Abstract Conventional seismic refraction methods aim to determine the spatial distribution of seismic wave velocities in the subsurface. Seismic wave velocities can be related to such geologic and petrophysical parameters as rock type, porosity, weathering, jointing, water saturation, and elasticity. Seismic refraction methods have been applied to petroleum exploration, the search for groundwater, the investigation of engineering sites, the exploration of alluvial deposits, and the correction of weathering effects for seismic reflection surveys. Descriptions of instrumentation and field operations, as well as the fundamental principles based on raypath theory, can be found in Dobrin (1976) and Telford et al (1976). An introduction to the theoretical development using the wave equation was presented in Grant and West (1965). There are numerous interpretation methods, ranging from the very simple in basic assumptions and ease of use to the complex. Dobrin (1976) gives an excellent summary of most of the published methods, and, together with the outstanding volume on seismic refraction prospecting edited by Musgrave( 1967), provides an ideal starting point for those who seek familiarity with one of the most challenging fields of geophysics. The aim of this monograph is to propose a new interpretation method, the generalized reciprocal method (GRM), which has many advantages compared with the previously published methods. The GRM can define layers with varying thicknesses and seismic velocities, unlike the conventional intercept time method (Ewing et al, 1939; Dooley, 1952; Adachi, 1954; Mota, 1954), or the critical distance method (Heiland, 1963, p. 527). However, a redefinition of the intercept time in chapter 9

Abstract The two-dimensional model chosen for the derivation of GRM parameters consists of multiple plane-dipping layers with constant seismic velocities. This model does not represent the limitation of the method but has been selected for mathematical convenience. There are several methods of specifying depths and raypath parameters. For example, Dooley (1952) and Adachi (1954) used vertical depths. However, a more convenient approach was used by Ewing et al (1939) and Mota (1954), who specified thicknesses normal to the refractor surface. The surface of the refractor is taken as the envelope of arcs of appropriate radii; hence loci, rather than actual depth points, are determined. The dip information, which is not always readily determined for undulating refractors, is recovered with the construction of the envelope. Therefore, the common assumption of the seismic profile being normal to the strike of the refractor is not necessary. This also permits convenient extension to three-dimensional (3-D) analysis. Another advantage of the specification of Ewing et al (1939) is the symmetry of the resulting mathematical expressions. This symmetry, in turn, results in a depth conversion factor which is insensitive to dip angles up to about 20 degrees. Therefore, depth calculations are extremely convenient, both when the refractor is undulating and when there are complex velocity distributions above the refractor. These advantages are not readily achieved with the expressions of Mota (1954), who also used perpendicular thicknesses. Accordingly, layer thicknesses and angles of incidence used in the following analysis are similar to those used by Ewing et al (1939). However, dip angles

Abstract When the subsurface can be approximated with plane layers and uniform velocities, the refractor velocity can be obtained from the forward and reverse apparent velocities on the time-distance plot, together with the overlying velocities, using equation (1) of Ewing et al (1939, p. 265). If these approximations cannot be made, or when the velocities of all layers above the refractor are not known, it is still possible to obtain a reasonable estimate of the refractor velocity by the following approach. Using the symbols of Figure 2, the velocity analysis function t v is defined by the equation The value of this function is referred to G, which is midway between X and Y . In routine interpretation, values of t v , calculated using equation (2), are plotted against distance for different XY -values. By a series of tests to be described in chapter 6, an optimum value of XY is selected, and a refractor velocity is taken as the inverse slope of a line fitted to the t v values for the optimum XY . For the special case of XY equal to zero, equation (2) reduces to equation (7) of Hawkins (1961, p. 809). It is similar to the minus term in the plus-minus method (Hagedoorn, 1959). The velocity analysis formula quoted by Scott (1973, p. 275) is a least-squares fit of data values which are mathematically similar to equation (2), but with XY equal to zero. One method of testing the efficacy of determining refractor velocities with equation (2) is to apply the equation to a plane-layer case.

Abstract Following the determination of the refractor velocity, the next step in defining undulating refractors is the formation of generalized time-depth functions at each geophone location. The generalized time-depth function in refraction interpretation corresponds with (but is not identical to) the one-way traveltimedepth function in reflection methods. Using the symbols of Figure 2, the generalized time-depth t G (hereafter referred to as “time-depth”) at G is defined by the equation Several special cases of the generalized time-depth can be derived, depending upon the XY separation used. For XY equal to zero, the conventional time-depth (Hagiwara and Omote, 1939, p. 127; Hawkins, 1961, p. 807, eq. 3; Dobrin, 1976, p. 218, eqs. 7-35, 7-36) is obtained. It is similar to the plus term in the plus-minus method (Hagedoorn, 1959; Hawkins, 1961, p. 814) and to a term in the method of differences (Heiland, 1963, p. 549, eq. 9-68). For the calculation of the conventional time-depth, no knowledge of the refractor velocity is required. For XY selected such that the forward and reverse rays emerge from near the same point on the refractor, a result similar to the mean of the migrated forward and reverse delay times, as defined by Barry (1967, p. 348), is obtained. The delay time method was first described by Gardner (1939, 1967), and has been developed by many others (Barthelmes, 1946; Wyrobek, 1956; Bernabini, 1965; Layat, 1967; Peraldi and Clement, 1972). Although all theoretical derivations assume negligible dip angles, the method is generally considered valid for dips less than 10 degrees.

Abstract In the previous two chapters, the GRM parameters of velocity analysis function and generalized time-depth were defined, and then successfully applied to an extreme model with steeply dipping interfaces. Although plane-layer conditions are not uncommon, irregular layers are more usual and are generally of more interest. The following synthetic models permit the GRM to be examined in a variety of cases where departures from plane uniform layering occur. In the time-depth graphs to follow (Figures 7, 22, 38, 44, and 50), the upper sets of points (circles)are the values for zero XY , the crosses are the values for a 5-m XY -value, and so on. Also, to avoid overplotting of points for various XY -values, each set of calculations uses a different reciprocal time. This results in a simple vertical displacement of plotted values which can be readily corrected if required (see chapter 9). Perhaps the model of most interest is the irregular refractor. The model shown in Figure 4 has a plane horizontal ground surface and a highly irregular refractor with dips on the sloping surfaces of approximately 18 degrees. The first arrival times for this model, shown in Figure 5, were obtained by wavefront construction, since this method conveniently accommodates dipping refractors, interfering head waves, and diffraction (Thornburgh, 1939; Rockwell, 1967; Palmer, 1974). The traveltimes are also listed in Appendix A. In Figure 6, the velocity analysis function is plotted for XY -values ranging from 0 to 30 m. For a 20-m XY spacing, the velocity analysis data fall very close to two straight lines,

Abstract Small-scale surface irregularities are defined as variations in thickness and/or velocity of near-surface layers (Gardner, 1967, p. 344) that extend over only a few geophone intervals at most. These irregularities are significant enough to invalidate interpolation between shotpoints, but are not sufficiently common to justify a field program which fully maps the surface layers. Most interpretation methods aim to define an irregular refractor which is usually assumed to lie below uniform surface layers. However, the accuracy in defining deep refractors often depends upon the recognition and definition of small-scale surface irregularities. If the time anomalies caused by the surface irregularities are assigned to deeper layers, then the computed depths can be quite inaccurate, and the inferred refractor irregularities may not even exist. Furthermore, if XY spacings greater than zero are used in defining deeper layers, then depth anomalies computed from the time anomalies may be migrated away from their sources. Because the surface layers usually have low seismic velocities, any variations in thicknesses or velocities produce time anomalies which can be many times larger than the anomalies produced by the same variations in layers nearer the refractor. For example, at G in the model shown in Figure 3, a change of 1.2 m in thickness of the surface layer results in a variation of 1 msec in the arrival time. However, a change of 3.2 m in the thickness of the third layer is required for the same variation in the arrival time. This effect can be even more accentuated in areas where the

Abstract In elementary treatments of the seismic refraction method, each layer is assumed to have a uniform velocity and to be bounded by plane surfaces. For these simple models, the field data consist of traveltime curves, each segment of which represents a different refractor. A depth section is readily obtained by assigning a refractor to each segmenta nd employing one of the standard formulas. When the geologic situation deviates from the plane interface model, then the more advanced interpretation methods are used to map the irregular refractor surface. However, while more advanced routines recognize the existence of irregular refractors, it is still commonly assumed that the velocity stratification can be unambiguously inferred from the traveltime curves. This assumption constitutes probably the most serious shortcoming of the refraction method (Hagcdoorn, 1959, p. 164–166; McPhail, 1967, p. 260). In many cases, improved field procedures are sufficient to resolve the inherent ambiguity of single traveltime curves. To separate the effects of changing refractor dip from the recording of other refractors, at least four shotsotwo from different locations at each end of the geophone spreadware necessary (see Hawkins, 1961, p. 810). For example, more thorough field programs might have resulted in Duguid's (1968) paper being less open to discussion( Sendlein, 1968). Unfortunately, an increase in the number of shotpoints is not a solution to all problems of ambiguity. One example is the hidden layer where energy from a refractor of higher seismic velocity arrives at the surface before energy from an overlying refractor. Since only first arrivals are

Abstract The use of an average velocity above the refractor permits depth calculations without defining all layers. It can also be useful in accommodating undetected layers, as discussed in the previous chapter. The method described below uses the optimum XY -value, but, unlike the methods of Hawkins [1961, equation (5)] and Woolley et al (1967, p. 279–280), a depth to the refractor is not required. With the substitution of the horizontal-layer approximation, equation (12) becomes These equations can be combined to form the following expression For field examples, the calculations of time-depths using equation (10) and refractor velocities using equation (6) present few problems. Therefore, if an optimum XY -value can be determined, then an average velocity can be calculated with equation (27). The total thickness of all layers can then be computed by rearranging equation (25). An appreciation of the efficacy of equation (27) can be obtained by comparing depths calculated using the average velocity with the actual depths for a fully defined model. The model to be considered (Figure 27) has two layers above the refractor. Although all interfaces are plane and horizontal for ease in computation, the results are considered valid for dips up to 20 degrees, the limit of the GRM horizontal-layer approximations. The total depth is calculated from equation (25), after an average velocity has been determined by substituting time-depth and XY -values into equation (27). Since there are no field data for this synthetic example, appropriate values of time-depth and XY must first be computed with equations (21) and (23).

Abstract In the computation of time-depths and velocity analysis functions, the reciprocal time, the time from shotpoint to shotpoint, is required. However, of all the times determined in a seismic refraction profile, the reciprocal time is the most difficult to determine accurately. There are several reasons for this. First, the reciprocal geophone is the most distant from the shotpoint. It receives the least amount of energy because head waves are attenuated approximately as the inverse square of the distance (Grant and West, 1965, p. 181). Furthermore, the earth acts as a low-pass filter, with the higher frequencies being attenuated morer apidly than lower frequencies (Attewell and Ramama, 1966). Both of these factors result in arrivals at distant geophones having onsets on the seismic record less distinct than those of closer geophone traces. Second, excessive shotpoint offsets may make the planting of a geophone at the reverse shotpoint impractical. An arrangement employed by the Bureau of Mineral Resources in Australia for many years uses the shot firing cable to transmit the signal from a geophone at the reverse shotpoint, when it is not required for shot firing (Hawkins, 1961, p. 811). However, for large shotpoint offsets, this system may be inconvenient. Third, it is possible that, even with a reciprocal geophone in place, the first arrival is from another deeper refractor. Finally, disturbed ground caused by previous shotpoints may result in unknown significant irreversible delays, as shown by Domzalski (1956, p. 145). Although geophones are usually planted away from earlier shotpoints, the region of the disturbed

Abstract The construction of time sections using the GRM is a very convenient and powerful intermediate stage in the processing and interpretation of seismic refraction data. The time sectioni s an orthogonalp lot of time-depthsa nd half-interceptt imes below the points on the surface to which each refers. The horizontal axis represents the seismic line on the earth's surface. For a geophone time-depth [equation (10)], the reference point is the midpoint of XY ; for a time-depth near a shotpoint [equation (15)], it is 1/2 XY from that shotpoint toward the reverse shotpoint; for the half-intercept time [equation (39)], it is below the shotpoint. The vertical axis has the units of time positive downward. Time sections have been used previously in seismic refraction processing for the adjustment of delay times (Wyrobek, 1956; Pakiser and Black, 1957; Layat, 1967). However, the most common use of time sections is in the seismic reflection method (Dobrin, 1976, p. 236). The time section is an extremely convenient work area for seismic refraction processing because (1) it is not affected by uncertainties in determining velocities above refractors, (2) it can be constructed while still preserving consistency with the original traveltime data, and (3) it provides a criterion for field work requirements. For the calculation of a time-depth using equation (10), the only velocity required is that of the refractor. This can be readily obtained using equation (6). The velocities of layers above the refractor being mapped are not required to form equation (10). However, to convert time-depthsin to depthsu singe quations( 12)

Abstract One of the well-known shortcomings of the seismic refraction method is the disproportionate length of time required to produce final detailed results, when compared with the time taken to acquire data. Processing is not a major problem because digital computers and plotters facilitate rapid computation and presentation of results (Peraldi and Clement, 1972; Scott, 1973). Most delays occur in the interpretation phase, which requires high levels of expertise and judgment (Dobrin, 1976, p. 294). In the majority of refraction interpretation routines (e.g., Hawkins, 1961, p. 811, 812), processing follows interpretation of data. This procedure is adequate when there are only a few spreads to interpret or when the processing facilities are convenient. However, when there are large amounts of data, or when consistency with cross-lines or drillholes is required, then reprocessing following each reinterpretation may be inconvenient as well as costly. With the GRM, the interpretation routine involves examination of both the basic traveltime data and the processed data, viz., the velocity analysis functions and time-depths, in order to recognize optimum XY -values, surface irregularities, etc. Therefore, for the most efficient use of the GRM, the interpretation phase should follow the data processing phase. The interpretation phase then requires an editing phase, where meaningless computations are removed from further consideration. Processing using the GRM is best carried out using a computer and plotter because of the large number of points produced when a range of XY -values is used. A program has been published by Hatherly (1976) for the processing and plotting of seismic refraction

Abstract Within this presentation, fully defined synthetic models have been used to illustrate various features of the GRM. The benefits of this approach are obvious. Very few field examples have sufficient drillholes or other forms of sampling to guarantee the same control. Furthermore, models can be designed so that one aspect is emphasized, while other factors are held constant or are removed entirely. However, like all methods of seismic refraction interpretation, the GRM will ultimately be judged on its ability to accommodate complexities of the real geologic environment. The seismic refraction survey at the Welcome Reef dam site (Hatherly, 1977) provides data which permit an assessment of the GRM, because field methods were appropriate. These methods included: The use of geophone separations considerably smaller than the depth to the deepest refractor; the measurement of arrival times to an accuracy of about one percent, despite the problems of introducing sufficient energy into the ground; and the use of sufficient shotpoints to resolve the ambiguity problem for the majority of layers. A listing of locations and first arrival times for the refraction survey of the Welcome Reef dam site is given in Appendix B. The proposed Welcome Reef damsite is on the Shoalhaven River, approximately 50 km east of Canberra in southeastern Australia. Outcrop in the area consists of interbedded, steeply dipping, Ordovician metasediments,w hich are mainly quartzitesa nd phyllites. Weathering, particularly in the phyllites, can be extensive. In drillholes, the top of the weathered bedrock surface can often only be distinguished from the unconsolidated sediments by color changes,

Abstract The GRM provides an integrated approach to seismic refraction interpretation cognizant of the realities of the geologic environment. These realities include undetected layers, and layers with variable thicknesses and seismic velocities. For the most effective use of the GRM, accurate optimum XY -values are necessary. Improved accuracy may result through the application of statistical methods to parameters derived from first arrival times. However, the powerful methods of time series analysis, such as those used in seismic reflection processing, probably hold more promise. In fact, even though many methods of seismic refraction interpretation are either special cases of, or closely resemble the GRM, it may be more prudent to pursue the similarities between the GRM and the seismic reflection method. These similarities include the correspondenceb etween the time-depth and the one-way reflection time, as well as that between the average velocity and the RMS velocity. Furthermore, in each case it is possible to construct a time section which is independent of the accuracyo f the seismicv elocity determinationsi n the overlying layers. Research and development into routine seismic refraction interpretation have been rather dormant for some time. I believe the development of time series analysisi n seismicr efraction processingt o be long overdue.

Abstract I am indebted to Manus Foster and Kenneth Burke. Without their support and efforts, this work would not have been possible. I am also indebted to my able colleague Peter Hatherly for carrying out the field work, processing of the example, and providing searching comments. Comments by John Ringis, Adelmo Agostini, and Ted Tyne were invaluable. The Cartographic Section of the Geological Survey of New South Wales prepared the figures, and Cheryl Smith prepared the manuscript more times than she would care to remember. Their contribution and patience are sincerely appreciated. The work is published with the permission of the Under Secretary, New South Wales Department of Mineral Resources