GG450 April 8, 2008

1. GG450 April 8, 2008 More Refraction Principles

2. Refraction - 2 Flat Layers over half space • The important points of this section on arrivals from 2 flat layers are: • 1) The angle of incidence on the layer 1-2 boundary needed for the ray to be critically refracted at the layer 2-3 boundary is easily determined since the ray parameter is constant : 2) The SLOPE of the arrival refracted in layer i is equal to 1/Vi for that layer, and thus equals the ray parameter of the critical ray in that layer.

3. 3) The equation that gives the travel time for the refracted arrival in layer 3 is the equation of a straight line, with slope 1/V3 and y-intercept equal to the sum of the last two terms. • How can we tell from the data whether we have one, two, or more layers to deal with? This is a VERY practical problem that you will need to deal with in your refraction lab.

4. How do we get layer depths? For the 1st layer, we can ignore the lower layer and the y- intercept is: so the thickness of the layer is : If we have a lower layer, the thickness of the top layer is determined from the equation above (which won't change just because there's another layer below), and the intercept time for the 2nd refraction is: and , solving for h2:

5. Don’t be intimidated by this equation – it’s a bunch of constants!

6. What if we get the first layer thickness and/or velocity wrong? How will h2 change if h1 is estimated too large? How will h2 change if v1 is estimated too small?

7. This figure shows the reflections as well as the refractions for the 2-layer over a half space model. Note that the reflections are asymptotic to the refractions. The dots show critical points - where refractions begin, and cross-over points - where refractions become first arrivals.

8. Refraction - dipping layers The important points of this section on dipping layers are: 1) The ray parameter no longer is a constant for any particular ray. A ray that is affected by a dipping layer will change direction based on a combination of its incident angle, the layer velocities, and the layer dips. When it reaches the surface again it will have a different ray parameter. 2) If shots are fired and recorded from BOTH ends of a refraction line, the forward refracted arrivals come in at different times than those from the reversed arrivals. (With one exception)

9. 3) The equations that give the travel time for the refracted arrivals yield straight lines. • 4) The SLOPE of the refracted arrivals from any dipping layer is NOT equal to 1/V for that layer. It depends on the dip. If dips are small, the AVERAGE slope between the forward and reverse lines is very close to the actual velocity. • 5) The ONLY true reciprocal path for forward and reversed lines are the two end points. Since reciprocity must work, the travel time on the two ends of the forward and reverse lines must be the same if the shot and receiver are in the reciprocal locations.

10. 6) Since nothing is changed for the direct arrival, the slope of the direct arrival for both the forward and reverse lines should be the same. • 7) The dip observed on one refraction line is the APPARENT dip. We need to shoot two orthogonal lines to determine true dip. And, that assumes that the boundary between layers is a plane. • RECALL: THESE STATEMENTS ARE FOR A MODEL, NOT for reality. Never try to fit your data to the model, try to fit the model to the data. If it doesn't fit, do the best you can and state how you think the model might differ from reality. This requires GEOLOGICAL INSIGHT.

11. The above figures show the travel time curve and model for a dipping layer case. If there were no dip, the forward and reverse lines would have the same shapes. The up-dip end of the line has a smaller intercept time and smaller velocity.

12. low v

13. Using raytrace.m, you can make models of almost any horizontal-layer model. The one below has nearly constant velocity layers: