How can you find the depth of refractor by time (t) - distance (x) Plot?
As one of the primary objective of many seismic refraction surveys is to determine the depth of layers (refractor) from the ground surface.
There are many softwares and techniques you can utilize to solve this problem on hand. But as a rule of thumb it is important to have a basic skill and knowledge on how to do things rather than blindly relied on softwares , that is why I hope this tutorial will help you to find the depth of layers from the surface by using simple time-distance (t-x) plot.
However you should not quote me wrong that softwares are useless in geophysics, No? That was not my intention, Softwares have their own vitality in geophysical processing and science in general!
Okay! Let's be together until the end of this tutorial,
We have given the seismic refraction data as shown in figure 1, our task is to achieve the primary objective as stated above by using spreadsheet.
I have choose spreadsheet because this tool is good for giving a basic knowledge and learning environment and most of us, we are familiar with this tool, Also we isolate ourselves from software licence issues so there will be no any need to extend further more our tutorial. Just have a basic skill on Microsoft excel spreadsheet
So this is just a learning curve! You can follow the same way to deal with your real data.
Figure 1: Table showing seismic refraction data
You have to follow these procedures to achieve this objective. However you should have basic knowledge on Ms. Excel in order to do it right, these are just guides.
1. Open the new document in Ms.excel
2. Enter the data given in figure 1, above in your opened Ms. Excel doc
3. Highlight or select the data in your opened Excel doc.
4: Go to the insert tab and select scatter plots you like, you will see the plot as shown in figure 2, pop up on your screen.
5. Label your axes and title. Make sure you stretch it out so that you can see it well on your screen
Figure 2: Time (t) - distance (x) Plot
6. Save the work in your computer (local drive) file space. Make sure you use an easy name when saving your file.
That was the first part of our task, the second part is to extract some data from our plots and finish out the overall task.
Our approach: open the work you saved above,
1: Insert the red line between two points as shown in figure 3,
2: Extrapolate the red line to the time axis (t = 210s), and the line after redline by dotted blue line to (t = 300s) as shown by the dotted line in the figure 3 (a) and 3 (b) respectively.
Figure 3 (a): time - distance plot
3: Extracts the values for t and x from plot as shown in the figure 4
4. Compute the the slope 1 (from first straight line) and slope 2 (from red line) and slope 3 (from line 3) from values extracted in step 3 above
Figure 4: time - distance plot with extracted t, x values
Then slope 1 = 0.585s/m, slope 2 = 0.132s/m, slope 3 = 0.052s/m
We can finish out the task by recalling here that
V1 = 1/slope 1, V1 = 1/0.585s/m = 1.71m/s
V2 = 1/slope 2, V2 = 1/0.132s/m = 7.58m/s
V = 1/slope 3, V3 = 1/0.052s/m = 19.23m/s
If we follow V1<V2<V3 rule for refraction to occur. Then, Yes! We are still on the right track!
When t = 210s
Depth (Z) = tV1V2/2√(V22 - V12)
Z1= 210×1.71×7.58/2√(7.582 - 1.712)
Z1 = 184.3m
The depth of layers bed from the surface to the first refractor is 184m
Put those variables in spreadsheet and let it done the work for you, as I put see my screenshot below.
The task was done!
It is the best to check how to do this tutorial for second refractor, non - planner many layers, and their models using the seismic refraction (t - x) plots guide
You can let me know, if you didn't get this tutorial. But I hope it is clear!
Golden Tip: This is three layer case, as a rule of thumb, we worked for n-1 top layers. Remember we assumed it is a horizontal layers. If the layers are dipping you may use another trick.We will explore those tricks to our next talk.
To work in units of milliseconds for time and Velocity in Km/s, is also highly recommended.
To know the site subsurface geology of where your data is came from is important!
There are many interesting cases, and simple tricks we can talk, however the time and space is limited. See seismic refraction (t - x) plots guide.
Meet you in upcoming talk.
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2 Comments
This is indeed helpful for those who don't know how to plot a graph of T (Time) against Distance (X) and how to find the Depth (thickness) using the necessary data.
ReplyDeleteThanks, ! Sure it is very helpful.
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