#### Seismic Refraction, Physics tutorial

Refraction Surveys:

Ideally interfaces studied in the small refraction survey must be shallow, roughly planar and dip at less than 150. Velocity should increase with depth at each interface. First arrivals at surface will then come from successively deeper interfaces as distance from shot point increases.

The Principal Refractors:

In shallow refraction work, it is frequently adequate to consider ground in terms of dry overburden, wet overburden and weathered and fresh bedrock. It is very hard to handle with more than three interfaces. P-wave velocity of dry overburden is at times as low as 350 ms, velocity of sound in air, and is seldom more than 800 ms. There is generally a slow increase with depth that is almost impossible to estimate, followed by abrupt increase to 1500-1800 ms at water table.  Fresh bedrock usually has P-wave velocity of more than 2500 ms-1 but is probable to be overlain by the transitional weathered layer where velocity, that may originally be less than 2000 ms, generally increases steadily with depth and accompanying reduction in weathering.

Critical Refraction and Head Wave Snell's Law:

This signifies that if V2 is greater than V1 and if sin i = V1/V2, refracted ray will travel parallel to interface at velocity V2. This is critical refraction.  After critical refraction, some energy will return to ground surface as head wave represented by rays that leave interface at critical angle. Head wave travels through th upper layer at velocity V1 but, due to its inclination, seems to move across ground at V2 velocity with which wave-front expands below interface. It will thus finally overtake direct wave, despite longer travel path. Cross-over or critical distance for which travel times of direct and refracted waves are equal is:

xc = 2d [(V2 + V1)/(V2 - V1)]

This equation forms basis of simple method of refraction interpretation.

xc is always more than double interface depth and is large if depth is large or difference in velocities is small. Critical time, achieved by dividing critical distance by direct-wave velocity, is also at times utilized.

The term critical distance is also at times utilized for minimum distance at which refractions return to surface, i.e. distance from shot point at which energy arrives after reflection at critical angle. This usage is not common amongst field crews as refractions arrive after direct wave at this point, and for some distance beyond, and are hard to observe. If more than one interface is involved, the ray which is critically refracted at lowermost interface leaves ground surface at angle i provided by:

sin i = V1/Vn

Therefore, angle at which energy leaves ground surface for final critical refraction at a deep interface depends only on velocities in uppermost and lowermost layers involved, and not on velocities in-between. Although this is amazingly uncomplicated result, cross-over interpretation becomes rather complicated for multiple layers and intercept-time method is generally preferred.

Line of geophones laid out for refraction survey is called as a spread, term array being reserved for geophones feeding single recording channel. Arrays are common in reflection work but are almost unknown in refraction surveys where sharpest possible arrivals are required. Enough information on direct wave and reasonable coverage of refractor is attained if length of spread is about three times the crossover distance. Simple but frequently incorrect rule of thumb defines that spread length must be eight times the expected refractor depth.

Positioning Shots:

In many refraction surveys, short shots are fired very close to ends of spread. Interpretation is simplified if such shots are really at the end geophone positions so that travel times between shot points are recorded directly. If this system is utilized, geophone usually at short shot location must be moved half-way towards next in line before shot is really fired (and replaced afterwards). Damage to geophone is avoided and some extra information is achieved on direct wave. Long shots are placed adequately far from spread for all first arrivals to have come via refractor, and short-shot data may thus be required before long-shot offsets can be decided. Distances to long shots need be estimated accurately only if continuous coverage is being achieved and long-shot to one spread is to be in same place as a short or centre shot to another. If explosives are being utilized, it may be valuable using very long offset if this will allow firing in water.

Centre Shots:

Information given by conventional four-shot pattern may be supplemented by centre shot. Centre shots are mainly helpful if there are significant differences in interpretation at opposite ends of spread, and particularly if these appear to involve different numbers of refractors. They may make it possible to attain a more dependable estimate of velocity along intermediate refractor or to monitor thinning of intermediate layer that is hidden, at one end of the spread, by refractions from greater depths. The additional dependable depth estimate is achieved that doesn't depend on assumptions about ways in which thicknesses of different layers differ along the spread, and there will be additional data on direct wave velocity. Centre shots are utilized less than they deserve. Extra effort is usually trivial compared to work done in laying out spread, and extra and possibly vital information is cheaply achieved.

Annotation of Field Records:

Hard-copy records can be generated in field from most of the seismographs now utilized for shallow refraction surveys. Several dozen records created in a day's work which comprises repeats, checks and tests and the completion of number of different spreads should be carefully annotated if confusion is to be avoided. Annotations must obviously comprise date and name of observer-in-charge, along with survey location and spread number.

Features like use of S-wave geophones at some points or peculiarities in locations of some of geophones must always be noted. Several items listed above can be printed directly on to hard-copy record, if they are first entered in machine. This is frequently a more tedious, and more error-prone, procedure than just writing information on each record by hand.

Picking Refraction Arrivals:

Choosing first arrivals on refraction records depends on subjective estimates of first break positions and may be hard at remote geophones where signal-to-noise ratio is poor. Few later peaks and troughs in same wave train are probable to be stronger, and it is at times possible to work back from these to evaluate position of first break. Though, as high frequencies are selectively absorbed in ground, distance between first break and any later peak slowly increases with increasing distance from source.

In addition, trace beyond first break is affected by several other arrivals and by later parts of primary wave train and these will adjust peak and trough locations. Using later features to evaluate first arrival times must always be considered as poor substitute for direct picking.

Time-Distance Plots:

Data extracted from refraction survey comprise of sets of times (generally first-arrival times) estimated at geophones at different distances from source positions. As these are plotted against vertical time axes and horizontal distance axes, gradient of any line is equivalent to reciprocal of velocity, i.e. steep slopes correspond to slow velocities. All data for the spread are plotted on single sheet which has a working area covering only ground where there are really geophones. It is not essential to illustrate long-shot positions. As many as five sets of arrivals may have to be plotted, and a set of time differences, different colors or symbols are required to differentiate between data sets. If arrival times lie on number of clearly defined straight-line segments, best-fit lines may be drawn. It is frequently best to draw lines through only direct-wave arrivals (that must plot on straight lines), leaving refracted arrivals either un-joined or linked only by faint lines between adjacent points.

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