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Here we compare two different methods for interpreting data from a seismic survey.

The data from a seismic survey appears in the form of time series vectors, representing samples of the received acoustic signals over a fixed period of time. In our simulation example, the samples come every 4 ms (Fs = 250 Hz) and the vectors are 512 samples (2.048 s) in length. There is one time vector for each source/receiver combination, so for our example, we have 32 sources and 128 receivers for a total of 4096 time vectors. Therefore, our raw data will be represented as a 512x4096 matrix which we will load into MATLAB.

At this point, it is necessary to process this matrix and map this data onto a grid so that the shape of the formations we are studying may be determined. The basic technique involving ellipses has been described above, so all the program needs to do is to draw the ellipses, weighted by the magnitude of the time samples, and add the results for each time vector.

We consider now, two possible algorithms for drawing the necessary ellipses. The first method will traverse every pixel on the grid and at each point plot the value of the correct sample from the time vector. The second method will traverse the time vector and for each sample will plot an ellipse of appropriate magnitude.

What do we need to consider when comparing these two methods? First of all, there are 4096 vectors so this problem can become computationally very costly. For each method, we seek to find a standard run-time and evaluate different methods of optimizing this run time. Additionally, we hope to resolve as clear a picture as possible, so we should compare the graphs of the final answers to see which resolution is clearer.

Method 1 – traversing the grid

For every point, we can calculate the total distance required to travel from the source to that point and then to the receiver using the distance formula on the (X,Y) coordinates of the point, the source, and the receiver.

D Y Y S 2 X X S 2 Y Y R 2 X X R 2

We may now divide by velocity to get the time in seconds, and then we may again divide by the sample period to get an index for the time series vector that corresponds to this point.

t i D V T s

Note that this value for time will not be an integer, so we must interpolate using the time series indices above and below it.

t + ceil t i

t - floor t i

A simple linear interpolation method will give us an appropriate value that is weighted based on how close t is to t-minus and t-plus.

Mag TimeSeries t - t + t i TimeSeries t + t i t -

We finish by applying these equations to every point on the grid. This will trace out the ellipse patterns we desire for a given source-receiver pair.

Method 2 – traverse the time vector

Taking one source-receiver pair's time vector, we first find the distance between the source and receiver. This distance is the minimum distance a signal must traverse. Since each sample in a time vector is 4ms, and we know that a wave travels at 1500m/s, the n th sample in a time vector takes n *4ms to travel n *0.004s*1500m/s. If the n th sample distance less than the distance between the source and receiver, it is ignored since it is bad data. Usually these samples have a received signal value of 0 anyway.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Seismic imaging. OpenStax CNX. Dec 16, 2004 Download for free at http://cnx.org/content/col10251/1.1
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