic trace or its amplitude envelope (or
instantaneous amplitude, synonymous with amplitude envelope). The
derivatives are calculated in the following way, where si = the ith seismic
or amplitude envelope sample, d1i = the ith first derivative, d2i = the ith
second derivative and Dt = the sample rate:
Derivatives
Derivative
Derivative Instantaneous Amplitude
Second Derivative
Second Derivative Instantaneous Amplitude

April 2014 57
With and without
color amplitude fill
Second Derivative of inline 95. Second Derivative at well 08-08.

April 2014 58
1


 i
i
i I
s
I
At the end of the running sum the integrated seismic trace is filtered by
running a default 50 point smoother along it and removing the resulting low
frequency trend. The integrated amplitude envelope is normalized by
dividing by the difference between the minimum and maximum samples
over the total number of samples. Note that the defaults can be changed in
the Attribute / Attribute Parameters dialog, shown earlier.
Integrated Attributes
A fifth set of attributes in EMERGE is based on the integrated seismic trace
or its amplitude envelope. The integrated values are calculated in the
following way, where si = the ith seismic or amplitude envelope sample, Ii =
the integrated value. Note that this is a running sum.
Integrated
Integrate

April 2014 59
Integrated Absolute Amplitude inline 95.
Integrated
Integrate

April 2014 60
Time Attribute
The last attribute is the time
attribute. This is simply the
time value of the seismic trace
and thus forms a “ramp”
function that can add a trend to
the computed reservoir
parameter.
Time inline 95.
Time

April 2014 61
EMERGE can also import
external attributes. These
are seismic attributes that
cannot be calculated
internally because:
They are proprietary, e.g.
• Coherency
They require previous
generation, eg.
• Seismic inversion
• AVO attributes.
P-Impedance inline 95.

April 2014 62
An example set of attributes for one well
Target Impedance 2nd Deriv Filter Amp Wt Phase

April 2014 63
One way of measuring the correlation between the target
data and any one attribute, is to cross plot them.
Cross Plotting
Target Impedance

April 2014
64





N
i
i
i )
bx
a
(y
N
E
1
2
2 1





N
i
y
i
x
i
xy )
m
)(y
m
(x
N
σ
1
1
where the means are:
The covariance is defined as:
The regression line has the form:
x
b
a
y 


This line minimizes the total prediction error:
Regression
.
1
and
,
1
1
1

 



N
i
i
y
N
i
i
x y
N
m
x
N
m

April 2014 65
The prediction error is the RMS
difference between the actual target
log and the predicted target log.
Applying the regression line gives a prediction of the target attribute:
The normalized covariance is defined as:
Original Log
Red : Log
predicted using
regression line
from a single
attribute
y
x
xy



 
Covariance and prediction error

April 2014 66
The correlation can sometimes
be improved by applying a non-
linear transform to either the
target or the external attribute
or both:
P-wave vs Zp P-wave vs 1/Zp

EMERGE
….
Exercise 2: Crossplotting and the
Single Attribute List

April 2014 68
First let’s look at some
of the internal attributes
for a particular well.
Click on Well Display:
Exercise 2

April 2014 69
Fill in the dialog as
shown. Note that the list
of all available internal
attributes is shown on
the left, while we have
chosen to display one
particular attribute
Amplitude Envelope on
the right.
Click Ok:
Exercise 2

April 2014 70
We will see this
plot, which shows
the amplitude
envelope of the
composite
seismic trace
extracted at well
01-08.
This is a purely
visual display.
Exercise 2

April 2014 71
To quantitatively see how well the
same attribute correlates with the
target log in all wells, click on
Crossplot:
Exercise 2
Select the options shown and
click Ok:

April 2014 72
The cross plot appears.
The vertical axis is the
target sonic log value,
and the horizontal axis
is the selected attribute.
Exercise 2

April 2014 73
In addition, we could apply one
of the non-linear transforms to
the target and/or to the external
attribute. But for now, we will
not do so.
Exercise 2
Again, click on Crossplot. Fill
in the dialog as shown and
click Ok. The cross plot
appears:

April 2014 74
The cross plot has used all
points within the analysis
window of every well.
A regression curve has
been fitted through the
points and the normalized
correlation value of 0.47
has been printed at the top
of the display.
The normalized correlation
is a measure of how useful
this attribute is in predicting
the target log.
Exercise 2
Target
Log
Attribute

April 2014 75
We have just looked at examples of crossplotting a single attribute.
But EMERGE allows us to quickly calculate the correlation coefficients
against the target log, for all attributes in turn and to rank their values.
Click on Single Attribute
List on the Emerge
window:
Exercise 2

April 2014 76
The upper box of the dialog shows
all the available wells
Exercise 2
The center left box shows all the
available attributes (internal and
external) in the project. In the
attribute list, we have a series of
default frequency bandpass
filters range from 5 Hz to 70 Hz.

April 2014 77
Nowadays, some seismic surveys (i.e. oil
sands) may contain frequencies higher
than 100 Hz. Our default set of frequency
bandpass filters may not be enough to
include all the frequencies of the seismic
data. Fortunately, EMERGE allows us to
define a set of frequency bandpass filters
rather than the default ones.
Check on User Customized Filter
Attributes and click Define Bandpass
Filters:
Exercise 2
On the dialogue that appears, click Apply
and we will see 15 filters. The seismic
data in this project does not contain high
frequency components, so click Cancel:

April 2014 78
Check off Use Customized Filter
Attributes:
Note that we are also selecting to
test non-linear transforms of both
the target log and the external
attribute.
Non-linear transforms
Click Ok:
Exercise 2

April 2014 79
In the first row, we note
that the minimum error of
298.757 results from using
the inverse of the Inversion
attribute.
The resulting table ranks
in descending order, the
crossplot correlations
against the target log, for
all attributes and non
linear transforms.
Exercise 2

April 2014 80
Reminder.
Because the crossplotting
is a sample by sample
operation, accuracy
depends critically on the
time-alignment of the
target and attribute.
Sometimes the correlation
can be improved by
applying residual time-
shifts to the target log
relative to the attribute.
Target Attribute
(Steps are
visible
because of
the 2ms
sampling
interval)
Time
Exercise 2

April 2014 81
Go to the Input tab and select Log
Operations>Shift/Unshift Logs to get
this window:
The initial list shows zeroes.
Click on Optimize:
Exercise 2

April 2014 82
Accept the defaults and
click Ok.
The Optimize Shifts dialog
allows you to select any
transform – in this case, the
single attribute transform:
1/Inversion.
Exercise 2

April 2014 83
The program then tries a series of time shifts for each well to find the set of
shifts that will maximize the correlation, subject to a Maximum Shift of
10 milliseconds. The suggested shifts are displayed:
To accept these shifts, click on Ok.
Click Yes on the warning message
window to apply these shifts. The
EMERGE main window will be
updated to show the shifted logs.
Exercise 2

April 2014 84
Exercise 2
The time-shifted target
sonic curves are
displayed in red
overlaying the original
sonic log curves.

Now we are going to recalculate the single
attribute transforms (using the time shifted
logs). Go to the Single Attribute List tab, and
click on Create Single Attribute List.
April 2014 85
Exercise 2
Accept the defaults, and recompute
the single attribute list with the
shifted target logs by click Ok:
Note that the minimum error in row 1
has now decreased from 298.757 to
289.748, corresponding to predicting
the square root of the target log with
the attribute 1/(Inversion).
The Single Attribute List shows the
result of cross-plotting each attribute
and ranking the result by increasing
error.

April 2014 86
If we select any row in
this table by clicking
in one of the fields,
and then click the
Cross Plot button at
the bottom of the
table, the
corresponding cross
plot will be displayed.
Exercise 2

April 2014 87
The first row shows the single
attribute that has the lowest error
when predicting the target.
Click in one of the cells of the first
row (Sqrt(P-wave) vs. 1/Inversion)
and press the Apply button. The
Application Plot window will appear:
We can see result of the predicted
target logs, by applying the
regression line from crossplot of any
attribute.
Exercise 2

April 2014 88
This display shows the target log for each well along with the “predicted” log
using the selected attribute and the derived regression curve. To get a closer
look at the result, click on Zoom to Analysis Zone of the First Well button:
Exercise 2

April 2014 89
The target logs are in black.
The predicted logs (using the
crossplot regression line applied to
a single attribute) are in red.
…
The Average Error at the top of the
plot is the root-mean-square
difference between the target log
values and the predicted values.
(End of Exercise 2)
The result matches the general
trend of the target logs, but
does not adequately predict the
subtle features.
In order to improve our
predictions, we will use the
Multi Attributes process to use
a combination of attributes
instead of a single attribute in
the next exercise.
Exercise 2

EMERGE
….
Multi–Attributes and Validation

April 2014 91
Cross plotting against 2
attributes (best fit is a plane):
Cross plotting against 1 attribute
(best fit is a line):
An extension of the conventional cross plot is to use multiple attributes.
Linear regression with multiple attributes

April 2014 92
We can extend this
to as many
attributes as we
want. At each time
sample, the target
log is modeled as a
linear combination
of several attributes.
Target Log Attribute 1 Attribute 2 Attribute 3
W1 W2 W3

April 2014 93
.
1
where
sample,
at the
all
frequency,
inst.
and
envelope,
amplitude
impedance,
acoustic
porosity,
:
where
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In matrix form, we can
write:
Consider the problem of predicting porosity with three attributes, plus a
DC component w0:
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April 2014 94
or:
This can be solved by least-squares minimization to give:
( ) ,
1
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As a detailed computation, note that:
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April 2014 95
Decreasing Prediction Error
The prediction error for N+1 attributes can never be larger than the
prediction error for N attributes.
How can we be so sure?
If it were not true, we could always make it so by setting the last coefficient
to zero.
These weighting coefficients minimize the total prediction error:
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f

April 2014 96
Given the set of all internal and external attributes, how can we find
combinations of attributes which are useful for predicting the target log?
EMERGE uses a process called step-wise regression:
(1) Step 1: Find the single best attribute by trial and error. For each
attribute in the list:
 Amplitude Weighted Phase,
 Average Frequency,
 Apparent Polarity, etc.,
calculate the prediction error. The best attribute is the one with the
lowest prediction error. Call this attribute1.
(2) Step 2: Assuming that the first member is attribute1 find the best pair
of attributes. For each other attribute in the list, form all pairs,
 (attribute1, Amplitude Weighted Phase),
 (attribute1, Average Frequency), etc.
The best pair is the one with the lowest prediction error. Call this
second attribute attribute2.
Choosing Combinations of Attributes

April 2014 97
(3) Step 3: Assuming that the first two members are attribute1 and
attribute2 find the best triplet of attributes. For every other
attribute in the list, form all triplets:
 (attribute1, attribute2, Amplitude Weighted Phase),
 (attribute1, attribute2, Average Frequency), etc.
The best triplet is the one with the lowest prediction error. Call
this third attribute attribute3.
Carry on this process as long as desired.
Decreasing Prediction Error
The prediction error, EN, for N attributes
is always less than or equal to the
prediction error, EN-1, for N-1 attributes,
no matter which attributes are used.
Choosing Combinations of Attributes

April 2014 98
How can we know when to stop adding attributes?
Adding attributes is similar to fitting a curve through a set of points, using
a polynomial of increasing order:
Fourth Order
First Order Third Order
Fourth Order

April 2014 99
The problem is that while the higher order polynomial predicts the training
data better, it is worse at interpolating or extrapolating beyond the limits of
the data as shown below. It is said to be over-trained:
For each polynomial, we can calculate
the Prediction Error, which is the RMS
difference between the actual y-value
and the predicted y-value.
As the order of the polynomial is
increased, the prediction error will
always decrease.
Fourth Order

April 2014 100
To determine the validity of attributes, EMERGE uses the following Validation
procedure:
(1) Remove the target log and attributes for one well, from the training data.
(2) Calculate the multi attribute coefficients without the removed well.
(3) Apply the coefficients to the removed well. (i.e. Blind-predict that well by
…..only using the other wells.)
(4) Repeat for each well in turn.
(5) Average the errors for all blind-predicted wells.
As the figure to the right shows, a
high order polynomial which fits
the Training Data well, may still fit
the Validation Data poorly. This
indicates that the order of the
polynomial is too high.

April 2014 101
EMERGE performs Validation by systematically leaving out wells.
Assume we have 5 wells:
{Well1, Well2, Well3, Well4, Well5}
Assume we have 3 attributes:
{Impedance, Envelope, Frequency}
Perform the Validation
(1) Leave out Well1. Solve for the regression coefficients using
only data from {Well2, Well3, Well4, Well5}. This means solving
this system of equations, where the rows contain no data from
Well1 (which has n1 points):
N
N
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n
N F
w
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F
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f
f
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





April 2014 102

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1
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(2) With the derived coefficients, calculate the prediction error for
Well1. This means calculate the following:
(3) Repeat this process for Well2, Well3, etc., each time leaving the
selected well out in the calculation of regression coefficients,
but using only that well for the error calculation.
(4) Calculate the Average Validation Error for all wells:
where now only data points for Well1 are used. This gives us the
Validation Error for Well1, E1.
( )
5
5
4
3
2
1 E
E
E
E
E
EA






April 2014 103
This is a validation plot for
an EMERGE analysis:
The horizontal axis shows
Number of Attributes used
in the prediction. The
vertical axis shows the
Root-Mean-Square
Prediction Error for that
number of attributes.
The lower (black) curve shows the error calculated using the Training Data.
The upper (red) curve shows the error calculated using the Validation Data.
The figure above shows that when more than 4 attributes are used, the
Validation Error increases, meaning that these additional attributes are
over-fitting the data.

EMERGE
….
Exercise 3: Multi Attributes

April 2014 105
Exercise 3
In this exercise, we apply Multi-Attribute Analysis to the data from the
previous exercises.
To initiate the multi-attribute
transform process, click on
Multi Attribute List:

April 2014 106
This dialog contains three
sequential pages of
parameters.
The first page is used to
select the wells that will be
used in the training. To
accept the default, which
includes all the wells, click
on Next:
Exercise 3

April 2014 107
Usually, we want to create a list by
examining all the available
attributes using the process of step-
wise regression.
Set the maximum number of
attributes to 8. Then click Next:
The second page of the Create
Multi-Attribute List dialog looks like
this:
An important parameter is the Maximum number of attributes to use. In this part
of the analysis, EMERGE searches for group of attributes that can be combined to
predict the target. It does this by the process of step-wise regression. The
parameter Maximum number of attributes to use tells EMERGE when to stop
looking. This of course affects the run-time for the analysis.
Exercise 3

April 2014 108
We will be testing non-
linear transforms for both
the target and the external
attributes.
When the dialog has been
filled in as shown, click on
OK.
Non-linear transforms
Exercise 3

April 2014 109
Each row corresponds to a particular multi-attribute transform and includes all
the attributes above it. For example, the first row, labeled 1/Inversion, tells us
that the best attribute to use alone is 1/Inversion. The second row, Time, actually
refers to a transform that uses both 1/Inversion and Time together as the best
pair.
When the analysis
completes, you will see
the Multi-attribute
table…. showing the
results of the step-wise
regression.
Exercise 3

April 2014 110
The Multi-Attribute list has several QC options, which we will examine. Click on
Row 5 and the rows above row 5 will be automatically selected.
Exercise 3
Click History. On the
history page, it shows
the five attributes that
are selected. This
confirms that the
results at row 5 include
a combination of the
first 5 attributes.

April 2014 111
On the dialog that shows
up, we can select a few
wells that are of our
interest. Here, we want to
look cross plot all the
wells, so click OK:
Exercise 3
With row 5 selected, click
Cross Plot:

April 2014 112
The resulting cross
plot shows the
predicted target value
plotted against the
actual target value.
The actual correlation
and error values are
printed at the bottom
of the cross plot. We
can see that the result
of using 5 attributes
achieves a 60.9%
correlation.
Exercise 3

April 2014 113
Select row 2 on the multi-attribute list, and click Cross Plot. Click Ok on the well
selection dialog. This cross plot shows a lower correlation of 55.7% with a pair
of two attributes.
Exercise 3

April 2014 114
The decreasing Training
Error shows that the
prediction error
decreases with
increasing number of
attributes, as expected.
Exercise 3
The lower (black) curve
shows the training error
on the vertical axis and
the number of attributes
on the horizontal axis.
The upper (red) curve is
the Validation Error, which
tells us that 7 attributes
can be used.
Select Error Plot>Versus
Attribute number:

April 2014 115
Click on row 8 on Multi-
attribute List. Select
Error Plot>Versus Well
Number. The Error Plot
vs Well Number
identifies the relative
success of training and
validation.
Exercise 3

April 2014 116
Select Row 7, then click List:
This table lists all the weights for
each of the seven attributes, as well
as the constant. Click Cancel to
close this window.
Exercise 3

April 2014 117
Ensure that the seven attribute
transform is still selected on the
Multi-attribute table and click
on Apply>Training Result.
The Application Plot window
shows the predicted log from
this multi-attribute transform
overlaid on the actual target
log. Click the button Zoom to
Analysis Window of the First
Well:
Exercise 3

April 2014 118
Finally, select Apply>Validation
Result with the 7th attribute
selected.
The Validation shows the
result of blind prediction of
each well. The first two wells
show very little change
compared to the previous
slide, though as expected the
correlation has been slightly
reduced.
End of exercise 3
Exercise 3

EMERGE
….
The Convolutional Operator

April 2014 120
This approach ignores the
fact that there is a big
difference in frequency
content between logs and
seismic data, as shown in this
zoomed display.
Using the Convolutional Operator
The Multi-Attribute Analysis so far
correlates each target sample with
the corresponding sample on each
seismic attribute.
Log Seismic
10
ms

April 2014 121
Each target sample is predicted using a weighted average of a group of
samples on each attribute. The weighted average is convolution.
The convolutional operator extends the cross plot
regression to include neighboring samples:

April 2014 122
is now replaced by:
N
N A
w
A
w
A
w
w
P 



 
2
2
1
1
0
N
N A
w
A
w
A
w
w
P 
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2
2
1
1
0
The previous equation:
where * represents convolution by an operator.
In practice, an equivalent way to solve for the weights is to create new
attributes which are “shifted” versions of the original attributes.

April 2014 123
Using the Convolutional
Operator is like adding
more attributes: it will
always improve the
Prediction Error, but the
Validation Error may not
improve – the danger of
over-training is increased.
As the operator length is
increased, the Training
Error always decreases.
The Validation Error
decreases to a minimum
and then increases again
for longer operators.

EMERGE
….
Exercise 4: The Convolutional
Operator

April 2014 125
In this exercise, we apply Multi-Attribute
analysis using a convolutional operator.
Make sure the multi-attribute transform
tab is selected, click on Create Multi
Attribute List. We will create a new list,
using all of the wells.
Accept the defaults of the
first page. Click Next:
Exercise 4

April 2014 126
On the second page, set
the Maximum number of
attributes to use to 7 and
click Next:
Exercise 4

April 2014 127
On the third page, we can specify
the range of convolutional
operators to test.
Try Operator Lengths from 1 to 9,
incrementing by 2.
Click OK.
This will take a minute or
two to complete.
Exercise 4

April 2014 128
The multi-attribute table that is
returned has 5 different versions of
List 2, each for a different length
convolutional operator.
List 1 (from the previous exercise) is
also available.
As you select different multi-
attribute lists, the corresponding
Final Attribute list will change.
Exercise 4

April 2014 129
On the left side of the
window, it displays the
validation error plot for
all 5 different operator
lengths.
The minimum
Validation Error occurs
when a 7 point
operator is used with 6
attributes.
Exercise 4

April 2014 130
Select Multi Attribute
List2_7pt, and click on
Error Plot>Versus
Attribute Number:
This shows the plot of
validation and training
error plot for the 7
point convolutional
operator.
Exercise 4

April 2014 131
To see a cross-plot of
one of the multi-attribute
operators, highlight the
words Amplitude
Weighted Frequency, the
sixth attribute, and click
on the Cross Plot button.
Click Ok on the dialog
that shows up to use all
wells. The following plot
appears:
Exercise 4

April 2014 132
Comparing the 7 point operator to the 1 point, we see that the effect of using
a convolutional operator was to increase the correlation from 61% to 70%
7 points 1 point
Exercise 4

April 2014 133
Select the sixth attribute
again, and click on
Apply>Training Result.
A plot appears, showing
the results of applying
the multi-attribute
transform along with the
target logs. Again, click
the zoom button to zoom
to the target log zone.
Exercise 4
Turn off the Multiple
Window Mode:

April 2014 134
This display is similar to
the previous one, but
each predicted log has
used an operator
calculated from the other
wells.
This validation display
shows how well the
process will work on a
new well, yet to be
drilled.
Another useful display can be seen if you select the sixth row on the multi-
attribute transform list and click on Apply>Validation Result.
(End of Exercise 4)
Exercise 4

EMERGE
….
Exercise 5: Processing a 3D
Volume

April 2014 136
Now that we have derived the multi-
attribute relationship between the
seismic and target logs, we will apply
the result to the entire 3D volume. We
no longer require the Emerge Training
window, so close it down by clicking
File>Exit on that window:
This dialog appears, which confirms
that all the training we have done is
saved under the name Emerge
Session_1. Click Yes:
Exercise 5

April 2014 137
To apply the derived
relationship, go back to the
Geoview window. Under the
Processes tab, double-click
Emerge Apply:
Exercise 5

April 2014 138
By default, the process is applied to
the entire volume. We are also
specifying that this is a Multi
Attribute Transform from Emerge
Session_1, and that it is the 7-point
operator we are using:
The attribute list is where we specify
which combination of attributes to
use.
During the training, we concluded
that the best combination is to use
the first 6 attributes, as determined
by step-wise regression. The last
attribute in that list was Amplitude
Weighted Frequency. Click on that
name:
Exercise 5

April 2014 139
To confirm the details of this transform,
click the History button:
A window appears, showing all the
details of the training process:
Close this window by clicking the “x”
on the upper right, as shown.
Exercise 5

April 2014 140
Click Show Advanced Options. Under the
Time Window tab, limit the processing
window as shown. There are two reasons
for doing this. One is to save on run-time.
The second is that we expect the
transform to be most applicable around
the time zone used for the training.
If we had imported or picked horizons, we
could use them to bracket the application
window. For now, we will use constant
times:
When you have completed this page, click
OK to run the process.
800 ms
1200 ms
Exercise 5

April 2014 141
When the process completes, the result is shown in the split-screen mode.
Use the well icon to jump to well 08-08.
Exercise 5

April 2014 142
Right-click in the P-wave
display and choose Color Key
>Color Key and Histogram:
To remove the distracting
green zones above and below
our processing time-window,
we will reset the colour for the
lowest values.
Exercise 5

April 2014 143
Double click in the green
cell. On the window that
pops up, replace the green
cell with white color by
double clicking on the white
cell. Click Ok:
Exercise 5

April 2014 144
In the tab for Edit
Scale, set the range
from 3400 to 4500
m/s, as shown, and
click OK:
Exercise 5

April 2014 145
The Geoview window now looks like this:
Zooming-in, we can see a
low velocity channel at about
1065ms at well 08-08.
Exercise 5

April 2014 146
The final display we will create
with this data is a data slice
through the time of interest.
Double click on Slice Processing
> Create Data Slice:
Exercise 5

April 2014 147
On the Create data slice dialog, we are
choosing to create a slice from the
volume computed_P-wave:
Ideally, we should be defining the
slice window by a picked horizon, but
we don’t have any. So we will center
the data slice at a time of 1065 ms,
which is close to the target zone.
Around that time, we will average
samples over a 10 ms window, as
shown. Click Ok:
Exercise 5

April 2014 148
(End of Exercise 5)
The slice shows a low
velocity area in green.
Exercise 5

April 2014 150
Log
Non-linear prediction:
Attribute
Linear prediction:
Log
Attribute
Why use a Neural Network?
The previous method
of prediction has used
combinations of
straight regression
lines in crossplot
space (with the
refinements of non-
linear transforms and
convolutional
operators).
But it would be better
to account directly for
non-linear
relationships between
logs and attributes.

April 2014 151
The potential improvement using Neural Networks

April 2014 152
Set of input
attributes:
Attribute 1
Attribute 2
Attribute 3
Attribute n
Output Value
A Neural Network
The outputs from each
layer are the inputs to the
next layer.

April 2014 153
Each neuron receives many
inputs, combines them, performs a
function and transmits the result
as an output to other neurons.
One Neuron
Attribute 1
Attribute 2
Attribute 3
Bias or
constant
W1
W2
W3
Output Value
One type of Sigmoidal
Function : Wikipedia
Each input value is
weighted

April 2014 154
Neural Networks in EMERGE
EMERGE has four ways of using Neural Networks:
MLFN Multi-Layer Feed Forward
- Similar to traditional back-propagation.
PNN Probabilistic Neural Network
- Can be used to classify data, in which case it is similar
to Discriminant analysis, or to predict data, in
which case it is similar to regression analysis.
RBF Radial Basis Function Neural network.
Discriminant A linear classification system.

April 2014 155
MLFN Neural Network
Each training example consists of the input attributes plus
the known target value for a particular time sample.

April 2014 156
MLFN Training Parameters
The training of MLFN consists of determining the optimum set of weights
connecting the nodes. By definition, the “best” set of weights is the one
which predicts the known training data with the lowest least-squares
error. This is a non-linear optimization problem. EMERGE solves this by
a combination of simulated annealing and conjugate-gradient.
The main parameter controlling the training time is the number of Total
Iterations. Within each one of these iterations, there is a fixed number of
Conjugate-Gradient Iterations to find the local minimum.

April 2014 157
Within each of the Total Iterations, simulated annealing may be used to
look for improvements by searching in other areas of the parameter
space. The decision about whether to perform simulated annealing in
any iteration is controlled by the program and depends on the degree of
improvement in the previous iteration. Theoretically, more iterations is
always better than fewer because it allows more scope for finding the
global minimum.
While the training is going on, the prediction error may be monitored:
Pressing Stop on this menu allows the training to be terminated at any time.

April 2014 158
The parameter which controls how well the network predicts the training
data is the Number of Nodes in the Hidden Layer:
The default value follows the rule-of-thumb that it should be equal to 2/3
the number of input attributes. (Note that the number of input attributes
equals the number of actual attributes multiplied by the operator length).
Increasing the Number of Nodes in the Hidden Layer will always predict the
training data more accurately, but the danger of over-training is increased.

April 2014 159
2 nodes in
hidden layer:
5 nodes in
hidden layer:
Number of Nodes in Hidden Layer
These displays show the effect of changing the number of hidden layer
nodes for the simple 1-attribute case:

April 2014 160
These displays show the effect of changing the number of hidden layer
nodes for the simple 1-attribute case:
5 nodes in
hidden layer:
10 nodes in
hidden layer:

April 2014 161
MLFN Neural Network
Advantages:
(1) Traditional form is well described in all Neural Network books.
(2) Once trained, the application to large volumes of data is relatively fast.
Disadvantages:
(1) The network tends to be a “black box” with no obvious way of
interpreting the weight values.
(2) Because simulated annealing uses a random number generator to
search for the global optimum, re-running training calculations with
identical parameters may produce different results.

April 2014 162
Probabilistic Neural Network (PNN)
The Probabilistic Neural Network, or PNN, is a second type of neural
network used in EMERGE. The PNN can be used either for classification
or for mapping.
In classification, EMERGE classifies an input seismic sample into one of
N classes (e.g. sand, shale, carbonate, or oil, gas, water, etc.)
In mapping, EMERGE maps an input seismic sample into a reservoir
parameter such as porosity. This is the same thing that we did with
multi-linear regression and MLFN, but PNN uses a different approach.
(Another term for PNN applied to mapping is the Generalized Regression
Neural Network, or GRNN, but we will use the term PNN for both mapping
and classification.)
To understand PNN, we will first review the concept of linear regression.

April 2014 163
Let us start with the simple case in which we try to predict an
unknown target log value ‘y’ from a seismic attribute value ‘x’, using
three pairs of known training values (x1 , y1), (x2 , y2 ), and (x3 , y3 )
that are close to each other in crossplot space.
Attribute X
Training
Attribute X
Training
Target Y
Target
value of y?
y1
y2
y3
x1
x2
x3
x
Target Y

April 2014 164
The Basic Prediction Problem
The basic prediction problem
from the previous slide is re-
shown on the right in
graphical form. Given a set of
known training points we want
to predict an unknown target
value y at attribute position x.
x1 x2 x3
x
y1
y2
y3
y ?
Attribute x
Target
y

April 2014 165
Linear Regression
In linear regression, we fit
the line y = w0 + w1x
to the points.
In the example on the right,
w0 = 2 and w1 = 0.5, and the
predicted point is as shown.
However, notice that the
training points are not
correctly predicted by the
regression line.
y = 4.5
0
8
8
0 2
2
4
4
6
6
x = 5
Attribute x
Target
y

April 2014 166
PNN
In PNN, the weights are fitted
to the points themselves:
y = w1y1 + w2y2 + w3y3 ,
Notice that in addition to the
target point, the training
points are also correctly
predicted in the PNN example
shown on the right.
x = 5
y = 5

April 2014 167
To more accurately predict
the target value, we use two
additional values which are
combined to create a weight:
1. We use the distance ‘d’ in
attribute space.
x3
y1
y2
y3
x
x1 x2
d1
d2
d3
Attribute x
Target
y
y ?

April 2014 168
The Effect of Sigma
2. We use a function ‘ ’ (Sigma)





 

 2
2
2
2
)
(
exp
)
(

x
x
x
g
Notice that the effect of  is to
widen the curve as  increases.
 = 0.5
 = 1.0
 = 2.0
x
x2
The sampling of x is normalised
for each attribute. The values
are one standard deviation.

April 2014 169
PNN Weights
The PNN weights are given as:



















































2
2
3
2
2
2
2
2
1
2
2
3
3
2
2
2
2
2
2
1
1
exp
exp
exp
1
:
where
,
exp
,
exp
,
exp






d
d
d
S
d
S
w
d
S
w
d
S
w
di is the distance from the i th training point to the output point, the
factor S forces the weights to sum to 1, and  determines the fit.
x3
y1
y2
y3
x
x1 x2
d1
d2
d3
Target
y
y ?
Attribute x

April 2014 170
In the previous PNN result,  = 1.0. The above displays show values
of 0.5 and 2.0. As  increases, the fit becomes smoother, but does
not fit the training points perfectly.
 = 0.5  = 2.0

April 2014 171
PNN Validation
To determine which value
of sigma is correct, we
use cross-validation, in
which known values are
left out of the training
process.
The simple example on
the right shows that the
validation points (open
circles) are fit best using a
sigma value of 2.0, even
though this value
produces a curve which
does not correctly fit the
training data.

April 2014 172
Now let us consider the same problem using 2 attributes, but still 3
training points and one unknown point.
PNN using Two Attributes
Log Seismic Attributes
X Y
x1
x2
x3
x
y1
y2
y3
y
p1
p3
p ?
p2

April 2014 173
Note that the only change is that we now can think of the points in attribute
space as being 2-dimensional, and that distance is now computed by:
( ) ( )2
2
2
y
y
x
x
d i
i
i 



p1 p2
p3
d1
p
d2
d3
x1
x x3 x2
y3
y
y1
y2

April 2014 174
Practical PNN
• In practice PNN is performed in M-dimensional space, where M
equals the number of attributes. This cannot be visualized, but the
mathematics is the same.
• Also, the training dataset consists of N points, where N is much
larger than 3.
• As we have seen,  is the most important parameter in PNN, and
needs to be optimized. Optimization is done using cross-validation,
in which each well is left out of the training process and predicted,
one at a time.
• Finally,  is allowed to vary for each attribute.

April 2014 175
PNN Application Example
The figure on the left shows the application of multilinear regression on
four well logs, using six attributes, and the figure on the right shows the
application of PNN.

April 2014 176
PNN Validation Example
The figure on the left shows the validation of multilinear regression on four
well logs, using six attributes, and the figure on the right shows the
validation of the PNN.

April 2014 177
PNN Summary
The PNN is used in EMERGE for both classification and mapping.
In classification we need only the weights that depend on the “distance”
from the desired point to the training points.
The “distance” is measured in multi-dimensional attribute space.
The “distance” is scaled by smoothers (the sigma values), which are
determined automatically by cross-validation.
In mapping, the weighting functions are multiplied by the known log
values to determine the unknown log values.
We will now look at the specific menu items in EMERGE.

April 2014 178
PNN Training Parameters
Training the PNN means finding the “best” set of sigma values for each
attribute.
By definition, the “best” set of sigmas is the one which produces the
minimum cross-validation error.
Cross Validation means hiding data on a well-by-well basis or on a point-
by-point basis. The well-by-well default is always recommended:

April 2014 179
Sigma optimized
automatically:1
Sigma reduced
to 1/10th the
optimized value:
PNN Effect of Changing Sigmas
These displays show the effect of changing the single sigma value for the
simple 1-attribute case:

April 2014 180
Sigma optimized
automatically:
Sigma reduced to
1/2 the optimized
value:

April 2014 181
Sigma optimized
automatically:
Sigma increased
to 2 times the
optimized value:

April 2014 182
Probabilistic Neural Network
Advantages:
(1) Because the PNN is a mathematical interpolation scheme, the derived
sigmas may be interpreted as the relative weight given to each attribute.
(2) Unlike the MLFN, the training process is reproducible.
(3) In classification mode, the PNN may produce probability estimates.
Disadvantages:
(1) Because the PNN keeps a copy of all the training data, the application
time to the 3D volume may be very large. This application time is
proportional to the number of training samples. This problem may be
alleviated by applying to a small target window.

April 2014 183
Radial Basis Function Neural Network (RBFN)
• A third type of neural network available in EMERGE is the radial basis
function neural network, or the RBF network.
• The RBF network is similar to the PNN in that there is a weight for each
training point and the weights are multiplied by gaussian functions of
attribute distance that are controlled by a sigma parameter.
• However, the RBF network is different to the PNN (and similar to
multilinear regression) in that the weights are pre-computed and then
applied. (Note that in the PNN, the weights are computed “on the fly”
from the data, and only the sigma value needs to be pre-determined).
• Again, the best way to understand the RBFN is to look at a simple
example.

April 2014 184
RBFN
In the RBF network the fitting
function is given as:
.
exp
:
where
,
2
2
3
3
2
2
1
1












i
i
d
g
g
w
g
w
g
w
y
Note that gi is equal to the PNN
weight without the scaling. In
the example shown, the
individual curves (light lines)
and the final result (heavy line)
are shown. The training points
are correctly predicted.
 = 1.0

April 2014 185
RBFN – Effect of Sigma
Two different  values are shown above. As sigma decreases, the weights
converge to the training values (i.e. wi = yi). As  increases, the fit becomes
smoother. Also note that the training points are always correctly predicted.
 = 0.5  = 2.0

April 2014 186
RBFN Validation
Again, we will use the cross-
validation technique to
determine which value of
sigma is correct, in which
known values are left out.
The simple example on the
right shows that the
validation points (open
circles) are fit best using a
sigma value of 1.0, even
though this value produces a
curve which is not as smooth
as for a sigma of 2.0.

April 2014 187
RBFN – Computing the Weights
For the three point problem just discussed, the RBFN weights are
computing by solving the following 3 x 3 matrix equation:
.
)
(
exp
exp
:
where
1
1
1
2
2
2
2
3
2
1
1
23
13
23
12
13
12
3
2
1
1
33
32
31
23
22
21
13
12
11
3
2
1







 




































































j
i
ij
ij
x
x
d
g
y
y
y
g
g
g
g
g
g
y
y
y
g
g
g
g
g
g
g
g
g
w
w
w
In the general case, we solve for an N x N matrix inverse, where N is equal
to the number of training points. However, notice that the matrix is
symmetrical, and there are efficient ways to solve this problem.

April 2014 188
RBF Application Example
The figure on the left shows the application of the PNN on four well logs,
using six attributes, and the figure on the right shows the application of the
RBF network.

April 2014 189
RBF Validation Example
The figure on the left shows the validation of the PNN on four well logs, and
the figure on the right shows the validation of the RBF network.

April 2014 190
Practical RBFN
• In practice the RBF network is applied in M-dimensional space, where
M equals the number of attributes. As with the PNN, this cannot be
visualized, but the mathematics is the same.
• Also, the training dataset consists of N points, where N is much larger
than 3.
• As in the PNN,  is the most important parameter in the RBF network
and needs to be optimized. Optimization is done using cross-
validation, in which each well is left out of the training process and
predicted, one at a time.
• Unlike the PNN,  is not allowed to vary for each attribute in the RBF
network.

April 2014 191
Radial Basis Function Neural Network (RBFN)
Advantages:
(1) Because the RBF network is an exact mathematical interpolation
scheme, the training data will be optimally fit.
(2) For small training datasets, the RBF network may give a higher
frequency result than the PNN.
(3) The RBF network can run considerably faster than the PNN.
Disadvantages:
(1) Unlike the PNN, in which sigma is allowed to vary for each attribute,
the RBF network is optimized for a single value of sigma.
(2) For small values of sigma, the fitting function can have large
“swings” between points.

April 2014 192
Comparison of Neural Network Results
PNN
MLFN RBF
Regression
Target Log Porosity
Filtered Un-Filtered

EMERGE
….
Exercise 6: Using Multi-Attributes for
Porosity Prediction
(The following exercise, 7, will apply PNN to this dataset)

April 2014 194
In this example, we will estimate
porosity from seismic attributes. The
analysis data will consist of seven
wells with measured porosity logs,
along with the seismic and impedance
3D volumes
Exercise 6 will use multi-attribute
transforms .
Exercise 7 will use a Neural Network,
which we can compare to the results
from the Exercise 6 multi-attribute
method.
We will start a new project, with different input logs, but
the same seismic as in the previous exercises.
Exercise 6

April 2014 195
The first thing to do is to create
a new project to perform this
analysis. On the Geoview
window, select the Start tab
and click New Project:
Exercise 6
Type in the project name
“Porosity” and click OK:

April 2014 196
Exercise 6
To use the pre-prepared database, click
Specify database>Open:
On the File Selection dialog, select
the file porosity.wdb and click OK:

April 2014 197
Click OK to complete
the well loading
Exercise 6
The Geoview Start
Window now looks like
this. Double click on the
first well 01-08:

April 2014 198
Each well contains a sonic log, a density log, and a density-porosity log. In
this project, we will be using the porosity log as the target.
Exercise 6

April 2014 199
Next, we will load the Seismic and
Impedance 3D volumes. Click on the
Seismic tab:
On the dialog that appears, Click
the Select All to import both
volumes. Click Next and Ok
where necessary. You should not
need to change anything.
Exercise 6
The window to the right of this tab
shows all seismic data loaded so
far. This is empty. Go to the
bottom of the window and select
Import Seismic>From SEG-Y File :

April 2014 200
After loading, the
seismic window
will look like this.
Exercise 6

April 2014 201
To start the Emerge training, click on
the Processes tab. This shows a list of
all processes available in Geoview:
Click the triangle sign next to the
Emerge name to show the Emerge
processes:
Finally, double-click Emerge
Training. This causes the training
dialog to appear.
Exercise 6

April 2014 202
In this exercise, we wish to
predict Porosity throughout the
seismic volume, so select that
as the Target from the pull-
down menu:
Exercise 6
Click Select All to use all the
available wells. Click Next:

April 2014 203
We wish to use both the
imported seismic volumes,
so click Select All:
Verify that the ‘Type of
Data’ is shown correctly.
Then click Next:
Exercise 6

April 2014 204
In the third tab, click Next to accept
the defaults for the Composite
Trace extraction. This extracts one
traces from the seismic volumes at
each well location.
Exercise 6

April 2014 205
On the last page, specify
the analysis window for
training. Select Top
instead of Log Start and
Log End:
Finally, click Ok:
Exercise 6

April 2014 206
The Emerge
Session window
appears:
Exercise 6
Target
Log
Seismic
Trace
Inversion
Trace

April 2014 207
Click on Single Attribute
List:
Exercise 6

April 2014 208
Note that we are choosing to
test non-linear transforms
applied to both the target
(porosity) and the external
attribute (inversion).
Accept all the defaults and click
Ok:
Exercise 6

April 2014 209
We note that the best correlation of
about 36% is rather poor. One
reason for this may be residual
time-shifts between the target
porosity logs and the seismic data,
in spite of the check shot
corrections.
Exercise 6

April 2014 210
Go to the Input tab and select Log
Operations>Shift/Un-shift Logs to
get this window:
The initial list shows zeroes.
Click on Optimize:
Exercise 6

April 2014 211
Accept the defaults and
click Ok.
The Optimize Shifts dialog
allows you to select any one
transform – in this case, the
single attribute transform:
1/Inversion.
Exercise 6

April 2014 212
The program then tries a series of time shifts for each well to find the set of
shifts that will maximize the correlation, subject to a Maximum Shift of
10 milliseconds. The suggested shifts are displayed:
Exercise 6
To accept these shifts, click on Ok.
Click Yes on the warning message
window to apply these shifts. The
EMERGE main window will be
updated to show the shifted logs.

April 2014 213
Exercise 6
The time-shifted target
sonic curves are
displayed in red
overlaying the original
sonic log curves in
black.

Now we are going to recalculate the single
attribute transforms (using the time shifted
logs). Go to the Single Attribute List tab, and
click on Create Single Attribute List:
April 2014 214
Exercise 6
Accept the defaults and click Ok.
The single attribute list will be
recomputed with the shifted target
logs.
Note that the maximum correlation
has now increased from 36% to
46%.

April 2014 215
Exercise 3
Now Create the multi-attribute
transform process by clicking on
Multi Attribute List:
This dialog contains three
sequential pages of
parameters.
To accept the default, which is
all the wells, click on Next:

April 2014 216
Set the number of attributes to 8
and the operator length to 5. Click
Next. On the third page, click Ok to
accept the defaults.
Exercise 6

April 2014 217
Exercise 6
When the analysis
completes, you will
see the Multi-attribute
table and the
prediction error plot.
This display indicates
that it is best to use six
attributes.

April 2014 218
We have now achieved
a 61% correlation
between the predicted
logs and the target
logs. In addition, the
average RMS error is
0.040, or 4% porosity.
To see the application,
select the sixth row of
the Multi-attribute
Table (Y_Coordinate)
and click on
Apply>Training Result.
Click the zoom button
to zoom to the target
zone.
Exercise 6

April 2014 219
During this exercise, we did not previously look at the single attribute
application, but it is interesting to compare the results between single
attribute and multi Attribute application.
Single Attribute Multi Attribute
Exercise 6

April 2014 220
Exercise 6
We no longer require the
Emerge Training window, so
close it down by clicking
File>Exit on that window:
This dialog appears, which
confirms that all the training
we have done is saved
under the name Emerge
Session_1. Click Yes:

April 2014 221
To apply the multi-attribute
transform, double-click Emerge
Apply in the Geoview window:
Exercise 6

April 2014 222
To save time, we will apply to
the Single Inline 95:
We are also specifying that this is
a Multi Attribute Transform from
Emerge Session_1:
Not yet
During the training, we concluded
that the step-wise regression
showed a combination of the first 6
attributes to be best. The last
attribute in that list was Y-
Coordinate. Click on that name:
Exercise 6

April 2014 223
Notice that this automatically
highlights all the attributes before.
This is because, when we select Y-
Coordinate, we really mean the
combination of this and the previous
five attributes.
Click History. The History file
provides confirmation of all
parameters. Close the History
file.
Exercise 6

April 2014 224
Click the button at the bottom
Show Advanced Options:
Click the Time Window tab. This
page allows us to apply the
Emerge transform to a selected
time window around the zone of
interest.
There are two reasons for doing
this. The first is to save on run-
time. The second is that the
transform will be most applicable
only near the time zone used for
Training.
Exercise 6

April 2014 225
If we had horizons, we
could use them to
bracket the application
window. For now, we will
use constant times of
900 to 1200ms.
When you have completed
this page, click OK to run
the process.
Exercise 6

April 2014 226
When the process completes, the result is shown in split-screen mode. Drag
down to our processed window. The color scale of the output is porosity.
Exercise 6

April 2014 227
Let’s change the numerical
range of the color display.
To do that, right-click in the
display and choose Color
Key > Modify Range:
Exercise 6
Specify the range to be from
0 to 0.15 and click OK:

April 2014 228
After zooming-in to the target
interval, a high porosity
channel is evident at 1065ms
with porosity of 15%.
(End of Exercise 6)
Exercise 6

EMERGE
….
Neural Network Parameters

April 2014 230
Training the Neural Network
This dialog allows you to create a
new network or to overwrite an
existing one. There is no limit to
the number of networks stored in
an EMERGE project. You may
also choose to write out the
training data to an ASCII file for
another Neural Network program
to read.
This page also determines which wells to use in the training. Note that
there may be two reasons to leave a well out of the training:
(1) The well-to-seismic tie is poor.
(2) You may wish to use the well for “blind well testing” or validation later.

April 2014 231
This is usually
recommended since step-
wise regression is the best
way to determine which
attributes to use.
This page determines whether a previously calculated multi-attribute
transform is used as a “template” for setting up the neural network.
Choosing “yes” here means
that the neural network will
have exactly the same
attributes and the same
operator length as the
selected multi-attribute
transform.

April 2014 232
This page is used only if a
multi-attribute transform is not
being used as a template. In
that case, any attributes with
(optional) non-linear
transforms may be specified
here.

April 2014 233
This page determines important
general network properties.
The first parameter is the type of
network:

April 2014 234
These parameters control the option to cascade the Neural Network with
the trend from the multi-attribute transform. This option exists because
Neural Networks usually work best with stationary data containing no long
period trend.
Sometimes it is best to remove the trend from the target data and use the
Neural Network to predict the residual data which is left after trend
removal.
In this option, the following steps are followed:
(1) The multi-attribute transform is used to predict the target logs.
(2) The predicted logs are smoothed using a running average.
(3) The smoothed predicted logs are subtracted from the original logs.
(4) The Neural Network is then trained on the residual or difference.

April 2014 235
Trend predicted from
multi-attribute transform
PNN Prediction of residual PNN Prediction without
cascading
The only way to tell if this option is helpful is to create Neural Networks
both ways and look at the training and validation errors.

EMERGE
….
Exercise 7: Using Neural Networks
to refine the previous Porosity
Prediction

April 2014 237
If the EMERGE main window is not
already open, it can be re-opened by
selecting Emerge>Emerge Training:
Exercise 7
Select Emerge Session_1 and
click Open:

April 2014 238
Now the Emerge
window appears with
the previous training
session. This is the
starting point for the
NN exercise.
Exercise 7

April 2014 239
To start the Neural Network
analysis, click on Neural
Network:
In this exercise, we will use the Neural Network capabilities of EMERGE to
improve the porosity prediction from the previous exercise.
Exercise 7

April 2014 240
Accept the defaults, which
will cause a new network to
be created with the name
Network_1.
Using all the wells and click
Next:
Exercise 7

April 2014 241
The NN does not determine by
itself, which are the best
attributes to use, so we must tell
it to use the combination of 6
attributes which we determined
in the previous exercise.
Highlight the Y Coordinate, then
click Transform History:
Exercise 7
A window appears, showing all
the details of the training process.
Close this window by clicking the
“x” on the upper right.
Click Next on Emerge Train
dialog:

April 2014 242
We will start by creating a Probabilistic
Neural Network, as shown. For this
network, we will not cascade with the
trend from the multi-attribute transform.
We will do this later and the process will
be explained then.
By choosing the type of analysis as
Mapping, we are specifying that we
wish to predict numerical values for the
porosity and not classification type.
Exercise 7
Accept the defaults for the PNN
Training process by clicking on OK.
A Progress Monitor can be seen:
The error will decrease as the
process runs.

April 2014 243
The PNN training
result appears. Zoom
to the target zone by
clicking the button
Zoom to Target Zone
of the First Well.
Exercise 7

April 2014 244
Note that the correlation of 0.82 is much higher than that achieved with multi-
attribute regression. This is usually the case with Neural Networks because of
the non-linear nature of the operator. Note also that the Neural Network has
been applied only within the training windows. This is done for two reasons:
(1) The application time for the
Neural Network can be very long
if applied to the entire window.
(2) Neural Networks are not very
good at extrapolating beyond the
known training data. For this
reason, it is expected to be less
valid outside the training
windows than the multi-linear
regression.
Exercise 7

April 2014 245
Now we would like to see how the
network performs in Validation Mode.
This means that we will hide one well at a
time and use the network trained on the
remaining wells to predict the hidden
well.
Exercise 7
Click on Validate Neural Network:
Since all the wells were used for training,
only the first selection is appropriate.
This means that each of the training wells
will be “hidden” in turn and predicted
using the remaining wells. Click on OK
to start this process.

April 2014 246
Now, the PNN
validation result
appears. Zoom to
the target zone by
clicking the zoom
button.
Exercise 7

April 2014 247
Note that the correlation after Validation is lower at 51% than
for Application at 82%.
Exercise 7

April 2014 248
To see how the errors
are distributed over the
wells, click on Error Plot.
We see that the
validation errors for the
first two wells are higher
than the others,
indicating that we might
improve the analysis by
leaving out those wells.
Exercise 7

April 2014 249
To evaluate this option, we will create another
new network. Click on Train Neural Network.
Another possibility for improving the PNN result is to use the trend from the
multi-linear regression calculation. This is sometimes useful because Neural
Networks operate best on data with stationary statistics, i.e., data sets without
a significant long period trend.
Exercise 7

April 2014 250
Accept the defaults to
name the new network
and to use all the wells.
Click Next:
Exercise 7

April 2014 251
We will use the same
with six attributes as the
basis for this network.
Click Next:
Exercise 7

In this mode, the first calculation that the network performs is the multi-linear
regression with the same four attributes. The predicted log from that calculation is
then smoothed with a smoother length given on the Neural Network training dialog.
The PNN Neural Network is then used to predict the residual, which is the high-
frequency component of the logs which is not contained within the smooth trend.
The final predicted log is obtained by adding the trend from the multi-linear
regression and the predicted residual from the Neural Network.
April 2014 252
Finally, on the last page,
we come to the parameter
which must be changed.
We choose to cascade
with the trend from the
by selecting Yes. Click Ok:
Exercise 7

April 2014 253
The first thing we can see is that the low-frequency trend from the target
logs has actually been predicted outside the analysis windows.
With Trend Without Trend
Exercise 7

April 2014 254
The second thing we
can see is that the
correlation is not quite
as good as that
obtained with the
Neural Network
without a trend.
Exercise 7
The Neural Network
List is displayed on
the right side of the
window.

April 2014 255
Click on Network
1 and then Cross
Plot. Click Ok on
the well selection
dialog that pops
up. The cross plot
of the actual and
predicted porosity
appears.
Exercise 7

April 2014 256
Exercise 7
Click on
Network 1 and
then History:

April 2014 257
We have completed the Neural Network
training, so all the training windows can be
closed by selecting File>Exit:
Exercise 7
To apply the derived relationship, return to
the Geoview window and double-click
Emerge Apply:

April 2014 258
Set the Output Volume name to
pnn_result:
We will choose to process the
Entire Volume:
Select the Neural Network
transform:
We choose to apply Network_1:
Finally, click OK to apply the
process:
Exercise 7

April 2014 259
When the calculation has
completed, the result
appears on the right side of
the seismic display tab.
PNN Porosity IL 95
Exercise 7

April 2014 260
To compare our PNN and Regression results, drag the ‘Computed
Porosity’ volume into the left window
PNN Porosity IL 95
Regression Porosity IL 95
Exercise 7

April 2014 261
Turn on the color on the
View 1 display by right-
clicking as shown:
Exercise 7

April 2014 262
PNN Porosity IL 95
Exercise 7
The window should look like this:

April 2014 263
Use the eye icon, or right
click in the display to
access the many display
options.
Find the Curve Selection:
Exercise 7

April 2014 264
Make the changes shown and then move to the
Curve Plotting options:
Exercise 7

April 2014 265
Select the Plotting
method as ‘Between
traces:
Exercise 7
Then click OK.

April 2014 266
PNN Porosity IL 95
If we repeat the process of setting display parameters for the left display, we can
make a visual comparison of the EMERGE results against the well log.
Exercise 7

April 2014 267
A further display improvement is
to add the tops. Again, click the
eye icon and select Modify
Attributes for View 1. Modify the
display options as shown on the
right figures.
Then click OK:
These steps would need to be
repeated for a second display
window if wished.
Exercise 7

April 2014 268
PNN Porosity IL 95
The finished display with Tops.
Exercise 7

April 2014 269
To see a more complete view of the PNN
result, turn off View 1:
Then select Xline mode
and position the display
near well 01-08:
Exercise 7

April 2014 270
The display now looks like this:
(End of Exercise 7)
Exercise 7

Case Study
Using EMERGE to predict Vclay from
Simultaneous Inversion attributes

April 2014 272
New developments in EMERGE use
The original use of Emerge:
To predict porosity, using
CDP Stack
Acoustic Impedance Inversion.
Advanced use of Emerge:
To predict water saturation, gamma-ray, or Vshale, using
CDP Stack
Zp from simultaneous inversion.
Zs from simultaneous inversion.
ρ from simultaneous inversion.
This case study shows a recent use of Emerge for predicting Vshale.

April 2014 273
Objective
Utilize pre-stack P-wave seismic data combined with well information to
produce a Vclay volume using pre-stack Simultaneous Inversion.
Main goal: Discriminate between sands and shales to
help with steam injection program.

April 2014 274
Geologic Setting
Cretaceous reservoir: sand and shales deposited in fluvial lowstand tract within
valleys incised into paleo-karsted carbonate terrain.
Braided channel sands deposited in the incised valleys, with laterally
discontinuous mudstones and shale plugs occurring as overbank deposits and
channel fill.
The objective of the project is to identify shale plugs.

April 2014 275
Geologic Setting

April 2014 276
Facies cross-section from core
CORE STUDY 1- PP Overlay with large-scale dipping bedforms.
McMURRAY
DEVONIAN
DEPOSITIONAL
ANALOG—
FLY RIVER DELTA,
PAPUA, NEW GUINEA
Depositional Analog:
Fly River Delta, PNG
Braided channel
sands with laterally
discontinuous
mudstones and
shale-plugs
occurring as
overbank deposits
and channel fill.

April 2014 277
Organization of project
The project consisted of four phases:
1. Acquisition of multi-component (PP and PS) data
2. Seismic processing for PP and PS
3. Seismic modeling and simultaneous inversion for Vp, Vs, and Density
using PP data
4. Emerge analysis for Vclay.

April 2014 278
Workflow
The interpretation workflow consisted of four elements:
1. Petrophysics and synthetic modeling
2. PP well ties and horizon picking
3. Simultaneous pre-stack PP seismic inversion
4. Probabilistic neural network using EMERGE for Vclay
Petrophysics
Seismic
Forward
Modeling
Horizon
Interpretation
Prestack
Deterministic
Inversion
Deterministic
AI
Inversion
Emerge
Stochastic
Property
Modeling
Structural
Framework
Simulation
&
Forecasting

April 2014 279
Petrophysical Analysis
Petrophysical analysis and modeling: log and core data from 42 wells.
Core, density and P- and S-wave velocity logs: available in most wells.
Standard processes:
•log editing
•normalization and invasion correction
•reservoir parameter interpretation: clay volume (Vclay), porosity and
water saturation (Sw)

April 2014 280
DEPTH
M
DEPTH_FT
ft
GR
GAPI
0 100
SP
MV
-190 10
CALI
MM
100 200
VCL_FIN
v/v
0 1
PHIE_FIN
v/v
1 0
BVW_TMS
DEC
1 0
0 VCL_FIN
RES_D
OHMM
0.2 2000
RES_M
OHMM
0.2 2000
RES_S
OHMM
0.2 2000
RHOB_RAW
g/cc
1.65 2.65
NPSS
V/V
0.6 0
PEF
B/E
0 5
RHOB_RAW NPHI
VP_FINAL
ft/s
4000 10000
VS_FINAL
ft/s
2000 5000
VS_FLAG
0 20
QUAL_VS
20 0
AI
g/cc-f/s
10000 20000
PR
v/v
0 0.5
VPVS
v/v
0 5
G
GPa
0 5
SI
ft/s-g/c
0 10000
120
130
140
150
160
170
180
190
200
210
220
230
240
250
400
450
500
550
600
650
700
750
800
Density
IP
IS
Mud Plug
Vs,
Vp
McM

April 2014 281

April 2014 282
LR = Ip2 – 2Is2
MR = 2Is2
Sands Shales

April 2014 283
Sands Shales

April 2014 284
Rock properties with highest correlation to Vclay:
Density and Lambda-Rho.
Density is the best discriminator parameter between
sands and shales.

April 2014 285
Simultaneous Inversion of P-wave data
Integration of horizon interpretation
and petrophysical analysis.
Wavelets extracted from multiple
angle stacks using the well ties: 4
angles from 5 to 50 degrees.
42 wells used to build initial
impedance model for Ip, Is and
density used as the background
model.
PP
Angle Gathers
Multi-well/angle
Dependent Wavelets
Background Model for
Ip, Is, Density
Invert for
Ip, Is, Density, Vp/Vs
Transform for
Vp, Vs,  and 

April 2014 286
Final PP migrated stack, Vclay log inserted

April 2014 287
Final PSTM gathers

April 2014 288
Super Gathers and Filter

April 2014 290
Typical PP well tie and wavelet

April 2014 291
Simultaneous Prestack Inversion
P-Impedance

April 2014 292
S-Impedance

April 2014 293
Density

April 2014 294
Lambda-Rho

April 2014 295
Simultaneous Inversion
Resulting inversion volumes: Vp, Vs, Density,
Vp/Vs, Lambda-Rho and Mu-Rho.
Inversion and reflectivity volumes were used to
estimate Vclay via probabilistic neural network
(PNN) analysis using EMERGE.

April 2014 296
EMERGE: PNN Error Analysis
Validation Error - All Wells Average Error – All Wells
Total correlation (Vclay from seismic/logs) = 0.88
Cross validation correlation = 0.79

April 2014 297
EMERGE: PNN Correlations

April 2014 298
EMERGE: PNN for Vclay Correlations
Probabilistic Neural Network (PNN) using seismic inversion:
Total correlation = 0.88
Cross validation correlation of PNN = 0.79
Ordered attribute list to train the PNN:
Density**2
LambdaRho
1/Ip
(Vp/Vs)**2
Post-stack
2nd Derivative

April 2014 299
Vclay volume illustrating channel system

April 2014 300
Vclay volume illustrating channel system
Reflectivity Volume of Clay

April 2014 301
Vclay cross section (sands in red)

April 2014 302
Conclusions
EMERGE is a powerful tool for predicting log properties from seismic
attributes.
While EMERGE has been used for a number of years, recent new success has
come from using pre-stack and simultaneous inversion results as attributes.
This case study has shown the successful prediction of a Vclay volume from
simultaneous inversion results.

EMERGE
….
PNN for Classification

April 2014 304
Next, we will show
how to use PNN for
classification. On
the right, we see two
different classes, A
and B (e.g. sand and
shale), each defined
by three points. We
want to classify
point p0 into one of
the two classes.
Note that we are not
trying to predict the
values on the log, as
in mapping.
Log Seismic Attributes
X Y
x1
x2
x3
x0
y1
y2 y3
y0
x4
x5 x6
y4
y5
y6
Class A
Class B
PNN for Classification
p1
p2
p3
p4
p5
p6

April 2014 305
On the right the
points have been
plotted in attribute
space and the
“distances” between
point p0 and all the
other points are
shown, where
Notice that point p0 is
“closer” to Class A
than it is to Class B.
X
Y
p1
p2
p3
d1
p0
d2
d3
p6
p4
p5
d4
d5
d6
Class A
Class B
( ) ( )2
0
2
0 y
y
x
x
d i
i
i 




April 2014 306
2
2
6
2
2
5
2
2
4
2
2
3
2
2
2
2
2
1
)
(
and
,
)
( 0
0






d
d
d
B
d
d
d
A e
e
e
p
g
e
e
e
p
g












This leads us to the famous Bayes’ Theorem, which allows us to assign a
probability to each class, as follows:
The decision is then simple. If PA > PB, the point p0 is in Class A and if PA <
PB, the point p0 is in Class B.
As with the mapping option, PNN classification does not use distance on its
own, but applies an exponential weighting function to the distance (called the
Parzen Estimator). For the two classes, we can write:
0 0
0 0 0 0
( ) ( )
, and
( ) ( ) ( ) ( )
A B
A B
A B A B
g p g p
P P
g p g p g p g p
 
 

April 2014 307
Classification can sometimes be useful even for numerical data, by
blocking the data and reducing the range of possible output values:
Mapping Classification

April 2014 308
Mapping is the process of predicting numbers. This is the default option in
EMERGE.
Classification means to predict classes or types of data. If this option is
chosen, parameters must be supplied which tell EMERGE how the target
data is to be classified:
If the target logs have been classified previously, they must still be read
into EMERGE as numerical values, where the numbers represent the
classes.
These are the button items which control the use of Classification:

April 2014 309
For a network trained in classification mode, the option exists to calculate
and output the probability associated with each class. This option appears
when the trained network is applied to the seismic volume:

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