lab3 fortran eserc

Due Date: Monday, October 22, 2012TA: Mandy Wong ([email protected])

Lab 3: Normal move-out, multiples and velocity

analysis (Fortran version)

John D. Rockefeller 1

ABSTRACT

This lab is based on material from Chapters 3 and 4 of BEI. In the first portionyou will be asked to compute Vnmo using a (x2, t2) plot based on (x, t) pairs you’llpick from a cmp gather. In the second portion of the lab you will be given avelocity scan of the same cmp gather and asked to reselect the velocity function.In the final portion you will be given a multiple-contaminated CMP gather, andasked to correct it based on both the primary and multiple trend of the data.

Once again, this lab is available online. For this Lab you’llhave to log onto sad from vostok. First download the sourcecode for this lab, lab3 fortran.tar from the BEI class webpage(http://sep/doku.php?id=sep:courses:gp210 labs), and save it in theappropriate directory. Then type tar -xvf lab3 fortran.tar to create yourLab3 fortran directory.After you have begun this lab, do not type make clean or you will have to startall over. Once you have printed your final paper, you can clean the directory.

PART 1: NORMAL MOVEOUT

Introduction

Chapter 3 of Jon’s book Basic Earth Imaging (BEI) discusses the concept of normalmoveout (NMO) velocity. It is closely related to the “RMS velocity” and so-called “stacking velocity”. The basic notion is that, in a horizontally layered earth,

1e-mail: [email protected]

BEI - Lab 3 2 NMO and VA

reflection travel-times from the flat layers approximately satisfy a hyperbolic move-out trajectory:

t2 ≈ τ 2 +4h2

V 2(τ),

where t is the two-way hyperbolic reflection travel-time, τ is the two-way verticaltravel-time to the reflector, h is half of the source/receiver offset, and V is the NMOvelocity.

Exercise

You’ll be looking for the velocity that best describes the hyperbolic traveltime. Vnmo

is the short spread hyperbola approximation for the velocity. Vrms is an approxi-mation that uses all the offset information.

In this section, you are given a CMP gather from which you must determineVrms for reflections with t0 at 1s, 2s, and 3s. The water bottom reflection has t0around 0.25s. Use the figure below, or type make cmp.view while logged into sad.To determine Vrms:

• Select some (x, t) pairs for each of the reflections

• Plot these values in (x2, t2)

• Perform a linear regression to obtain the value of Vrms. (Note: The slope ofthe line is the inverse of V 2

rms) .

The velocities you determine are to be compared with the velocities you’ll pick inthe next exercise.

Questions

Now edit paper.tex to answer the questions below.

1. List the rms-velocities you obtained at t0 =1s, 2s, and 3s

Your Answer:


PART 2: VELOCITY ANALYSIS

Introduction

Chapter 4 of Jon’s book Basic Earth Imaging (BEI) discusses the concept of NMOvelocity analysis. This is a method to estimate the “rms” by finding the “NMOstacking velocity” which optimizes the CMP stack in some sense.

As with the first part of the lab, the basic notion is that, in a horizontally layeredearth, reflection travel-times from the flat layers approximately satisfy a hyperbolicmove-out trajectory.

In the first exercise you obtained the RMS -velocities in an “old-fashioned way”.Now you’ll do the same thing but with the help of velocity “scans”. The velocityscans in this lab display semblance, which is the normalized output-to-input energyratio.

This lab uses a brand-new viewer developed by Bob Clapp. You will be interactingwith icube to select velocity functions and perform NMO.

Type make vrms1.H to bring up your first icube display. There are three panelsdisplayed. The left panel is the original CMP gather that you will be NMO correcting.The center panel is the CMP gather NMO corrected interactively according to thevelocity function you pick.

The right panel is where you will be picking your velocity function. It has time(increasing downwards) as its vertical axis and velocity (increasing to the right) asits horizontal axis.

To pick a point in the velocity panel (right panel), press ctrl-p to activate thepicking mode. The left mouse button adds picks, the middle mouse button deletepicks and the right mouse button moves picks. An o will appear at the point youpicked. If you don’t see the o click on Picks tab on the left panel, then click on colortab and change the lineptgroup from line to point.

As you pick, you’ll see two lines (or groups of points): one red and the other oneis blue. They correspond to the NMO velocity and the interval velocity computedusing Dix formula. (which is which ?).

Remember to pick velocities for the reflections with t0 at 1s, 2s, and 3s to comparewith the values you obtained in Part I.

The line representing your interval velocity will probably extend beyond theboundaries of the right panel. This is expected behavior and will be considered a“right” answer, but you can minimize it with careful picking.

When you are happy with your NMO corrections, save your work by clicking thesave button in the picks tab. Then you can quit icube by pull-down menu underMain.


The program vrms1.x reads the ascii file, output from icube, and transforms yourpicked velocity into an SEP data file. You’ll be asked to input the filename of thevelocity picks.

Questions

For some of the questions below you have to write equations. Either use LATEXtoformat them (recommended - you need to learn how!), or use the \vspace{3in} togive yourself 3 inches more space, and write them in by hand.

1. How does a reflection event change in the NMO corrected gather when thechosen velocity was too high/too low?

Your Answer:

2. While making your picks, pay attention to the interval velocity curve. Dra-matic changes in interval velocity are unreasonable considering seismic reflectionmethodology. Why?

Your Answer:

3. If you look at the NMO corrected gather, you notice that the wavelet broadenswith the increase of offset for the top events. If you look at lowest event, thewavelet doesn’t change too much. Why?

Your Answer:

4. Compare and contrast your experience in determining the velocities by selectingx, t pairs as in Part I versus picking a good stacking velocity curve with the aidof a velocity scan (this portion).

Your Answer:

5. RMS vs interval velocity


(a) How accurate do you think your estimates of RMS velocity are (in km/s) ?

Your Answer:

(b) How about your estimates of interval velocity ?

Your Answer:

In your makefile, read and understand the makerule for vrms1.H. The programvrms1.x convert the velocities you obtained in Part I into SEP format. TheNMO command applies NMO to cmp.H with this velocity. Plot your result andcomment on the differences between the NMOed gather from Part I and PartII. (Note: remember to include a (t, v) pair for the water bottom velocity) .To plot your velocity functions and the NMOed gather you’ll need to edit yourMakefile and add figures to your paper .tex .

Your Answer:

6. Assume you want to fit a parametric NMO velocity function to your scan of theform:

V (τ) ≈ V0 + ατβ .

For your velocity scan, what are the approximate values of V0, α and β? Youcan do explicit curve fitting using your favorite method/software if you want,but you are not required to (if you do, Matlab can be quite useful).

Your Answer:

Use the Dix relationship to convert the parametric V (τ) expression above intoa parametric interval velocity function vi. Check your general result by consid-ering the special case of constant velocity. There are two choices of α and βyou can make – do both. Show all derivations in full and with clarity.

Dix Equation:

v2i =

τiV2i − τi−1V

2i−1

τi − τi−1

where vi is the interval velocity of layer i, tau is the time in each layer, and Vis the rms velocity.

Your Answer:


7. You may have noticed some artifacts in the velocity scanning process. These arecaused by CMP data truncation at (a) near offsets and (b) far offsets. Considera CMP gather which contains only an impulse at (a) zero offset, and (b) thefarthest offset. Write down a mathematical expression for the trajectory eachimpulse will make in velocity space. Use the hyperbolic travel-time equation.Make a sketch of the artifact trajectory for each case in velocity space. Be clear.

Your Answer:

PART 3: MULTIPLE INFESTED DATA

Exercise

Now type make vrms2.H for a new CMP gather and its semblance panel. This gatheris heavily infested with multiples.

Select a velocity function that flattens the primary reflections and save the result.You will find this a much more difficult task, the CMP gather is infested with multipleswhile the semblance scan energy is concentrated at the multiple energy velocity. Quiticube after saving your velocity picks. Again, these picks will be transformed intoan SEP file.

Now type make vrms3.H for a display of the same CMP gather and semblancepanel. This time select the multiple train so that the multiples are flattened in theNMO corrected gather. Quit icube after saving your velocity picks. Again, thesepicks will be transformed into an SEP file.

This portion of the lab demonstrates a large problem in seismic imaging, namelythe existence and strength of multiples. Often, as in this example, the strength ofthe multiples is so much greater than that of the primaries that primary energy isoverwhelmed. This makes picking a suitable velocity function, difficult, and severelyhinders any automated picking approach.

Questions

1. How could either

• the prominence of the multiple energy be decreased, or

• a criteria be designed that would pick the primaries rather than the mul-tiples?

Your Answer:


Don’t forget

• that multiples are not limited to the sea floor bottom

• rms velocity can decrease as a function of time

Extra credit

Read sections 3.1 to 3.3 of Yilmaz’s book and answer questions 3.4 and 3.15 [1987edition] or questions 3.3 and 3.8 [2001 edition] at the end of chapter 3 (see me if youneed to borrow the book).

Your Answer:

Extra (no credit): With a green pen mark all spelling and grammar error’s inthis Lab. Also comment on confusing statements in the Lab or other broken andoutdated features/questions.

HAND IN

When you are all done, type scons paper.pdf at a shell prompt to rebuild a postscriptversion of this lab, or make paper.pdf for a PDF version. Print out a copy of yourhomework and hand it in to your TA’s office or email it to the TA.

lab3 fortran eserc

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