Use of Matlab for Analysis and Plotting of

Accoustic Well Data

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Introduction

MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation

MATLAB is an interactive, matrix based system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non interactive language such as C or Fortran

However, the speed when running a Matlab script or function may be described as ”slow as a turtle” compared to Fortran (”fast as a rabbit”)

The name MATLAB stands for MATrix LABoratory. Matlab may …

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Introduction

MATLAB may be used directly from the command window, but you should use m-file programming. This is quite similar to Fortran programming but the file is denoted .m rather than .f

There are two types of m-files; scripts and functions, where the first is the simplest and easiest-to-use.

When you invoke a script, MATLAB simply executes the commands found in the file. Scripts can operate on existing data in the workspace, or they can create new data on which to operate. In addition, scripts can produce graphical output using functions like plot.

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Start Matlab

There are two ways you can start Matlab:

1. In Windows from your Start Menu2. In Unix, logged on Petra, simply write matlab in the terminal

window

Creating m-files in:

1. Windows: when you have started matlab, click file-> new-> m-file

2. Unix: use a text editor, emacs is preferred (type emacs file.m)

Running m-files: type the name of the file (without .m; if the filename is test.m, type test) in the matlab command window and hit enter (both Windows and Unix)

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Open and Controlling Data

When you have created an m-file, you should start your script by opening the file from which your data is to be imported

For a file in ASCII format use the following command:

fp = fopen( ’c33.dat’ , ’ r ’)

opens the file c33.dat and labels it fp

For control of your data you should convert it into a matrix

To do so, you should use the command

[w,c] = fscanf(fp,'%e %e %e %e %e %e %e %e',[8, inf])

reads data from fp in e-format (%e) into the matrix w that has 8 columns and unknown number of rows (8, inf)

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Operators

Arithmethic operators in matlab are the familiar expressions:

+ - / * ^

Note: If you want to perform an element by element operation of two or more matrices, instead of / * ^, use ./ .* .^

If you want to extract the first column from a matrix x and store it as the variable v, use the following command:

z = x(1,:)

If you want to make a new vector acimp(i)=vp(i)*rho(i), use:

acimp = vp.*rho

where vp and rho has already been defined

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Handling Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well as annotating and printing these graphs

Creating a plot:plot(x, y) produces a graph of y vs x

Multiple graphs in one figure:plot(x1, y1, x2, y2, ...)

Typically, you often want to plot several different plots in different windows for easy comparison. To do so use the command:

figure(n) where n is the number of the figureColors and Styles

Subplots

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Colors and Styles

It is possible to specify color, linestyle, and markers, such as plus signs or circles, with:

plot(x,y,'color_style_marker')

Color strings are 'c', 'm', 'y', 'r', 'g', 'b', 'w', and 'k'. These correspond to cyan, magenta, yellow, red, green, blue, white, and black.

Linestyle strings are '-' for solid, '- -' for dashed, ':' for dotted, '-.' for dash-dot, and 'none' for no line.

The most common marker types include '+', 'o', '*', and 'x'.

Plot(x,y,’c:+’) plots a cyan, dotted line and places plus sign markers at each data point

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Subplots

The subplot function allows you to display multiple plots in the same window:

subplot(m,n,p)

breaks the figure window into an m-by-n matrix of small subplots and selects the p’th subplot for the current plot.

Subplots are best illustraded with an example

Example

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In this exercise we will be using accoustic well logs from well C-33 in the Gullfaks field. This well is one of few wells on Gullfaks that has also been logged some distance above the actual reservoir. In addition, shear wave velocities has also been logged.

The file c33.dat (can be downloadedfrom the course homepage), contains the following data:

Column 1: Depth in meters Column 2: P-wave velocity (m/s) Column 3: Density, (g/ccm) Column 4: P-wave velocity for 10% water saturation Column 5: Density, for 10% water saturation Column 6 :P-wave velocity for 80% water saturation Column 7 :Density, for 80% water saturation Column 8 :S-wave velocity (m/s)

Next

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1. Use MATLAB to read all data from c33.dat to a matrice with 8 columns. Plot Vp , Vs and as a function of depth. Plot the three curves below each other.

2. Use MATLAB to compute accoustic impedance (Vp* ) and shear wave accoustic impedance (Vs* ), and plot the two impedances either in the same plot or in to equal plots right below each other. This way, a comparison between the two curves can easily be made.

3. Compute the Vp/Vs ratio. Comment the deflections around top Kritt (ca 1675 m) and top Brent (1835 m). Also compute the difference in p-wave velocity between 10% and 80% water saturation as a function of depth.

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4. In seismic AVO-analysis and inversion it is common to use Elastic Impedance. Elastic Impedance (EI) is defined as

where

Compute Elastic Impedance as a function of depth and make a plot where you plot both accoustic impedance and elastic impedance (vs depth). Assume that is 30 degrees. Comment the difference between the two curves, again particularly around top Kritt and top Brent

)sin1()sin8()tan1( 222 KKsp VVEI

2

2

p

s

V

VK

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The whole exercise in a printable format here

Web sites:

http://www.stud.ntnu.no/info/programmer/matte/matlab/matlab-info.html

http://www.ntnu.no/itea.info/programvare/matlabdoc/rel11doc/techdoc/basics/getstarted.html

Short list of MATLAB Commands

Use of Matlab for Analysis and Plotting

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If you simply type a statement and press Return or Enter, MATLAB automatically displays the results on screen. However, if you end the line with a semicolon, MATLAB performs the computation but does not display any output. This is particularly useful when you generate large matrices. For example

A = magic(100);

As long as you do not want a computation to be shown on the screen, you should always include a semicolon at the end of each line

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This section includes a quiz on the topics covered by this module.

The quiz is meant as a control to see if you have learned some of the most important features

Hit object to start quiz (Depending on your connection, this may take a few seconds...)

Quiz

Shockwave Flash Object

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General information

Title: Use of Matlab for Analysis and Plotting of Accoustic Well Data

Teacher(s): Professor Jon Kleppe

Assistant(s): Per Jørgen Dahl Svendsen

Abstract: Provide a good background for solving problems within petroleum related topics using numerical methods

4 keywords: Matlab, Seismic Data, Visualization

Topic discipline:

Level: 2

Prerequisites: None

Learning goals: Develop problem solution skills using computers and numerical methods

Size in megabytes: 0.7 MB

Software requirements: MS Power Point 2002 or later, Flash Player 6.0

Estimated time to complete:

Copyright information: The author has copyright to the module and use of the content must be in agreement with the responsible author or in agreement with http://www.learningjournals.net.

About the author

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FAQ

No questions have been posted yet. However, when questions are asked they will be posted here.

Remember, if something is unclear to you, it is a good chance that there are more people that have the same question

For more general questions and definitions try these

Dataleksikon

Webopedia

Schlumberger Oilfield Glossary

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References

”Getting started with Matlab”

http://www.ntnu.no/itea.info/programvare/matlabdoc/rel11doc/techdoc/basics/getstarted.html

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Summary

Subsequent to this module you should...

be familiar with Matlab and how to use it to visualize computed data

know how to use scripts in Matlab

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Example

See the plots this matlab script would

produce:

Figure 1

Figure 2

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