# 0.5 Comparing seismic imaging algorithms

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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.

$D()=\sqrt{(Y()-{Y}_{S}())^{2()}+(X()-{X}_{S}())^{2()}}()+\sqrt{(Y()-{Y}_{R}())^{2()}+(X()-{X}_{R}())^{2()}}()$

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.

${t}_{i}()=\frac{D()}{V(){T}_{s}()}$

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

${t}^{+}()=\mathrm{ceil}({t}_{i})$

${t}^{-}()=\mathrm{floor}({t}_{i})$

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.

$\mathrm{Mag}()=\mathrm{TimeSeries}({t}^{-})({t}^{+}()-{t}_{i}())+\mathrm{TimeSeries}({t}^{+})({t}_{i}()-{t}^{-}())$

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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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