Seismic Refraction:  
Exercise #1: Introduction to seismic refraction surveying

 

Introduction

Estimating the thickness of geologic layers is commonly required for many engineering, environmental and geological tasks. Common invasive techniques (drilling, cone push, etc) provide information at points, but geophysical methods must be used to "connect the dots"; i.e. to build a more complete understanding of how layer thickness varies under a line. Seismic refraction is commonly used to obtain such information, however it is more labour intensive than many other geophysical survey techniques, both with regard to field work and data processing. Note that a short Seismic Refraction Glossary is also provided.

Goals and tasks

In this exercise you will gain some intuition about how seismic refraction surveys work by doing the following

  1. Sketch the configuration of a seismic refraction survey, including the geometry of transmitters, receivers and energy ray paths within the ground. Parameters about the earth that are obtainable with this type of survey will be included on the sketch.
  2. Use a prepared spreadsheet to calculate the response over a simple earth model consisting of 2 horizontal layers over a uniform basement. The necessary parameters are included in the spreadsheet, but the equations must be entered. This is “forward modelling” - calculating measurements for known subsurface situations.
  3. Explore how instrument configuration and geologic geometry affect survey results. In other words, you will practice using forward modelling to consider aspects of survey design.

Deliverables: hand in answers to questions labelled Q i. Some require pasting figures into your answer document. (Interpreting results of a survey will be done in future lab exercises.)

Instructions

To complete this exercise you will need a browser and Microsoft Excel, paper, a pencil & a ruler for sketching, and a word processor with which to answer questions and past spreadsheet graphs. Basically you must read instructions and answer questions labelled Qxx. as you come to them. Please be succinct (no essays) but complete.

PART I: survey configuration and signal paths

Save the spreadsheet called refrac_fwd.xls to your workspace by right-clicking the link, then open it in MS-Exel. First we will identify what the parameters are; later you will need to enter equations necessary for calculating direct and refracted signal travel times for all 12 geophones.

A neat and tidy sketch is required to illustrate the seismic refraction experiment specified by the default Survey parameters and Parameters about properties & structure found in the spreadsheet. The earth model consists of two layers overlying basement, and the seismic survey involves one shot and 12 geophones.

Q1. Sketch a cross-section of the geology characterized with default parameters in the spreadsheet, with the instrument positions marked on the surface. Include, and label, layers 1, 2, and 3, interfaces 1 and 2, the shot position, and the 12 geophones. Show where each of the three velocities are relevant, and the two layer thicknesses (note that “depth” and “thickness” are not the same except for the top layer).

Q2. On your sketch, add a direct ray path from shot 1 to geophone 2, a reflection ray path from shot 1 to geophone 4 via interface 1, and a refraction ray path from shot 1 to geophone 12 via interface 2.

If you are not reasonably clear about what these sketches should be ask an instructor for help before continuing.

Part II: seismic refraction response to a simple layered earth

Next we would like to calculate the travel times for all direct and refracted signal pathways.

Q3. For energy that travels directly to geophones from the source (no reflection or refraction) what is the equation relating arrival time, distance between source and receiver, and signal velocity?

Enter this equation into the “T_dir” column of the spreadsheet using source-receiver distance X for each geophone (adjacent to the T_dir column) and velocity of surficial material, V1 (cell G5). A graph of the arrival time vs X should appear in the “First Arrival Times” chart.

Q4. (a) What is the slope of this line (it’s meaning, value & units) and
       (b) what is the y-axis intercept (value, units)?

Energy travelling directly from source to receiver is not always the first energy detected at more distant geophones. Energy that travels down to the layer interface, along the interface, and back up to the receiver will arrive before energy taking the direct path if V2 is significantly larger than V1. The equation giving the refracted ray-path’s travel time includes X (source-receiver distance), Z (depth to the interface), V1 and V2 (velocities in both layers). The equation can also be expressed using θ, the “critical angle” at the first interface, and Ti, the “intercept time”.

Q5. What is the relation (equation) between critical angle and the two velocities?
Q6. Show on the sketch you made above, the critical angle for one of the refracted ray paths.
Q7. What is the relation between intercept time, depth, critical angle and surface layer velocity?

Enter these relations into the spreadsheet cells next to labels “theta1” and “Ti1”.

Now you have parameters necessary for building the relation for refraction travel times. Do this in the column labelled “T_refract1”. A corresponding line should appear on the graph.

Q8. For which geophones is the direct signal the “first arrival”, AND for which geophones is the refracted signal the first arrival?

Finally, we will complete the spreadsheet so that signals refracted along the second interface are plotted on the graph. Fill in the necessary relations for the Two Layer case versions of theta1, theta2, Ti1, and Ti2. Then add the formula for arrival times at all geophones using the column labelled “T_refract2”.

Q9. Now that we have travel times for direct and both refracted signals, at which geophones do first arrivals come from the second interface?

On the graph, travel times for refracted signals from both interfaces were plotted for all geophones. In fact, many of these arrivals are not first arrivals, and therefore will not be visible in a real survey. So, delete those cells giving refracted travel times that will NOT actually be seen. DO NOT SAVE HERE - YOU WILL PUT THE EQUATIONS BACK IN AFTER MAKING A COPY OF THE GRAPH.

Q10. Make a copy of the First Arrival Times graph at this stage and paste it into your answers document. We will be checking to see that you have removed the correct values.

Part III: exploring effects of instrument configuration and geologic geometry

Hopefully at this stage you understand how the travel times on your chart relate to the sketch you have drawn illustrating the geometry of a seismic refraction survey.

Now we will use this spreadsheet to explore how instrument configuration and geologic geometry affect survey results. This is forward modelling. Two types of useful questions can be asked using a forward modelling tool such as this one: (i) what range of geologic materials and structures (velocities and thicknesses) can be determined using a given survey configuration? and (ii) what survey geometry is required to determine a given geologic situation?

FIRST: Put the necessary equations back into the cells you deleted for the previous question. Now, we will use the spreadsheet slider bars to adjust the parameters describing the survey or the earth model (depths and velocities) to answer the following questions.

Q11. At least two geophones are necessary for determining surface material velocity from the corresponding slope on the graph. Consequently, what is the largest distance between the shot and the first geophone that will allow for an estimate of this velocity?

Set the offset back to 1m. Now, if geophones are further apart than 1m, a longer line can be surveyed, but larger spacings make it harder to see a “thin” middle layer.

Q12. What is the largest geophone spacing that still permits an estimate of V2?

Return the survey geometry back to it’s default values. Adjust parameters to answer the following, but read questions carefully!

Q13. How slow would the velocity of layer 2 have to be before we can no longer see layer 2 on our first arrival data? (To “see” a refracting horizon there must be at least 2 geophones with first arrivals from that interface.)

Q14. Return to default - then, how thick will layer 1 have to be before we loose evidence of the first refracting horizon (called interface #1)?

Q15. Return to default - now, how slow would the velocity of layer 3 have to be before we loose evidence of interface #2 from the data?

Q16. Return to default - how thin can layer 2 be before we loose sight of interface #1?

Q17. How thick can layer 2 be before we loose evidence of interface #2?

Q18. Return to default parameters. Change the survey so that geophone spacing and offset are both 2m. Now what is the maximum thickness of layer 2 before interface #2 becomes undetectible?

Q19. We want to characterize a situation with overburdon over a gravel layer over basement. Overburden is likely to be 5m thick with velocity ~ 300m/s, the gravel layer is expected to be 13m thick with velocity ~ 950 m/s, and the basement is expected to have a velocity of ~3000m/s. What are the smallest geophone spacing and offset that will characterize this geology with direct & refracted first arrivals at at least 2 geophones each? (Feel free to adjust the Y-axis of the “First Arrival Times” chart.)

Q20. Copy the forward modelling chart that answered the last question into your answer document.

Q21. Wrap-up1: Which of the steps in our 7-step framework have we been working on - and justify your answer.

Q22. Wrap-up2: We have only studied how seismic refraction behaves for extremely simple models of the earth. What type of generic model have we been using - and justify your answer.