GEOGRAPHICA
41 1
REFERE.NCES
ABOAV.D.A. (1970). ‘The arrangement of grains in a polycrystal,’ Metallography, 3: 383-90.
BOOTS,B.M. (1975). ‘Some observations on the structure of socioeconomic cellular networks,’ The
Canadian Geographer, 19: 107-20.
- (1977), ‘Contact number properties in the study of cellular networks,’ Geographical Analysis, 9:
379-87.
COX,K.R.and AGNEW,J.A. (1974) ‘Optimal and non-optimal territorial partitions: a possible approach
towards conflict,’ Papers of the Peace Science Society (International), 23: 123-38.
I.K. (1972), ‘Monte Carlo simulation of the random Voronoi polygons,’ Search, 3: 220-1.
CRAIN,
- (1978), ‘The MonteCarlogenerationofrandom polygons,’ComputersandGeosciences,4:
131-41.
DACEY,M.F. (1963),‘Certain properties of a polygon in a two-dimensionalaggregate of polygons having
randomly distributed nucleii,’ Warton School of Finance and Commerce, Unviersity of Pennsylvania (Mimeographed).
EVANS,U.R. (1949, ‘The laws of expanding circles ;and spheres in relation to lateral growth of surface
films and the grain size of metals,’ Transactions o f t h e Faraday Society, 41: 365-74.
MEIJERING,J.L. (1953), ‘Interface area, edge length, and number of vertices in crystal aggregates with
random nucleation,’ Philips Research Reports, 8: 270-90.
WEAIRE,D.(1974). ‘Some remarks on the arrangement of grains in a polycrystal,’ Metallography, 7:
157-60.
WOLDENBERG,
M.J. (1972), ‘The average hexagon in spatial hierarchies,’ in R.J. Chorley (ed.), Spatial
Analysis in Geomorphology (London: Methuen).
[B .N. BOOTS,
Wiljlrid Luurier University]
SEISMIC VELOCITIES OF UNCONSOLIDATED SEDIMENTS IN THE
VANCOUVER AREA OF BRITISH COLUMBIA
One of the major problems involved in developing specific geologic histories for the Quaternary is that one is confronted in the field with an often bewildering array of unconsolidated
sediments which are not dissimilar in appearance. The task of distinguishing among alluvium, glacial tills, glacio-marine, and marine units is often difficult, and the identification of
spatially discontinuous time units of the same facies is usually a still greater problem. Of
course, units which are indistinguishable in the field can usually be separated by a detailed
analysis of mineralogy, grain size and shape distributions, fabric, compaction, and so on. But
such techniques are very time-consuming and many local geological chronologies for the
Quaternary are established only after many years of analysis in both field and laboratory.
The need for more efficient techniques of characterizing sediment textural properties in
the field might be met by surveys of related seismic velocity. Although the positive relationship between seismic velocity and those factors influencing the bulk density of sediment
(such as composition, compaction, and water content) is widely recognized,’ it has not been
widely exploited in Quaternary field studies; recent work on Pleistocene river-channel fills
and on permafrost distribution provides several exceptions.2
The purpose of this paper is to examine the usefulness of seismic velocities in identifying
surficial geological units in the Vancouver area of British Columbia.
METHODS A N D PROCEDURE
Velocities of compressional waves were obtained in the field using a Terra Scout R-150
portable refraction seismic recorder. Means of the travel times based o n forward and reverse
transects were determined for each survey site; these were located in well-drained and
undisturbed areas. Velocity profiles typically indicated a very low velocity in a shallow
CANADIAN
GEOGRAPHER,
XXIV, 4,1980
412
THE CANADIAN GEOGRAPHER
FIGURE1. Seismic-velocitydistribution for selected geological units near Vancouver, British Columbia.
(0.5 m) zone of soil near the ground surface. Beneath this zone was another, usually about
2 m thick, in which velocities were somewhat higher than those above. It is this zone which is
considered representative of the sediment unit for the purpose of the seismic analysis.
Beneath this representative zone seismic velocities often increased to distinctly greater
magnitudes, probably indicating the presence there of groundwater. All velocities were
recorded during mid-summer; winter recordings could reasonably be expected to differ
because of moisture and soil temperature effects.
Seven geological units (from three distinct depositional environments) shown on the New
413
GEOGRAPHICA
TABLE I
SIGNIFICANCE LEVELS FOR DIFFERENCE O F MEANS TEST OF SEISMIC VELOCITIES
Geological units
2A
28
3
4
5
6
7
I
8.61
12.41
22.26
13.98
18.96
12.52
15.83
*No significant difference at
2A
2B
3
4
5
6
4.34
19.25
11.78
16.78
8.92
10.24
15.20
8.78
13.54
5.96
6.45
4.17
1.88*
5.58
7.83
4.93
2.07
3.34
5.62
7.63
0.78*
P =
0.025.
Westminster and Sumas map areas of the Geological Survey of Canada were examined in
detail.3 Velocity measurements were obtained at points spread as evenly as road access
would allow over exposures of the following units:
1. Fraser River Sediments: fluvial silty clay and organic silt.
2. Sumas Drift: glacio-fluvial gravels and sand deposited by streams flowing from wasting
) central gravel and sand ( 2 ~of
)
glacier ice; formerly mapped as the peripheral sands ( 2 ~and
an alluvial fan known as the Abbotsford Outwash.
3. Fort Langley Formation: glacio-marine silt and clay with minor sand and some gravel;
formerly mapped as Cloverdale Sediments.
4. Fort Langley Formation: glacio-marine till-like mixtures of silt, clay, and gravel; formerly
mapped as Whatcom Sediments.
5. Capilano Sediments: glacio-marine stony silts and clay; formerly mapped as Newton
Stony Clay.
6. Vashon Drift: sandy loam lodgement till; formerly mapped as Surrey Till.
7. Sumas Drift: sandy loam lodgement and flow tills; formerly mapped as Sumas Till.
RESULTS OF THE SURVEYS
The results of the seismic-velocity surveys are graphically summarized in Figure 1. The
significance matrix of ‘1’ values (Table 1) indicates that there are significant differences (at
P = 0.025) between the mean velocities of most pairs of geological units; only distinctions
between two of the glacio-marine units and between the two tills are not statistically
significant. Nevertheless, these results are clearly disappointing; the considerable overlap in
the velocity distributions indicates that it would be foolhardy to base identification of a
deposit onjust afew seismic measurements. In fact the results further suggest that the sample
sizes adopted in the survey represent near-minirnal sizes for distinguishing among the means
in several cases. This fact considerably limits the: diagnostic efficiency of a seismic analysis in
this particular region.
Nevertheless, where large samples (>50?) of velocity measurements are available, the
trends they describe may be useful in establishing or confirming geological boundaries in the
field area. For example, Figure 2 shows an 1I-km seismic velocity transect which appears to
be responsive to the type of surficial geology occurring along it. The transect from A to B
indicates seismic velocities of 500-600 mls in the Sumas Drift and a distinct drop to about
400 m/s just beyond the boundary with the Fraser River Sediments. This low velocity is
maintained with little variation until the Fort Langley Formation is encountered. Here the
seismic velocities increase abruptly to more than 1200 mls and subsequently drop across a
small wedge of Vashon Drift, only to increase yet again at the boundary with the Capilano
Sediments. The low velocity at B probably corresponds to apocket of Vashon Drift, although
it is mapped as a peripheral exposure of Capilano Sediments; it is often extremely difficult to
distinguish between these units in the field.
414
LE GEOGRAPHE CANADIEN
Fort Langley Formation \
Vashon Drift
Capilano Sediments
Fraser River Sediments
Sumas Drift
E I600
1wO
I
500
I
0
A
10
2.0
3.0
4.0
6.0
5.0
Km.
7.0
8.0
9.0
10.0
11.0
B
FIGURE
2. A seismic velocity transect across five geological units near Vancouver, British Columbia.
A far more convincing separation of the sample distributions of seismic velocity can be
made on the basis of the general environment of deposition. The units shown in Figure 1 tend
to cluster in three velocity groups corresponding with the three environments of deposition:
fluvial/glacio-fluvial (samples 1 , 2 A , and 2 B ) , glacio-marine (samples 3 , 4, and 5 ) , and ice
contact (samples 6 and 7). The basic data have been combined to provide the three velocity
distributions shown in Figure 3.
The fluvial/glacio-fluvial material (see Figure 3 ~has
) a relatively low median velocity (V,J
of 533 m/s, probably resulting from the intergranular shearing common in relatively dry, low
density, and noncohesive sands and from the plastic rather than elastic deformation of the
organics. The velocity distribution is quite peaked, is markedly skewed towards small
velocities, and has a relatively small range of about 1000 m/s. The marked skewness is
caused by the preponderance of very low-velocity organic sediments.
The second environmental group (see Figure 3 ~ )consisting
,
of the tills, has a considerably
higher median velocity of 1062 m/s. This distribution is more symmetrical than that for the
fluvial environment and includes a velocity range of about 2000 m/s. It seems rather likely
that the relatively fine grain size, together with glacial compaction, yield velocities in this
case that are higher than those associated with sediments of the first group.
The glacio-marine sediments display the highest seismic velocities ( V , = 1472 m/s) and
the greatest velocity range (about 3000 mls). These characteristics suggest that the glaciomarine sediments have a higher and more variable density than materials from the other two
environments. Actually, the relative seismic velocities of the second and third groups shown
in Figures 38 and 3c are somewhat surprising when compared with the findings of Easterbrook in northern W a ~ h i n g t o nhe
; ~found that ice-compacted tills have higher bulk-densities
and lower void ratios than glacio-marine units in that area. In contrast, it seems that any
compaction differences in the present case are obscured by the marked difference in grain
size between tills and glacio-marine sediments: the tills average 60 per cent sand, 37 per cent
silt, and 3 per cent clay, while the glacio-marine sediments consists of 10-40 per cent sand,
about 50 per cent silt and 10-50 per cent clay.5 Furthermore, the moisture content of the
glacio-marine units is likely to be higher than that in the tills during the summer months.
CONCLUSION
The foregoing analysis indicates that average seismic velocities can provide a means of
distinguishing between most of the selected geological units. It provides also the not surprising conclusion that seismic velocities are more effective when distinguishing between sediments from different depositional environments than between units of the same depositional
environment. But, in both cases, distinctions are possible only if relatively large numbers of
velocity measurements are available for analysis. Offsetting this disadvantage is the fact that
seismic velocity measurements are rapidly obtained (about one every 5 to 10 minutes on site).
GEOGRAPHICA
415
FIGURE
3. Seismic-velocity distributions for sediments from three depositional environments near
Vancouver. British Columbia.
NOTES A N D REFERENCES
1 See, for example, H. Brandt, ‘A study of the speed of sound in porous media,’ Journal ofApplied
Mechanics, 22 (1955). pp. 479-86, and ‘Factors affecting compressional wave velocity in unconsolidated marine sediments,’ Journal ofrhe Acousrics Society ofAmerica, 32 (1960), pp. 171-9; M.R.J.
Wyllie, A . R . Gregory, and L.W. Gardner, ‘Elastic wave velocities in heterogeneous and porous
media,’ Geophysics, 23 (1956), pp. 41-70, and ‘Experimental investigation of factorsaffecting elastic
wave velocities in porous media,’ Geophysics, 23 (1958), pp. 459-93; J.W. Nafe and C.L. Drake,
‘Variation with depth in shallow and deep water marine sediments of porosity, density, and velocities
ofcompressional and shear waves,’ Geophysics, 22 (1957), pp. 523-53; B.O. Hardin and R. Richart,
416
THE CANADIAN GEOGRAPHER
‘Elastic wave velocities in granular soils,’ Journal of Soil Mechanics (Foundations Division), 89
(1963), pp. 33-65; W. Brutsaertand N.J. Luthin, ‘The velocities of sound in soils near the surface as a
function of the moisture content,’ Journal of Geophysical Research, 69 (1964). pp. 643-51; G.P.
Eaton and J.S. Watkins, ‘The use of seismic refraction and gravity methods in hydro-geologic
investigations,’ in L. W. Morley (ed), Mining and Groundwater Geophysics (Geological Survey of
Canada, Economic Geology Report 26, 1967), pp. 544-68; and A.A. Briones and G. Vehara, ‘Soil
elastic constants: I . Calculations from sound velocities,’ Soil Science Society ofAmerica Journal, 41
(1977), pp. 22-5.
2 J.S. Watkins and A.M. Spieker, ‘Seismic refraction survey of Pleistocene drainage channels in the
lower Great Miami River Valley,’ UnitedStates GeologicalSurveyProfessional Paper, 605-B(1971),
pp. 1-17; and W.J. Scott and J.A. Hunter, ‘Applications of geophysical techniques in permafrost
regions,’ Canadian JournalofEarth Sciences, 14 (1979), pp. 117-27, and references therein.
3 The standard reference maps and geological reports for this area are by J.E. Armstrong, ‘Surficial
geology of Vancouver area, British Columbia,’ Geological Survey of Canada, Paper 55-40 and Map
55-40 (1956); ‘Surficialgeology of New Westminster map-area, British Columbia,’ Geological Survey
of Canada, Paper 57-5 and Map 16-1957 (1957); and ‘Surficial geology of Sumas map-area, British
Columbia,’Geological Survey of Canada, Paper 55-9 and Map 92~/1(1960).Although Armstrong has
updated the geological maps for the area they had not been published at the time of writing. Because
they will soon be available (as Maps 1 4 8 4 ~and 1 4 8 5 ~ofthe New Westminster and Mission map-areas
respectively), however, the revised nomenclature has been adopted in this study.
4 D.J. Easterbrook, ‘Void ratios and bulk densities as means of identifying Pleistocene tills,’ Geological Society ofAmerica Bulletin, 75 (1964), pp. 745-50.
5 These data are taken from the published Armstrong papers noted in 3.
[EDWARD
J. H I C K I N ,
Simon Fraser University]
THE TREATMENT OF COMPARATIVE ADVANTAGE IN ECONOMIC
GEOGRAPHY TEXTBOOKS
The principle of comparative advantage provides considerable insight into our understanding of two fundamental questions in the field of economic geography. These are, first, why a
region specializes in the production of specific goods and, second, why a specific movement
of goods takes place between particular regions. These two questions are closely related for,
as Isard (1956: 53) noted, ‘(1) location cannot be explained unless at the same time trade is
accounted for and (2) trade cannot be explained without the simultaneous determination of
locations. ’
Given the importance of the questions to which the comparative advantage concept is
relevant, it might be expected that it would have received a careful and thorough treatment in
introductory textbooks in economic geography. Surprisingly, this is not the case, as I will
attempt to show in this review. First, however, a brief theoretical exposition should prove
helpful.
Probably the best way to illustrate what is meant by comparative advantage is to consider a
simple example of the type used by Ricardo. Suppose that there are only two countries in the
world, x and Y,and that they produce only two goods, wheat and cloth. Assume that labour is
the only production factor used in producing the goods. Assume also that the wheat and cloth
can be transported readily between the countries at zero transport costs, but that labour
cannot move from one country to the other. Despite the lack of realism in these assumptions,
an examination of two cases involving the hypothetical countries can provide considerable
insight into the principles underlying specialization and trade.
In the first case suppose that, for each man-day of labour, country x can produce more
wheat but less cloth than country Y. x is said to have an absolute advantage over Y in the