Developing Synthetic Logs Using Artificial Neural Network: Application to Knox County in Kentucky Fedra Ghavami Problem Report submitted to the College of Engineering and Mineral Resources at West Virginia University in partial fulfillment of the requirements for the degree of Master of Science in Petroleum & Natural Gas Engineering Committee: Professor Samuel Ameri, Chair Dr. Khashayar Aminian Dr. Razi Gaskari Department of Petroleum and Natural Gas Engineering Morgantown, West Virginia 2011 Keywords: Reservoir; Well Logs; West Virginia; Artificial Neural Network
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Developing Synthetic Logs Using Artificial Neural Network:
Application to Knox County in Kentucky
Fedra Ghavami
Problem Report submitted to the
College of Engineering and Mineral Resources
at West Virginia University
in partial fulfillment of the requirements
for the degree of
Master of Science
in
Petroleum & Natural Gas Engineering
Committee:
Professor Samuel Ameri, Chair
Dr. Khashayar Aminian
Dr. Razi Gaskari
Department of Petroleum and Natural Gas Engineering
Morgantown, West Virginia
2011
Keywords: Reservoir; Well Logs; West Virginia; Artificial Neural Network
ABSTRACT
Developing Synthetic Logs Using Artificial Neural Network: Application to Knox County in Kentucky
Fedra Ghavami
The purpose of this study was to examine missing data from oil production logs as well as
predict oil reservoir production levels. Historically, data logs contain gaps or missing data
points due to limitations of the tools and methodologies that are used to collect the data. To help
predict and examine the gaps with no data points, Back Propagation was used to extrapolate both
existing and non-existing data.
Stemming from the research that was performed using the Back Propagation method, missing
data was identified. To validate and confirm the accuracy of the data, the extrapolated data was
compared against actual data logs from core samples.
A methodology to generate synthetic wireline logs is presented. Synthetic logs can help to
analyze the oil reservoir properties in areas where the set of logs that are necessary, are absent or
incomplete. The approach presented involves the use of Artificial Neural Networks, as the main
tool, in conjunction with data obtained from conventional wireline logs. Implementation of this
approach aims to reduce operation costs to companies.
There is a synthetic methodology to generate wireline logs. In some cases, we need to have
absent or incomplete logs. Synthetic logs will help to analyze the reservoir properties in this
manner. Artificial Neural Networks have been implemented as the main model to predict
wireline logs. Implementation of this technique will reduce the operation costs for oil and gas
companies.
Development of the neural network model was completed using a back propagation and five oil
wells. Data collected from the five wells was collected using the following logs:
1. Gamma ray,
2. Density,
3. Neutron,
4. Caliper logs.
Synthetic logs were generated through two different exercises. Exercise one involved four wells
for development and training of the network. Exercise two included four wells in series and one
well out.
Developing of the artificial neural networks model is implemented using a Backprpagation of
Artificial Neural Network and five wells that included gamma ray, neutron, density, and
resistivity logs. Synthetic logs are generated through two experiments. Experiment one has
involved five wells for training and development of the network.
Verification was used for each well to train the network. The second experiment involved four
wells for the development and training of the network. A fifth well that was not applied during
calibration and training was selected for verification. Four mixtures of inputs/outputs are
selected to train the network. Mixture “A” consists of the neutron log which contains the output
as well as density, gamma ray, and density caliper logs, which comprises the input.
In conclusion, it is demonstrated that the quality of data has an important role in the
implementation of the neural network model. It is really important to do a careful quality control
of the data before building a neural network model. It is concluded conversely; that the neural
network modeling doesn’t affect the performance of having lithologic heterogeneities in the
reservoir in generation of synthetic logs.
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Acknowledgments
First I thank god for giving me the capability and the courage to finish my thesis and complete
my MS in Petroleum and Natural Gas Engineering.
I would like to dedicate this thesis to my parents, who always gave me their support and
encouragement, and most importantly, their love. It kept me going during some of the difficult
moments of this work. I appreciate you and I love you.
I don’t have the words to express my thanks and appreciation to Professor Sam Ameri, chair of
my committee, who brought me to the Petroleum and Natural Gas Engineering Department and
encouraged me to complete my master’s degree. I wouldn’t be able accomplish this without his
support and advice, not only during this work but also throughout the time I spent at the
department.
I want to extend my sincere appreciation and gratitude to my research advisor Dr. Razi Gaskari,
for introducing me to the fascinating area of Natural Networks, for his friendship, and for his
continuous guidance, encouragement, support and patience throughout this work.
Special thanks to Dr. Khashayar Aminian for being on my committee and for the enriching
contributions and comments to this work.
Finally, my deepest gratitude to Mrs. Beverly Matheny for her assistance and enthusiasm during
4.2. Data Preparation ............................................................................................................................... 41
Figure 2.1.1. Cambrian and Deeper Tests of Kentucky, 1999. ..................................................................... 2 Figure 2.1.2. has shown the location of the Kentucky River and Irvine-Paint Creek Fault Systems. .......... 3 Figure 2.1.3. the Knox Group is composed of a thick sequence of dolomite of Cambrian and Ordovician age that underlies the entire state of Kentucky. ............................................................................................ 5 Figure 2.1.4. stratigraphic correlation chart for Cambrian rocks in the Rome Trough study area. Modified from Harris and Baranoski (1996). ............................................................................................................... 7 Figure 2.1.5. stratigraphic model for Conasauga Group in the outcrop belt in eastern Tennessee. .............. 8 Middle Cambrian paleogeography ................................................................................................................ 8 Figure 2.1.6. Middle Cambrian Paleogeography. ......................................................................................... 9 Figure 2.2.1. Gamma ray and sonic logs from the Alberta basin, and their response ................................. 11 to different lithologies (adopted from Cant, 1992). .................................................................................... 11 Figure 2.2.2. Gamma ray emission spectra of K-40, uranium, and thorium series ..................................... 12 (adopted from Bassiouni, 1994). ................................................................................................................. 12 Figure 2.3.1. biological neuron. .................................................................................................................. 17 Figure 2.3.2. A very simple neural network. .............................................................................................. 19 Figure 2.3.3. A single-layer neural net. ....................................................................................................... 20 Figure 3.2.10. identify function. ................................................................................................................. 24 Figure 3.2.11. Binary step function............................................................................................................. 24 Figure 3.2.12. Binary sigmoid, range (0-1) ................................................................................................. 25 Figure 3.2.13. Bipolar Sigmoid. .................................................................................................................. 26 Figure 3.2.14. Backpropagation neural network with one hidden layer. .................................................... 30 Figure 4.2.2. Density-Porosity log for five verified wells. ......................................................................... 44 Figure 4.2.3. Caliper log for five verified wells. ......................................................................................... 45 Figure 4.2.4. Neutron log for five verified wells. ....................................................................................... 46 Figure 4.2.6. Logs of Patterson well. .......................................................................................................... 48 Figure 4.2.7. Logs of Gibson well. ............................................................................................................. 49 Figure 4.2.8. Logs of Partin well. ............................................................................................................... 50 Figure 4.2.9. Logs of Gambrie well. ........................................................................................................... 51 Figure 4.2.10. illustrates distribution of wells used for training /testing and Production dataset through exercise 1. ................................................................................................................................................... 52 Figure 4.2.11. illustrates distribution of wells used for training /testing and Production dataset through exercise 2. ................................................................................................................................................... 53 Figure 5.1.1. result of R-squared for five wells in function of neutron vs. depth. ...................................... 55 Figure 5.1.2. Training R-Square in the application graph........................................................................... 56 Figure 5.1.3. Calibration R-Square in the application graph. ..................................................................... 56 Figure 5.1.4. Verification R-Square in the application graph. .................................................................... 57 Figure 5.2.1. actual and virtual results comparison in Well Hilton. ........................................................... 58 Figure 5.2.2. actual and virtual results comparison in Well Patterson. ....................................................... 59 Figure 5.2.3. actual and virtual results comparison in Well Partin. ............................................................ 61
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Figure 5.2.4. actual and virtual results comparison in Well Gibson. .......................................................... 62 Figure 5.2.5. actual and virtual results comparison in Well Gambrie. ........................................................ 63
LIST OF TABLES
Table 2.2.1. The values of matrix density for the type of different rocks… ................................................................ 13
Table 4.2.1. Segment of the matrix prepared for well HELTON ................................................................................ 42
Table 5.2.1. Results of R-Squered for training, calibration, and verification of the five wells.................................... 57
1
INTRODUCTION
Prediction of hydrocarbon production from geological formations using computer modeling
techniques has become very popular and widely accepted in the petroleum industry. There is an
analysis tool, known as artificial neural networks (ANNs), which imitates the thought process of
the human brain. Neural networks can be a useful tool to predict oil, gas or water in formations
using data from well logs and core samples. Traditional models have been used for many years
to make predictions from well logs, which are measurements of formation properties as a
function of depth. Well logging is performed with devices lowered into a well to measure
properties of the formations via electrical, nuclear or acoustic methods. Well logging is primarily
used after drilling a well or during the drilling of a well to determine the production potential in
hydrocarbon reservoirs. This data may be used to determine the feasibility of drilling additional
wells in the area, to select the final depth of the well being drilled, etc.
Moreover, the application of neural network in the oil and gas industry has increased rapidly in
recent years. Neural network results can be interpreted in terms of models that can be compared
with real or statistical data in well logs.
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BACKGROUND
1.1. Geological Setting
1.1.1. Description of Knox county in Kentucky
The Rome Trough is a basement structural feature filled with Precambrian and Paleozoic
sequences. The mostly dolomitic carbonate sequence that spans the Lower Ordovician and Upper
Cambrian periods in Kentucky is the Knox Group. The Lower Ordovician Beekmantown
Dolomite is the upper part of the Knox Group and the Upper Cambrian Copper Ridge Dolomite
is the lower part of the Knox Group. (Figures 2.1.1, and Figures 2.1.2)
Figure 2.1.1. Cambrian and Deeper Tests of Kentucky, 1999.
3
Due to a pre-Conasauga unconformity the upper Rome carbonate and lower Conasauga units
are absent on the shelf between these faults. Deeper in the trough, a full Rome section is
present. The upper Rome carbonate grades laterally into shale in an interpreted intrashelf
basin in south-central Kentucky (SW).
Figure 2.1.2. has shown the location of the Kentucky River and Irvine-Paint Creek Fault Systems.
Exploration Recommendations
Several recommendations for continued exploration in the Rome Trough area can be made based
on the results of this work.
4
Reservoir Trends
The percentage of sandstones commonly is showing 6-10% porosity in the Rome Formation and
Maryville Limestone of the Conasauga Group. In the high sandstone percentage areas there is a
risk that porosity development does not appear. In this study has shown the sandstone percentage
in the maps that two areas have the best probability for encountering porous sandstones. The
highest sandstone percentages has mapped in the structural shelf between the Kentucky River
Fault System and the Irvine-Paint Creek Fault System for the Rome Formation. Sandstones
increase toward the north against the Kentucky River Fault. This trend is prospective but it
narrows east of the Isonville Fault, into Carter and Boyd Counties.
A north-south sandstone trend has been mapped from the Rome Trough north into Ohio in the
Maryville interval. In the Homer Field in the Homer Field and also the sandstones are porous. An
area in the center part of the Irvine-Paint Creek shelf contains the highest percentage of
sandstone in both Rome and Maryville. The increase chances of multiple layers of good
sandstone quality in the area.
In this study the stratigraphic framework of the Rome Trough has refined greatly. Moreover, it
has been identifying areas with low sandstone potential which are deeper intrashelf basins,
deeper parts of the trough, and also high sandstone potential.
Due to neither porous carbonates nor dolomitized zones were observed, then Cambrian
carbonates are assumed to have a low potential for the reservoir development. Although,
dolomites; Hydrothermal similar to those in Ordovician carbonates have not been observed in
this study. Fractured carbonates are considered high risk but could have potential for reservoir
development, also Fractured Nolichucky is considered high risk shales produce in a well in
Johnson County, Ky. in this type of reservoir. This reservoir is the most attractive reservoir target
5
in the Trough because of abundance of porous sandstones at reasonable drilling depths on the
Irvine-Paint Creek shelf.
Figure 2.1.3. the Knox Group is composed of a thick sequence of dolomite of Cambrian and Ordovician age that underlies the entire state of Kentucky.
Regional Stratigraphy and Depositional History
There is a modification of the stratigraphic correlation chart by Harris and Baranoski (1996) for
the central Appalachian Basin as shown in Figure 2.1.4. There are some Key changes to this
interpretation follow:
1. In the outcrop belt in eastern Tennessee are correlated into eastern Kentucky and they
been defined by the Conasauga Group and its member formations. Rome in Kentucky
was the name of Conasauga that has been interpreted Much of the interval now.
6
2. The Rome Formation is restricted to the Rome Trough and south of the Kentucky River
Fault Zone, and does not extend north in Kentucky.
3. Pumpkin Valley Shale, Rutledge Limestone, and Rogersville Shale are confined to the
deeper parts of the Rome Trough in eastern Kentucky as the oldest 3 formations in the
Conasauga Group. The Maryville Limestone unconformably overlies the Rome
Formation in the place that those three units are absent on the shallower Irvine-Paint
Creek shelf, where. The Maryville Limestone unconformably is named the pre-
Conasauga unconformity.
4. Figure 2.1.4 retains the Mt. Simon Sandstone that is the time-equivalent to the lower
Maryville Limestone to the east and south.The original position of the Middle-Upper
Cambrian boundary from Harris and Baranoski (1996) has shown in Figure 2.1.4. This
boundary may be revised upward to the top of the Maryville Limestone in Ohio and
Kentucky.
7
Figure 2.1.4. stratigraphic correlation chart for Cambrian rocks in the Rome Trough study area. Modified from Harris and Baranoski (1996).
8
There are three major transgressive/regressive cycles that are present, composed of an upper
carbonate formation and lower shale formation. The minor cycle including the Craig Limestone
has not been observed in the Rome Trough area is shown in Figure 2.1.5. (Rankey, 1994).
Figure 2.1.5. stratigraphic model for Conasauga Group in the outcrop belt in eastern Tennessee.
Middle Cambrian paleogeography has shown in Figure 2.1.5 is paleogeography in northeast
Tennessee and southwestern Virginia. A Conasauga carbonate platform existed in Middle
Cambrian, described by cyclic progradation to cratonward into Kentucky. As shown here, the
location of the intrashelf basin has been reinterpreted to the west, in south-central Kentucky and
the cycles of shale-carbonate have been correlated into the Rome Trough.
9
Figure 2.1.6. Middle Cambrian Paleogeography.
2.2. Well logs fundamentals
2.2.1. Gamma Ray
By penetrating the wellbore and sending the natural gamma-ray, emission of the various layers
will be measured using a gamma-ray log. The radiogenic isotopes of potassium, uranium and
thorium will be related to its property. As shown in Figure 2.2.1.
Some tools might perceive gamma ray energies of less than 0.5 to more than 2.5 millivolts.
Figure 2.2.2 also shows the distinctive emission spectra for thorium, uranium, and potassium.
Thorium, uranium, and especially potassium are common in clay evaporates and some minerals.
The successions of terrigenous clastic in the log demonstrate the “shaliness” which is interpreted
as having high radioactivities on the API scale of the rock, averaged over an interval of depth.
This is also known as “cleanness” which illustrates a lack of clays in the formation (Figures 2.2.1
10
and 2.2.3). This characteristic effect on gamma-ray log patterns mimic vertical carbonate-content
or sand-content trends.
It should be emphasized that the gamma-ray reading is the proportion of radioactive elements not
a function of grain size or carbonate content. These readings could also be related to the
proportion of shale content as well. As an example, lime mudstone gives the same response as
grainstone, and also clay free sandstones or conglomerates that are mixed with sand and pebble-
clast sizes on average give similar responses.
There is a relationship between the concentrations of radioactive elements and increasing
compact in shale. Gamma Rays radiates through the Gamma Ray (GR) tool into sedimentary
formations to the penetration of wellbore. Compton-scattering collisions with formation atoms
occur when these gamma rays pass through a formation (Cant, 1992).
Compton-scattering collisions cause the aforementioned gamma rays to subsequently lose energy
(Bassiouni, 1994). These atoms absorb gamma rays energy through the photoelectric effect in
the formation. The function of the formation density is related to the amount of absorption.
Moreover, on the GR log the radioactivity level shown can be different for two formations that
have the different densities with the same amount of radioactive material per unit volume. The
accumulation of radioactive material will typically appear in lower density formations. With the
casing borehole, the application of GR Log is necessary for the tool to run to completion and in
work-over operations. In some cases, for example the SP resolution is poor in either cased holes
or open holes. In such situations the GR log can be run as a substitute for the SP log. In this case
the GR allows for an accurate positioning of perforating guns while run with casing collar
locator logs. Gamma Ray logs are useful for the locating of source beds and for the interpretation
of depositional environment (Ameri, 2009).
11
Figure 2.2.1. Gamma ray and sonic logs from the Alberta basin, and their response to different lithologies (adopted from Cant, 1992).
12
Figure 2.2.2. Gamma ray emission spectra of K-40, uranium, and thorium series (adopted from Bassiouni, 1994).
2.2.2. Caliper log
Caliper log uses as the set of measurements of the shape and the size of a wellbore that made
during the drilling oil or gas wells. Also, it measures the diameter deviation in bore hole. It is
built with two articulated arms that measure the borehole as far as it pushes against the bore hole.
The arms register the movements by creating electrical variation, and measuring electrical
resistance. The deviation is translated by changing the diameter as an output after calibration. In
the function of depth the caliper log is known as a continuous value of borehole diameter.
2.2.3. Density-Porosity logs
The formation density log measures the electron density of a formation. It also acts as a porosity
log which measures the porosity of the formation as well. It may assist the geologist to detect
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gas-bearing zones, determine hydrocarbon density, and evaluate shale sand reservoirs and
complex lithologies.
The gradiomanometer or a nuclear fluid densimeter is a density logging device. It is a contact
tool that consists of a medium-energy gamma ray source. This tool emits gamma rays into a
formation that will be scattered back to the detector to the electron density of the rock. The
electron density is related to the density of the solid material. The amount of density is
determined either by the percentage of pore fluids, or holdup which is the record of the fractions
of different fluids at different depths in the wellbore for the different fluids.
Formation bulk density (ρb) is a function of porosity, density of the fluid in the pores such as salt,
mud, hydrocarbons, or fresh mud, and also matrix density. To determine porosity, the density of
the fluid in the wellbore and/or density of the matrix (ρ ma) should be known.
Table 2.2.1 demonstrates the common value of ρ ma.
Rock Type Matrix density (g/cm3)
Sand or Sandstone 2.65
Limestone 2.71
Dolomite 2.87
Anhydrite 2.98
Table 2.2.1. The values of matrix density for the type of different rocks
Depending on temperature, pressure and salinity, density of formation water ranges various from
0.95 g/cc to 1.10 g/cc. Density of oil varies over an equally wide range and also is lower than
these values. According to Bassiouni (1994), the tool in the investigation ratio is shallow.
Moreover, this investigates in the invaded zone, ρ f is expressed by:
14
ρ f = S xo ρmf + (1 − S )ρ
Where Sxo is the mud filtrate saturation in the invaded, ρ mf is the mud-filtrate density, zone,
and ρh is the invaded zone hydrocarbon density.
2.2.4. Neutron Log
The neutron exhibits a high penetrating potential. This penetration power property is, due to the
neutron’s lack of an electric charge that plays an important role in well logging applications.
Moreover, hydrogen is responsible for measuring the concentration of epithermal neutrons that
indicates the concentration of hydrogen in the material and it also responsible for water-bearing
formations. The concentration of hydrogen reflects the lithology and porosity in shale-free,
water-bearing formations.
The neutron log measures the hydrogen index or hydrogen concentration in the rock. The tool
emits neutrons that will measure the energy of neutrons reflected from the rock. As a result, the
hydrogen concentration might be delineated due to the fact that energy is lost easily to particles
of similar mass.
2.3. Artificial neural network
An artificial neural network is a chain of information in a system that executes the data similarly
to mathematical models of human neural biology. In human cognition some performances occur
which use an artificial neural network as well.
• Neurons are the simplest elements for processing information.
• There are connections between neurons that pass signals.
• Every connection link has an allocated weight which transmits the signal.
15
• Every neuron has a function which is nonlinear to determine an output with input and
summation of weighted input signals
2.3.1. Characterization of Neural Network
A neural network has an arrangement of the connections between the neurons which is called
“Architecture”.
Training or learning algorithm is the method which determines the weight on the connections.
There is an activation function for neural network.
For recognition of artificial neural networks with other systems, information processing provides
an answer of “how” and “when”.
Each neuron is directly connected to another one. It means there is a communication link which
includes the weight. A neural consists of some elements for simple processing which are called
nodes or cells, units, and neurons. In each neural network cycle, weights participate to solve the
problem by using the information. A wide array of problems can be affected on neural networks.
Activation or activity level is an internal state for each neuron. Activation is a function of the
inputs it has received. Activation is defined as a signal from a neuron to the other neurons. Each
neuron can send one signal at a time which it can broadcast to one or several neurons.
2.3.2. Biological Neural Network
For some, a primary concern for neural network models is the extent to which they differ from
biological neural systems; for others, these differences are outweighed by the ability of the net to
play a role in performing certain tasks. There is a similarity between the structure of neuron and
element processing. Individual neurons from different species are much more similar than neural
networks within the same system.
16
A neuron is composed of a soma or cell body and two different types of branches. They are the
dendrites and the axon. The nucleus contains the information in the cell body. The information,
such as plasma, contains the tools for producing what is needed by the neuron.
Dendrites act as the receivers to transmit signals generated by the cell body along the axon
(transmitter) which then separates into strands and sub strands.
Synapses are at the ends of the strands. A synapse is a connection between a dendrite of one and
an axon of another. Neurotransmitters are released when the signal arrives at the synapse’s ends.
These chemicals cross the synaptic gap to improve the neuron’s ability to send impulses,
depending on the kind of synapse. The synapses can be trained to be more efficient by
repetition of these signals. This dependence on history acts as a memory, which is possibly
responsible for human memory.
In humans the cerebral cortex is a thin layer covering the surface of each cerebral hemisphere.
This cerebral cortex contains a vast number of neurons which are interconnected.
Neurons exchange information through a series of very short pulses. The communications of
train pulses in neurons are very short; usually the duration time is measured in milliseconds.
Pulse-transmission frequency modulates the message. This frequency is around a million times
slower than the switching speed of electronic circuits. However, humans are more efficient in
regards to complex perceptual decisions. A good example would be face recognition. Face
recognition for humans occurs within a few hundred milliseconds, even though the operational
speed of the neurons is only a few milliseconds (Figure 2.3.1).
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Figure 2.3.1. biological neuron.
There is a series of the processing components in neural networks which work on biological
neurons. They are:
1. All signals have to be received and be processed.
2. After releasing signals from a neuron, the signals could be modified by its weight then
receive information through synapse from the other neuron.
3. The summation weight which is merged with weighted inputs has to be included in the
processing element.
4. When the neuron conveys just one single output it shows that there was a sufficient input
to work appropriately.
5. The axon branches from the other neurons reach the output from a transmitter neuron.
6. Memory is distributed:
• There are two kinds of distribution of information which are called long-term
memory and short-term memory. Long-term memory wells or settles in the
weight or synapse and short-term memory is consistent with the signals when the
transmitter neurons send it.
• Short-term memory is the signals sent by the neurons.
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7. The strength of synapse is not steady, and it could be modified by practical situations.
8. Transmitting on the synapses could be provocative or prohibitive.
There are two types, artificial neural networks that share an ability with biological neural
systems which is called fault tolerance.
1. We can recognize input signals with slight differences from signals we have had before.
As an example, the human ability to distinguish a person from a picture which they have seen
before or distinguish a person after a while.
2. Despite continuing to lose neurons, humans can still learn. In some cases when the neural
is destroyed it can be trained by other neurons to pass over the function of destroyed cells.
Even for uses of artificial neural networks that are not intended primarily to model biological
neural systems, attempts to achieve biological plausibility may lead to improved computational
features.
Attempts to achieve biological plausibility may lead to improved computational features via the
use of artificial neural networks that are not originally intended to model biological neural
systems.
2.3.3. Typical Architectures
Arranging neurons in layers, gives us a good perspective to observe them in a different behavior.
Neurons with the same behaviors usually categorize in the same layer. Key factors are based on
sending and receiving signals; the definition of neurons behavior in their activation function
assembles on connection of weight pattern with sending and receiving signals. For simplicity of
what many neural networks do, is the neurons in the specific layer are either not interconnected
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or totally interconnected. Each hidden layer is the interconnection layer between input neurons
and output neurons.
The net architecture is the pattern of connections between layers and the neurons arrangement
into layers. In neural networks layer, the activation an input layer is equal to an external input
signal for each unit. In Figure 2.3.2 is a shown combination of input unit, one hidden unit, and
one output unit.
Figure 2.3.2. A very simple neural network.
Neural networks are usually categorized as multilayer or single layer. Definition of the number
of layers is based on the slabs of neurons between weighted interconnection links. The input and
output units are not counted as a layer by themselves. Obviously, the weights that exist in a
network contain very important information. Figure 2.3.3 is shown in two layers of weighted.