Effect of assumptions on refraction interpretation

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Problem

The interpretation of refraction measurements necessarily involves a number of assumptions. How do these affect the interpretation?

Background

Refraction measurements are of apparent velocities (the inverses of the slopes) and intercept times observed from time-distance plots. Refraction events are generally defined by several points that approximately line up to define a straight line, which is drawn through the points. Refractor apparent velocity is then determined from the slope of the line and depth from the intercept with the time axis. If the refraction event from shooting in the opposite direction is also observed, the dip and refractor velocity can be determined. Events from shooting in opposite directions must be correlated correctly.

The basic refraction equations generally assume the following properties:

  1. Homogeneous isotropic layers of constant velocity,
  2. Each layer’s velocity is larger than that of any shallower layer,
  3. Planar interfaces,
  4. The profile is perpendicular to the strike.

Solution

Uncertainties in the data and correlations and differences between the real situation and the foregoing assumptions affect the interpretation. Where more than one head-wave event is present, the differences in slope must be large enough to distinguish them as separate events (see problem 11.3). Head waves where offsets are large often show shingling, an en-echelon pattern which may make traveltime picks a cycle late.

In the following we assume that the apparent velocities and intercepts are all measured correctly. Assumption (1) of homogeneous constant-velocity overburden is usually not valid and the velocity in the horizontal direction often exceeds that in the vertical direction. One result is errors in calculating refractor depths. Gradual changes in velocity with depth cause raypaths to be bent or curved, changing calculations as to where a critical raypath reaches the refractor (that is, changing the critical distance) and the distance the head wave travels in the refractor. This is generally the most serious violation of the assumptions. The values for velocity above a refractor generally should be obtained from independent data rather than from the refraction data alone.

Failure of assumption (2) that velocity increases monotonically creates depth errors (see problem 11.3). Layers that have smaller velocity than an overlying layer constitute one type of hidden-layer problem. Layers whose thicknesses are so small that their head waves do not become separate distinct events constitute another type of hidden-layer problem. Changes in overburden velocity in the horizontal direction create similar effects, and they also affect the critical angle at the refractor.

Assumption (3), that the refractor is planar, contrasts with the usual objective of mapping the relief on the refracting interface.

A refraction profile not perpendicular to the strike [assumption (4)] simply results in measuring only a component of the dip rather than the entire dip, and probably does not introduce a large error unless the dip is large.

As will be shown in subsequent problems, refraction mapping often uses more complicated methods than simply applying the refraction equations.

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