GOODACRE - A Statistical Analysis of the Spatial Association of Seismicity With Drainage

Tectonophysics, 217 (1993) 285-305

Elsevier Science Publishers B.V., Amsterdam

285

A statistical analysis of the spatial association of seismicity with drainage patterns and magnetic anomalies in western Quebec

A.K. Goodacre a, G.F. Bonham-Carter b, F.P. Agterberg b and D.F. Wright b a Geophysics Division, Geological Survey of Canada, I Observatory Crescent, Ottawa, Ont. KlA OY3, Canada Mineral Resources Division, Geological Survey of Canada, 601 Booth Street, Ottawa, Ont. KlA OE8, Canada

(Received July 2, 1991; revised version accepted June 9, 1992)

ABSTRACT

Goodacre, A.K., Bonham-Carter, G.F., Agterberg F.P. and Wright, D.F., 1993. A statistical analysis of the spatial association of seismicity with drainage patterns and magnetic anomalies in western Quebec. Tectonophysics, 217: 285-305.

The weights of evidence statistical method, previously applied to the problem of relating mineral occurrences to geological and geomorphological features, has been applied to the question of whether in a particular area there may be a spatial correlation between seismic epicenters and various geological and geophysical parameters. We find that seismicity in western Quebec is associated with NNE-trending drainage features and positive aeromagnetic anomalies. Our interpretation is that NNE-trending zones of weakness are being re-activated in the presence of a NE-SW regional compressive stress field and that less competent zones in the upper crust, as delineated by positive aeromagnetic anomalies, are causing stress and, hence, seismicity to be concentrated in the subjacent middle crust.

Introduction

We know from both historical accounts and the output of present-day seismic observatories that much of the seismic activity in eastern Canada (as, for example, described by Adams and Basham, 1989) tends to occur in the vicinity of the Ottawa and St. Lawrence River Valleys (Fig. 1). There is a large concentration of seismicity beneath the St. Lawrence River in the region of Charlevoix (center of diagram) and two rather more diffuse regions to the northeast and the southwest. The question is: why does generally low-level but persistent seismic activity occur in these areas but not in others? Although the stress field in the Earths crust is essentially lithostatic, eastern Canada appears to be subjected to an

Correspondence to: A.K. Goodacre, Geophysics Division, Geo-

logical Survey of Canada, 1 Observatory Crescent, Ottawa,

Ont. KlA OY3, Canada.

additional small, but pervasive, NE-SW-oriented compressive tectonic stress field related to the motion of the North American lithospheric plate (e.g., Richardson et al., 1979; Adams, 1989). It is generally thought that earthquakes in eastern Canada occur along pre-existing zones of weakness (e.g., Goodacre and Hasegawa, 1980; Hasegawa, 1988; Talwani and Rajendran, 1991). If this is the case, then according to Andersons theory of faulting (Anderson, 1951) we would expect zones of weakness with certain favourable orientations to be preferentially reactivated. In addition, we would also expect the heterogeneous structure of the upper crust to concentrate stress in certain areas due to the different mechanical properties of various rock types (e.g., Campbell, 1978). The combination of these two mechanisms may contribute to a concentration of seismicity in some areas.

We have chosen to study the seismically active area in the Papineau-Labelle-Laurentides region of western Quebec (as outlined by the box in

0040-1951/93/$06.00 0 1993 - El sevier Science Publishers B.V. All rights reserved

286 A.K. GOODACRE ET AL.

Fig. 1) because there are a large number of well located events detected by the Eastern Canada Telemetered Network (ECTN) and the area is well mapped geologically, geophysically and topo- graphically. Our study extends earlier work of Forsyth (1981) which was done without the bene- fit of the full ECTN seismic array. In order to minimize the effects of errors in locations, we did not include earthquakes recorded prior to 1981. Nevertheless, as far as the extent and rate of seismic activity in the study area are concerned, our data set is typical of earlier epochs keeping in mind the reduced ability of earlier seismic net- works to detect small events.

In order to simplify the analysis, we are focus- ing on the problem of why seismicity is occurring in active areas and not on the equally important question as to why it is not occurring in the adjacent quiescent regions. Also, except for the effect of earthquake magnitude on the ability of the ECTN to provide precise locations, we generally are not making a distinction between large- and small-magnitude earthquakes. This is partly because individual subsets would contain only a few data points and partly because the earthquakes, which range in magnitude from about 0.9

up to 3.7, do not appear to exhibit any magnitude-dependent distribution.

Since topography is often a sensitive indicator of underlying structure (e.g., Kumarapeli, 1985) we have chosen drainage patterns to delineate potential planes of weakness in the Earths crust. We decided to utilize drainage patterns rather than to employ the more general class of linea- ments which might be obtained from satellite photographs, etc. because of the presence of water in the drainage system. The role of water in enhancing seismicity (e.g., Costain et al., 1987) is a controversial subject (e.g., Major and Iverson, 1988 and reply by Costain et al., 1988) but it seems clear to us from the pattern of seismicity in the Charlevoix region and the distribution of re- located earthquakes (Adams et al., 1989a) in the Sept Iles region to the northeast, where almost all of the seismicity lies beneath the St. Lawrence River, that the presence of water must play an important role. Certainly, one has the impression upon inspecting the diagram in Forsyths (1981) paper, showing the patterns of drainage and seismicity in the western Quebec seismic zone, that the epicenters in this region tend to be associated with drainage features.

Fig. 1. Seismic activity along the Ottawa and St. Lawrence River valleys from 1985 to 1990. Rectangular box delineates the study

area.

ASSOCIATION OF SEiSMiC1l-f WITH DRAINAGE PATTERNS AND MAGNETIC ANOMALIES, QUEBEC 287

One also notes in Forsyths paper that seismic epicenters tend to be concentrated in regions of positive aeromagnetic anomaly. This correlation was reiterated by Forsyth et al., (1983). Since aeromagnetic anomalies reflect geological structure, this suggests a possible relation between the spatial distribution of epicenters and near-surface geology.

In order to further pursue the idea that earthquakes may be spatially correlated with surface geology, drainage, magnetic anomaly patterns, and/or gravity data we have taken the earthquakes recorded in the time interval 1981 to 1988 in the Papineau-Labelle-Laurentides region of western Quebec (a somewhat smaller region than that considered by Forsyth) and applied the weights of evidence (e.g., Agterberg, 1989a) statistical modelling approach, which is used to study the spatial relationship of mineral occurrences to fault zones and geological formations, to investigate the spatial reIationship of seismic epicenters to geology, drainage and gravity and aeromagnetic anomaly patterns in the study area.

From a statistical viewpoint, the probiem of finding spatial associations between a set of earthquake epicenters and geological, geophysicat and geomorphological maps is similar to the problem of relating mineral occurrences to map patterns. Recent work by Agterberg (1989a,b), Agterberg et al. (19901, Bonham-Carter et al. (19881 and Bonham-~rter and Agterberg (1990) has employed a weights of evidence method to model mineral potential using a weighted combination of evidence from explanato~ predictive map patterns. Weights of evidence are determined for each map pattern, using the known distribution of mineral occurrence points, and a measure of spatial association is calculated between the points and the map pattern. Using a Bayesian statistical model, multipie map patterns are then combined with a prior probability to produce a postetior probability map reflecting mineral potential. Conditional independence of the explanatory patterns with respect to the points is assumed. The weights of evidence method is useful both as an inductive too1 to search and test for spatial associations between point distributions and map patterns; it is also used as a

deductive tool to determine the outcome of modelling the combination of explanatory maps.

In applying the weights of evidence method to earthquake epicenters, the principal goal of this study is to test whether epicenters are spatially associated with drainage patterns, geological map units, and regional gravity/magnetic anomaly patterns-this is the inductive phase. The deductive phase is to produce an epicentre probability map, based on the known epicenters, which could be used in a variety of ways: for characterizing the spatial distributions of earthquakes; for help- ing to understand their relationships to geological factors; and for predicting areas with an elevated potential for earthquakes.

An important difference between earthquake epicenters and mineral occurrences is the uncertainty in their respective point locations. Epicen- ter positions are usually only known to within a radius of a few kilometres; in the study area the uncertainties in location are estimated to be of the order of 2 to 4 km. On the other hand, mineral occurrences can usually be located to within tens of metres. Another important difference between mineral deposits and earthquakes is that mineral deposits are at or near the surface whereas many earthquakes in the western Que- bec region are at depths ranging from 5 to 20 km. Depending on the attitude of the zones of weakness upon which they are presumed to occur, the epicenter locations may be considerably displaced from the faults as mapped at the surface. As a result, it may be difficult to relate some epicenter locations with specific fracture zones. The statistical approach used here not only assumes that the fault zones are nearly vertical but that there are no appreciable systematic errors in the epicenter locations.

Data sets

Seismicity and drainage patterns are shown for the study area in Figure 2. The locations of the three closest ECTN seismograph stations are in- dicated by solid stars. The seismic observatories are spaced in such a way that epicenters in this area can be reasonably well located. After screen- ing out a few small events related to surface

288

blasting, etc., a set of 147 epicenters, recorded during the period 1981-1988, was selected for study. Because stronger events are, generally speaking, more accurately located than weaker ones, and because weak events in some areas of the network may go undetected, a sub-set of 96 epicenters, corresponding to events of magnitude 2.0 or greater, was also considered to see whether our results with the main set were affected by location errors and/or a non-uniform probability of being detected due to low earthquake magnitude.

A Geographic information System (GE) termed SPANST (Spatial Analysis System)

A.K GOODACRE ET AL.

(TYDAC, 1989; Bonham-Carter and Agterberg, 1990) was used for the study. GeoIogicai map units, lakes and streams were digitized from pub- lished maps, as summarized in Table 1. A spatial database was established with a UTM projection, central meridian 75W, with co-registered point (epicenters), vector (streams, geological contacts) and raster (geology, geophysics) components. The geology map was converted to a quadtree (hierarchical raster data structure used by the SPANSTM software) having a spatial resolution of about 30 m. The geophysical maps (Table 1) were imported from grid fries with a resolution of ZOO m and converted to quadtrees, having a spatial

76.0W 74.OW

Fig. 2. Location map showing drainage, seismic epicenters (dots) and the three closest seismic observatories (stars).

ASSOCIATION OF SEISMICITY WITH DRAINAGE PA?TERNS AND MAGNETIC ANOMALIES. QUEBEC 289

resolution of about 30 m. Spatial resolution in the raster database was therefore maintained at a level far in excess of the positional accuracy of actual locations of epicenters, geological contacts, stream locations or geophysical contours. This was partly for display purposes, and partly to ensure that digitizing errors could be ignored.

Even though the most of the earthquakes lie at depths of 5 to 20 km, it is clear from inspection of Figure 1 that many epicenters coincide with, or lie very close to, streams in the study area. This argues for some sort of verticality between seismicity and the drainage pattern. However, the drainage pattern, as obtained in digital form, consists of a series of many very short, straight-line segments which are often only a few tens of meters in length whereas the earthquakes are, as mentioned, several kilometers deep. It was therefore decided to generalize the drainage pattern to a set of straight-line segments which are of the order of 10 km or longer in the expectation that the longer segments are more likely to represent zones of weakness which extend deeper in the crust. In this way there is a better balance be- hveen length of straight-line segment and depth of seismic event and we are not trying to associ-

ate a deep seismic event with a small surface feature.

An interpretive lineament map (Fig. 3) was made by asking someone, who had no pre-con- ceived ideas what he could expect, to hand-fit straight lines to stream segments as depicted on standard 1:250,000 topographic maps covering the study area. After digitizing, these lines were bro- ken down by orientation into ten classes, each class being 18 wide. A set of proximity maps, one for each orientation class, was generated by re- placing the lines by strips which were made progressively wider at 1 km intervals up to a maxi- mum corridor half-width of 15 km. These proximity maps (15 maps per orientation class) were used to calculate the distance between a given epicenter and the closest straight-line segment with a precision of 1 km (an epicenter would lie outside a particular strip but inside the next wider strip). It should be noted, however, that beyond a certain corridor width, depending upon the geometry of the particular stream linears being considered, corridors corresponding to adjacent stream linears start may start to overlap making the identification of a particular epicenter with a particular lineament ambiguous.

TABLE 1

Inputs to the spatial database

Input

Geology

Maps units

Drainage Lakes

Streams

Stream linears

Geophysics

Total magnetic field

Bouguer anomaly (vertical gradient)

Seismic events

Spatial data type Digital source Reference

polygons table digitized 1

polygons table digitized 2

lines table digitized 2

lines labelled by orientation table digitized 2

raster geocoded grid file 4

raster geocoded grid file 4

points geocoded grid file 5

1. Feuilles: Ottawa (31G); Mont Laurier (315) (echelle 1:250,~~, Cites Mineraux Quebec, Ministere de IEnergie et des

Ressources, Quebec.

2. Map sheets: Ottawa (31G); Mont-Laurier (315) (scale 1: 250,000), Surveys and Mapping Branch, Energy, Mines and Resources,

Ottawa.

3. Interpretation by authors; local software for labelling lines by orientation.

4. Geophysical Data Centre, Geophysics Division, Geological Survey of Canada.

5. Seismology Section, Geophysics Division, Geological Survey of Canada.

290

Based upon epicenter density maps which were calculated by counting the number of epicenters within a circular moving window of radius 15 km, the study region for all the weights of evidence calculations was subsequently restricted to the area bounded by the scallop-shaped line in Fig- ure 3, thereby excluding the region in the northeastern corner of the map which had no recorded earthquake activity during the 1981-88 period.

Weights of evidence method

The weights of evidence method for binary maps, as discussed by Agterberg et al. (19901, is

A.K. GOODACRE ET AL.

summarized here and then an extension of the method for maps with multiple classes (e.g., grey-tone or contour maps), which was developed for this study, is presented. Further details of the extension are given in Agterberg and Bonham- Carter (1990). Both binary and grey-tone maps are used in this study for analysing magnetic anomaly data and for predicting earthquake epicenters. In employing the weights of evidence method we need to deal with the concept of overlapping areas. Therefore, instead of dealing with points and lines which have no area, we replace points by circles and lines by strips.

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Fig. 3. Map showing straight-line segment approximations to drainage and epicenters according to magnitude.

ASSOCIATION OF SEISMiCiTY WITH DRAINAGE PATTERNS AND MAGNETIC ANOMALIES, QUEBEC 191

Weights of e&fence for binary maps

Given a binary map, B, defining the presence or absence of some parameter (such as a particular geological formation) and a map of points, D, where each point is dilated to a circle of small, but arbitrary, area (e.g., 1 km), the weighting factors W+and W- can be caIculated from the ratios of conditional probabilities, as follows:

w+ = log, P(BID)

i I P(BID)

and

w-= log,

where B and E refer to the presence or absence, respectively, of the binary map pattern and D and D refer to the presence or absence, respectively, of the points (small circles). The contrast, C, which is a measure of spatial association between the binary pattern and the points, is given by C = Wf- W-. The conditional probabilities employed in these formulae are determined by mea- suring the areas of overlap between the points and the binary map pattern. For exampIe:

P(BID)= area( B i-l D)

area( 0)

is the conditional probability that a point coin- cides with the binary pattern; to determine this ratio requires the measurement of (a> the area where points occur on the binary pattern, and (b) the total area occupied by all the points. For cases where the points occur on the binary pattern more often than would be expected due to chance, W+ will be positive, W- wil1 be negative, and the magnitude of the contrast, C, reflects the overall spatial association of the points with the binary map pattern. To give an example, suppose we took all of the black pieces of a chess set and arranged them on a chess board. If all of the black pieces were on the black squares, the contrast would be termed positive, if all the pieces were on the white squares the contrast would be negative and if half of the pieces were on black

squares and the other half on white squares, the contrast would be zero.

The question of determining whether the magnitude of the contrast is large enough to be statistically significant can be tested as follows. The variance of the contrast, s(C), can be estimated from the expression:

S2(C) = 1 1

area(BnD) area(BnL))

1 1 +

area(BflD) + area(Bn D)

based on an asymptotic result which assumes that the number of points is large (Agterberg et al., 1990). Because the areas assigned to individual points are very small, the second and fourth terms are small in comparison with the first and third terms in this expression. Mathematically, as the number of points increases, the frequency distribution of the contrast becomes approximately normal (cf. Bishop et al., 1975). If C is normally distributed around zero, then the null hypothesis that there is a lack of spatial association can be rejected if I C 1 > 1.96 s(C) with 95% probability; i.e. in only 1 case out of 20 would you expect values of /C 1 greater than 1.96 s(C) due to chance. In some cases the number of points is not large and this situation will be discussed in a subsequent section.

These calculations employing binary patterns can be extended to maps which contain more than two classes by treating the area of a specific class as B and combining the areas of all the other classes and treating them as B. In the case of a categorical-type map (e.g., geology) each map unit can be independently tested to determine whether more points occur on that unit (class) than would be expected due to chance. In the case of maps where classes reflect intervals of some continuously varying numerical quantity such as, for example, magnetic anomaly, values of W+, W- and C can be calculated by choosing a threshold value which divides the classes into two groups, one group lying above the threshold value, the other below, and treating the groups as B and B. We can then progressively alter the threshold


value to seek the greatest (or least) contrast, C. We can also deal with the individual classes (intervals) and make a table showing cumulative binary area versus the weights and associated values of contrast. However, the resulting values of weights and contrast are usually quite noisy, because the number of points falling within a small contour interval of the predictor map is small. A method which helps to overcome this problem of estimating weights for non-cumulative classes by using the cumulative weights and areas for the calculation (Agterberg and Bonham- Carter, 1990) is described in the following section.

Weights of evidence for grey-tone (contour) maps

Two quantities N, and n., are determined for the variable x represented on the grey-tone contour map. N, is a measure of the sub-area A, containing all points with values greater than X, and n, is the number of epicenters within this sub-area. If N, is equal to the number of small unit cells (e.g., 1 km) within A, with or without epicenters, then P, = n,/N, can be defined as the probability that one of these unit cells contains an epicenter. It is noted that N, is practi- cally error-free whereas n, is subject to a consid- erable amount of uncertainty because it is regarded as the realization of a random variable. Using the same type of formula as before:

and the corresponding variance is:

1 1 s2( wX+) =

area( A, ll D) + area( A, n D)

Because the unit cell is about 2,000 to 20,000 times smaller than typical values of N, in our applications, we have:

P(A,ID) =n

and, consequently:

w, = log,{ P( A, I D)}

and

s2( Wz) = n;

Because the total area of the contour map and the total number of epicenters within the study area are both known, it is possible to estimate the weight of evidence, WX+, and its standard deviation, s(Wz ), for any sub-area A,.

If the unit cell area is sufficiently small, P, z 0, where 0, = P,/(l -P,> represents the posterior odds corresponding to P,. In the following derivation, it will be assumed that a very small unit cell has been selected for determining N, so that the odds can be replaced by the corresponding probability. Writing the prior probability as P, it follows that:

P,=P.exp(Wx+)

Suppose that AN, = Nx+bx -N, represents a small increase in the measure of A, for a small decrease AX in the contour value X. Because the enlarged sub-area A,+A, =A, + AA, contains n x+Ax = n, + An, epicenters, the posterior probability for the increase is PX,dX = AnJAN,. The double subscript (x, Ax) is used to indicate that P x,dx depends upon both x and Ax. In general, it is not possible to estimate PX,dX directly, because An, is too small. Moreover, differences between successive values of n,, e.g., for adjacent contours of x on the map, are subject to noise. However, the following indirect method can give useful results. We have:

where the tilde denotes average value. This nota- tion is introduced to show that we are dealing with expected values of random variables. Con- version to weights and dividing by the prior probability gives:

exp( !Ax)

N x+Ax = . exp( l&z+AX) - N, . exp( I&)

AN,

In this expression, L?*TAX represents the weight of the small area AA, contained between the con-

ASSOCIATION OF SEISMICITY WITH WRAINAGE PATTERNS AND MAGNETIC ANOMALIES. QUEBEC 293

tours for x and (x + Ax). Definition of an auxil- iary function:

with

AY =N,+*x. exp( @,&,) - N, * ew( J@)

gives:

and consequently:

4 =log, -g- I i x where the quantity:

Ax-+0

represents the weight associated with the contour for x itself. Note that y and w, are expected values of random variables. In general, y can be modelled as a monotonically increasing function of N,. A sequence of observed values for y as calculated from the measured values N, and n, can be plotted against N, and a continuous curve (e.g., a spline curve> fitted to the data. The pur- pose of this procedure is to reduce the variance associated with differences between successive measurements of n,. The first derivative, or slope, of the curve gives an estimate of w,. In practice, the curve can be approximated by a series of consecutive straight-line segments which may be labelled i (i = 1 2 > ,.*, p). In this case, each straight-line segment can be identified with a map area, bounded by two contours, such that within each area the associated values of w,, Wje and the posterior probability Pi = P exp(Wi.) may be regarded as being constant.

The preceding indirect method may be summarized as follows:

(1) the quantities N, and n, are obtained for an ordered sequence of values of X;

(2) values of Wz and s(Wz) are obtained by the usual method for estimating weights (of evidence);

(31 A spline curve is then fitted to values of the product y = LV~ exp(WT>;

(4) The first derivative of the resulting estimate of y, denoted by y^, is a variable weight, denoted by GX;;. which depends upon X;

(5) The resulting values of GX are grouped into a suitable number, p, of classes and the final weights W, are regarded as being approximately constant within the areas to which they apply.This type of model with p > 2 classes of constant weight may be more applicable in many cases than the binary model with p = 2.

integration of multiple sources of evidence

The deductive modelling step is carried out using a number of predictive maps, selected on the basis of the degree of their spatial association with the epicenters. A prior probability is calculated, usually assuming a constant value equal to the total area occupied by the small circles, which represents the point area, divided by the entire study area, i.e. the expected value if a large number of unit cells were chosen from the map at random.

Then:

Opkost = exp log, Oirior + k W, ( j-1 i

where the odds, 0, are related to probability by 0 =P,/(l.O -P> and for the j-th map out of rr maps, I$ is the weight for the k-th map class. The value of the index k will be 1 (for + > or 2 (for -) for the binary case, but will attain larger values for multi-state contour maps. In this latter case a weight II+ . IS calculated for each mutually exclusive class. The final product is a map showing the posterior probability that a point will occur in a unit cell after converting odds back to probability. These calculations can be carried out very efficiently in a GIS where a unique conditions map is generated, with each condition being a unique set of the overlapping input map classes. In cases where the number of unique conditions is small (say a few hundred), a variety of models with different weights can be evaluated and displayed interactively, even though the spa- tia1 resolution of the map may involve large raster images (1000 X 1000 or larger).

294

The model for combining maps to predict epicentre density is based on an application of Bayes Rule. The assumption must be made that the predictive maps are spatially independent of one another with respect to the epicentre points. In the case of binary predictive maps, this assumption can be tested using pairwise tests and an overall goodness-of-fit test (Agterberg et al., 1990).

Geology

A simplified geology map, with epicenters superimposed, is given in Figure 4. Precambrian basement rocks are exposed throughout most of the study area except for the southernmost portion which is covered by a relatively thin layer of flat-lying Palaeozoic sedimentary rocks. The orig-

A.K. GOODACRE ET AL

inal 25 geological units have been lumped to- gether into 12 units to reduce the complexity of the diagram. There is a one-to-one correspondence between the legend of Figure 4 and the units in Table 2 except for the term Undiff (erentiated) sediments in the legend of Figure 4 which comprises units 2, 5, 6, 7 and 25 in Table 2 and Migmatite/paragneiss in Figure 4 which corresponds to units 19 and 20. Each of the original 25 units is treated as a binary map in the calculations. Out of the original 25 map units, 17 units contain epicenters, but, as Table 2 shows, only 5 units have more than 10 out of 147 epicenters. Of these, only the Helikian monzonite (unit 11 in Table 2, area 927 km2) and the Aphebian mixed paragneiss/amphibolite (unit 18 in Table 2, area 4997 km21 have significantly more epicenters than expected by chance. When the total of

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BEDROCK GEOLOGY

Legend Undif f Sediments Marble and Calc-silicates Quartzite Mixed Paragneiss/Amphibolite Migmatite/Paragneiss Charnokitic Gneiss Granitic Gneiss/Granite Syenite Monzonite Mangeri te Anorthosite Gabbro/Gabbroic Anorthosite

I . . . 145.3ON 76.OW 74.OW

Fig. 4. Geological map, with some of the original map units combined, showing locations of epicenters. As explained in the text,

only the Aphebian paragneiss shows a consistently significant association with epicenters.

ASSOCIATION OF SEISMICITY WITH DRAINAGE PATTERNS AND MAGNETIC ANOMALIES. QUEBEC 29.5

TABLE 2

Map units with number of epicenters, areas of unit and weights. Italicized values are significant, i.e. I C I 1 1.96 s(C). The monzonite and paragneiss units have more epicenters than would be expected if epicenter locations were independent of geology. The anorthosite has fewer epicenters than expected, although ICI < 1.96 s(C). The values in brackets are for the 96 epicenters with magnitude > 2

Map unit Area # Points WC W- C s(C) (km)

2. Limestone/dolomite 84 5. Sandstone/dolomite 229 6. Sandstone 386 7. Conglomerate/sandstone 352

10. Syenite 693 11. Monzonite 927 12. Nangerite 1087 14. Anorthosite-gabbro 440 15. Anorthosite 1074 16. Marble 2729 17. Quartz& 1618 18. Paragneiss 4997 19. Migmatite 585 20. Migmatite, paragneiss 323 21. Gneiss charnockite 3995 23. Granitic complex 603 25. Undiff. Palaeozoic 3020 Total 23142

2 2

i 2

11 6

15 6

43 3 2

23 4

21 147

(0) (2) (1) (2) (2) (3) (6) (0) (3)

(11) (3)

(29) (2) (1)

(17) (3)

(111 (96)

1.38 t-1 - 0.01 f-) 1.39 (-) 0.72 (-) 0.37 (0.80) - 0.00 (-0.01) 0.37 (0.81) 0.72 (0.72)

- 0.86 t - 0.43) 0.01 (0.01) - 0.86 (-0.43) 1.00 (1.01) - 0.07 (0.36) 0.00 (-0.01) - 0.07 to.371 0.71 (0.72) - 0.75 t - 0.32) 0.02 @.W -0.76 (-0.33) 0.71 (0.72)

0.68 (- 0.20) - 0.04 (0.01) 0.72 t-0.21> 0.32 (0.59) -0.10 (0.33) 0.00 ( - 0.02) -0.10 (0.35) 0.42 (0.42) - 0.99 t-1 0.01 t-1 - 1.00 (-1 1.00 (-) - 0.78 1: - 0.35) 0.02 (0.01) -0.80 ( - 0.36) 0.58 (0.591 -0.10 (0.02) 0.01 (- 0.00) -0.11 (0.02) 0.27 (0.32) - 0.50 f0.76) 0.03 (0.04) - 0.52 ( - 0.80) 0.42 (0.591

0.35 (0.38) - 0.12 (-0.13) 0.47 to.sl) 0.18 (0.22) -0.17 t--&Is) 0.00 (0.00) -0.17 (-0.1% 0.58 10.72)

0.02 (- 0.25) -0.00 (0.00~ 0.02 (-0.25) 0.71 f1.01) - 0.05 to.71 0.01 f-0.01) - 0.06 (0.09) 0.23 10.27)

0.09 (0.23) - 0.00 t-0.01) 0.09 (0.24) 0.51 (0.59~ 0.14 ( - 0.68) - 0.02 to.011 0.16 (-0.10) 0.24 (0.32)

147 epicenters is reduced to 96, by excluding those seismic events with magnitude < 2, the number of epicenters on the monzonite drops from 11 to 3, and only the paragneiss has a significant value of C with values of WC of 0.35 (147 points) and 0.38 (96 points), This implies that the paragneiss may well be associated with earthquake activity, both small and large events. The monzonite appears to be associated with only small-magnitude earthquakes and may, therefore, be of limited significance. It should be mentioned that the seismicity in the southernmost portion of the study area, although correiat- ing spatially with the flat-lying Palaeozoic sedimentary rocks, actually occurs in the underlying Precambrian basement.

As expIained in the discussion of weights of evidence for binary maps (see previous section), the statistical test for significance of the contrast, C, is based on an asymptotic result for s(C) assuming that the number of points is large. This condition is not satisfied for several map units in Table 2 and it may be suspected that estimates of

s(C) in the last column are inaccurate when the number of points is small. In order to assess this problem, we have applied the following alterna- tive significance test based on a different statistical model. It can be shown (e.g., Stoyan et al., 1987, pp. 36-401, that if II points are randomly distributed in a region with area A$., then the number of points in a sub-region with area Ns is a random variable possessing a binomial distribution with mean np and variance nptl -D) where p = NB/NT. In Table 2, n is equal to either 147 or 96 where the latter number refers to the subset where earthquake magnitude is greater than or equa1 to 2.0. For the monzonite (unit Ii), p = 0.040, and for paragneiss (unit 18), p = 0.216. The corresponding binomial means are: 5.9 (3.8) for monzonite, and 31.7 (20.7) for paragneiss. These values are the ones expected when the points are randomly distributed. The observed numbers of epicenters are 11 (3) for the monzonite unit and 43 (29) for the paragneiss unit. According to tables for 95 per cent confidence limits for the binomiai distribution GIald, 19881,


the lower confidence limits are 6.2 (0.7) for the epicenters associated with the monzonite and 32.6 (20.5) for those associated with the paragneiss. Because this is a one-tailed test, there is only about 1 chance in 40 that these numbers would be obtained if the seismic&y were distributed at random. These results support those obtained using the asymptotic approximation for s(C) and confirm that when dealing with the full data set these two geological units appear to contain more epicenters than would be expected if the seismicity was randomly distributed but when dealing with the smaller data set we can not reject the hypothesis that the seismicity is not spatially associated with the monzonite.

r-----~~sic, - * I

N-S E-W N-S

Fig. 5. (a) Plot showing values of C f 1.95 s(C) for the stream segments in 10 orientation classes for the 147-epicenter data

set. (b) As above except for the 96-epicenter data set.

Stream segments

Using the proximity maps (derived, as described previously, from the straight-line segment approximations to the drainage pattern) in order to calculate distances between seismic epicenters and drainage features, values of weights and con- trasts based on the cumulative distribution of distance from the nearest line for the epicenters were calculated for all 150 (15 distances x 10 orientations) binary maps. Figures 5a and 5b show how C varies with orientation for the 147-epi-

center main data set and the 96-epicenter subset. To facilitate comparison between different orientations, this diagram displays the results obtained with a half-width of dilation of 5 km, but results for other distances are comparable. Notice that the 18 (NNE) orientation class is significant for both the 147-epicenter case and the 96-epicenter sub-set; the numerical results for this orientation class are given in Table 3. The direction azimuth 126 (SE) also shows a peak, which is not quite

TABLE 3

Table showing weights for spatial association between epicenters and stream segments oriented between 9 and 27 in azimuth. Values in brackets are for the 96 epicenter sub-set. Italicized values are those with 1 C 1 > 1.96 s(C)

Distance (km) Area (km*) # Points W W- C s(C)

1 1776 16 (9) 0.40 (0.25) - 0.04 ( - 0.02) 0.44 (0.27) 0.27 (0.35)

2 4023 35 (19) 0.36 (0.18) 0.09 (- 0.04) 0.45 (0.22) 0.19 (0.26)

3 6127 49 (27) 0.28 (0.11) -0.11 ( - 0.04) 0.39 (0.15) 0.18 (0.23)

4 8556 70 (42) 0.30 (0.22) - 0.21 (GO.141 0.51 (0.36) 0.17 (0.21)

5 10533 83 (52) 0.26 (0.22) - 0.26. (-0.21) 0.53 (0.43) 0.17 (0.21)

6 12270 94 (62) 0.23 (0.24) - 0.32 (-0.33) 0.55 (0.58) 0.17 (0.21)

7 14077 111 (73) 0.26 (0.27) - 0.54 (- 0.56) 0.80 (0.83) 0.19 (0.24)

8 15 323 115 (76) 0.21 (0.23) - 0.53 (- 0.57) 0.74 (0.801, 0.20 (0.25)

9 16607 121 (81) 0.18 (0.21) - 0.58 ( - 0.70) 0.76 (0.91) 0.21 (0.28)

10 17459 125 (84) 0.17 (0.20) - 0.63 (-0.81) 0.79 (1.00) 0.23 (0.31)

11 18281 128 (86) 0.14 (0.17) -0.64 ( - 0.86) 0.79 (1.03) 0.25 (0.33)

12 19224 128 (86) 0.09 (0.12) - 0.47 (- 0.69) 0.56 (0.81) 0.25 (0.33)

13 19 901 129 (87) 0.07 (0.10) -0.38 ( - 0.65) 0.45 (0.75) 0.25 (0.35)

14 20 678 133 (89) 0.06 (0.08) - 0.43 (- 0.70) 0.49 (0.78) 0.28 (0.39)

15 21205 135 (89) 0.05 (0.06) - 0.43 ( - 0.54) 0.46 (0.60) 0.30 (0.39) Total 24 228 147 (96)

ASSOCIATION OF SEISMICITY WITH DRAINAGE PATTERNS AND MAGNETIC ANOMALIES, QUEBEC 29-i

significant at the 5% significance level; this peak is not prominent for dilation sizes other than 5 km. Because the 147-epicentre case and the 96 epicentre case give very similar patterns with systematic trends and exhibit significant C values for the NNE azimuth we consider the epicentre pattern to be spatially related to the NNE linears.

Total magnetic field anomaly

We have considered the magnetic field in two forms: one a binary map where the total field anomahes are either above or below a regional

background level; the second where the magnetic anomalies have been subdivided into eight classes in order to apply the weights of evidence method for grey-tone maps. The multi-levei magnetic data will be employed in the calculations discussed in the next section; we consider here the binary map. The spatial association of epicenters with the binary magnetic map is shown in Figure 6 and it can be readily seen that many more epicenters lie in zones of elevated magnetic anomaly than would be expected if the seismicity pattern and the binary magnetic map were independent. Table 4A gives the values of W, W- and C.

7,ON

Fig. 6. T&al field aeromagnetic data in binary form. Dark areas represent magnetic anomalies greater than 156 nT; light areas less than 155 nT. Seismic epicenters are superimposed.


Gravity anomalies Binary model

We were unable to find any convincing relationship between the gravity anomaly data and the distribution of epicenters but this may be due, in part, to the rather wide spacing (= 10 to 15 km) of the gravity observations.

Predictive models of epicenters

Two predictive models have been constructed, the first based on the integration of evidence from geology, drainage and the magnetic field using binary patterns as approximations to the grey-tone contour maps. The second model is similar, but uses multiple weights for drainage- distance relations and magnetic-field grey-tone maps, in place of binary weights. It must be emphasized that we are using the term predictive in the spatial sense rather than in the more commonly used temporal sense and that in any given, fairly long, time interval we are trying to foretell whether an earthquake is more likely to occur in certain portions of the study area than in others.

Using a unit cell area of 1 km2, the prior probability was assumed to be the number of 1 km2 unit cells occupied by epicenters divided by the area of the study region, or 147/24228 = 0.00607. Table 4 gives a summary of the weights used in the model (A) and a resume of unique conditions (B). For each of the eight unique overlap conditions, the posterior probability, the associated standard deviation, and the area are shown.

Note that in class 1, with the highest posterior probability (0.014 epicentres per km2), 13 actual epicentres are observed whereas the predicted number is the probability times area, (0.014 x 714) = 10 (where we have rounded off to the nearest integer). In this region, the Helikian paragneiss is present, the magnetic field is 2 156 nT and north-northeastern streams are within 7 km, so that the probability calculation uses the W+ values for each map. In class 2, employing W+ for streams and geology, but using W- for magnetics, the posterior probability is 0.00953, with an area of 2293 km2, yielding an expected number of 22 epicenters, as compared with 16

TABLE 4

A. Summary of weighting parameters for binary model

Map Wf s(W) W- sew-) c s(C)

1. Dist. to NNE streams (> 7 km, < 7 km) 0.2639 0.0953 - 0.5395 0.1670 0.8033 0.1922

2. Total mag. field f > 156 nT, < 156 nT) 0.2272 0.1217 -0.1612 0.1128 0.3885 0.1660

3. Helikian paragneiss (present, absent) 0.3521 0.1532 -0.1157 0.0983 0.4678 0.1820

B. Unique conditions table for binary model

Class Streams Magnetics

1 + +

2 + _

3 + +

4 _ +

5 + _

6 - -

7 _ +

8 - -

Sum

Prior Probability = 0.00606

+ = Present

Geology P,,,, A km2

+ 0.01399 714

+ 0.00953 2 293

_ 0.00881 4791

+ 0.00631 435

_ 0.00599 6 280

+ 0.00429 1555

_ 0.00396 2 928

- 0.00269 5 233

P A post Observed epicenters

9.989 13

21.852 16

42.209 43

2.745 4

37.615 39

6.671 10

11.595 7

14.077 15

146.753 147

- = Absent

ASSOCIATION OF SElSMICIT? WITH DRAINAGE PATI-ERNS AND MAGNETIC ANOMALIES, QUEBEC 299

TABLE 5

Calculation of variable weights for distance to NNE streams. Weights for 15 distance corridors

Distance (km) Cumulative area (km) Wf s(W) Y S(Y) 9 *+

1 1776 0.40 0.25 2 645 664 2 667 0.30

2 4 023 0.36 0.17 5 784 982 5 652 0.25

3 6 127 0.28 0.14 8 092 1160 8 293 0.23

4 8556 0.30 0.12 11562 1387 11385 0.22

5 10533 0.26 0.11 13705 1510 13793 0.18

6 12270 0.23 0.10 15518 1606 15 847 0.15

7 14 078 0.26 0.10 18 329 1747 17 847 0.01

8 15 323 0.21 0.09 18982 1777 18 990 - 0.19

9 16608 0.18 0.09 19967 1821 19945 -0.41

10 17459 0.17 0.09 20 624 1852 20 464 - 0.58

11 18281 0.14 0.09 21117 1873 20 890 - 0.74

12 19 224 0.09 0.09 21109 1872 21315 - 0.84

13 19 901 0.07 0.09 2i 270 1887 21607 - 0.84

14 20 678 0.06 0.09 21930 1908 21946 - 0.82

15 21205 0.05 0.09 22 256 1921 22 178 - 0.82 -

observed. The (predicted, observed) number of epicenters for the other classes are (41,431, (3,4), (38,391, (7,101, (12,7) and in the final class where the patterns for streams, magnetics and geology are all absent, (14,151. The sum CB,iA,. (Ppostji is 146.8, very close to the observed number of 147, indicating a good fit of the model to the data.

Model with variable weights

In this model, each geological unit is again modelled as a binary pattern, but the corridor maps showing distance to north-northeastern streams and magnetic intensity are treated as contour maps having multiple map classes. For these contour maps, a weight, W+, is calculated for each map class as discussed previously.

TABLE 6

For example, in Table 5 showing the statistical results of various distances from the north-northeastern stream segments, the standard deviation, S( Wz), increases for larger values of N,. A cubic-spline curve was fitted to the data in Figure 7 using weights computed from s(Wz) and the method of cross-validation (c.f. Eubank, 1988) was employed to determine the factor controlling the overall smoothness of the curve. Estimated values, j and Gi)+, belonging to the curve and its first derivative, respectively, are given in the last two columns of Table 5. Next, the fitted curve was approximated by a sequence of straight-line segments with the slope of each straight line (Table 6) providing the value of Wf for a specific distance interval from the nearest stream (the straight-line segments were obtained from the spline-fitted curve). From the area, and knowing

Calculation of variable weights for distances to NNE streams. Weights for 6 distance zones

Class Distance (km)

1 15

Cumulative

area (km*)

1776

8556

14078

17459

21205

24 228

B

2 667

11385

17847

20 464

22 178

24 228

Area

(km)

1776

6 780

5 522

3 382

3 745

3 024

Ai W+ s(W) ICI s(C)

2667 0.41 0.25 0.45 0.26

8718 0.25 0.14 0.37 0.17

6 462 0.16 0.16 0.21 0.19

2617 -0.26 0.25 0.29 0.27

1714 -0.78 0.31 0.88 0.32

2 050 - 0.39 0.28 0.43 0.30

A.K.GOODACREETAL.

y vs. NY NNE Stream Linears

1 6

J 0 6.000 16,000 24.000

h km* Fig. 7. Spline curve fitted to a plot of y versus N,, where y = N;exp(W I. The best-fitting curve can be approximated by a series of straight-line segments. As explained in the text, the slopes of these straight-line segments provide estimates of W+ for the various distance zones involved in relating epicenters to NNE-trending streams. The numbers 1 to 6 refer to

classes.

Wf and the prior probability Pprior, it is possible to compute s(W), the standard deviation of W+.

Figure 8 shows the spline curve fitted to the magnetic intensity data, and the weights calculated for eight straight-line segments are given in Table 7. Notice in Table 7 that W+ is strongly positive for classes 8 and 7 (highest magnetic anomaly intensity), falls close to zero for class 6, rises to positive values for classes 5 and 4 and then turns negative for classes 3 and 2, with class 1 being nearly zero.

8 y vs./V, Aeromagnetic Anomalies 9 I

0 6,000 16.000 24,iOO

N, km*

Fig. 8. Spline curve as in Fig. 7 but for the magnetic intensity map.

It is interesting to note that the most statistically significant values of W+ and 1 C I in Table 7 are for magnetic anomaly intensity class 2 in which values range from - 442 to - 115 nT. Rather than saying that epicenters are associated with positive magnetic anomalies we might better say that epicenters are not associated with negative magnetic anomalies.

Figures 9 and 10 show the posterior probability maps, with epicenters superimposed, for the binary and variable-weight models, respectively. Figure 11 shows the cumulative proportion of epicenters plotted versus posterior probability for the two models. The binary model does quite well but the variable-weight model does a little better

TABLE 7

Variable weights for the magnetic intensity map

Class Intensity (nT1 Cumulative 5 area (km)

Area (km*)

A5 W+ s(W) ICI s(C)

< -441 24 228 24 228 1187 -442 to -115 23041 23 035 6 036 -114 to -24 17006 19 178 3041 - 23 to 1.54 13 965 16727 4 999 155 to 375 8 966 10 997 3 998 376 to 762 4 968 5 750 3 467 763 to 1202 1501 2329 984

> 1203 517 896 517

1193 0.01 0.37 0.01 0.38 3 857 - 0.45 0.21 0.56 0.23 2451 - 0.22 0.26 0.24 0.27 5730 0.14 0.17 0.18 0.19 5 247 0.27 0.18 0.34 0.20 3421 - 0.01 0.22 0.02 0.24 1433 0.38 0.34 0.40 0.35 896 0.55 0.43 0.57 0.44

ASSOCIATION OF SEISMICITY WITH DRAINAGE PATTERNS AND MAGNETIC ANOMALIES, QUEBEC 301

17.0N

EPICENTRE PROBABIUTY

(events per km2 per eight - year interval)

0.0100 - 0.0150

0.0090 - 0.0100

0.0070 - 0.0090

- 0.0070

45.3*N __...

Fig. 9. Map showing posterior probability for epicenters using the binary model, with actual epicenters superimposed. Small triangle indicates the location of a magnitude 5.0 earthquake recorded subsequent to our analysis.

at explaining the observed epicenters, and the predictive map shows more subtle variability in posterior probability levels.

The standard deviations of the posterior probability values for the variable-weight model are relatively large compared with those for the binary model. This is due to the relatively small number of points occurring in any one class of the multiple class maps of distance and magnetic anomaly as compared to the binary classes.

Discussion and summa~

We have taken techniques developed for relating mineral occurrences to various areaily distributed parameters, such as geological formations, and applied them to seismicity in the Pap-

ineau-Labelle-Laurentides region of western Quebec. In doing so we have extended the weights of evidence method, as applied to binary data (e.g., either a particular geological formation is present at a particular point or it is not present), to multi-level data such as that contained in a grey-tone aeromagnetic map. The predictive models are obviously incomplete as they do not explain why other areas, such as the northeast corner of the study area (Fig. 2), seem to be aseismic but, within the seismically active area, they do indicate where low-level seismicity is more likely to occur and to be recorded by the ECTN. It will be interesting to see how well the models perform over the next few years. It is worthwhile to note that since our analysis was completed, a widely felt magnitude 5.0 earth-

302

quake occurred (October 19, 1990) in a small zone of slightly enhanced probability in the northwest portion of the study area (see small triangle in Fig. 9 and Fig. 10).

Of the individual parameters used as predictors: distance to NNE-trending streams, positive aeromagnetic anomalies (greater than 156 nT), and Helikian paragneiss, the best single predictor appears to be the NNE-trending stream linears, followed by the positive aeromagnetic anomalies and then the paragneiss geological unit (see Table 4B). Interestingly enough, the paragneiss unit is characterized by generally negative aeromagnetic anomalies; positive magnetic anomalies tend to correlate with rocks such as charnockite gneiss, monzonite and mangerite. This shows that, from the point of view of prediction, the geological

A.K. GOODACRE ET AL.

predictor is not simply mirroring the aeromagnetic anomaly predictor and that all three parameters contribute to the model.

The fact that some geological formations and certain levels of aeromagnetic anomaly can be used as spatial predictors of seismic activity must ultimately reflect on the mechanical properties of rocks in the upper portions of the Earths crust. Although not quite significant at the two-standard-deviation level, Table 2 shows that there are fewer epicenters than would be expected by chance for syenite, anorthosite and quartzite (units 10, 15 and 17). According to data relating to the engineering properties of in&cl rocks (Hatheway and Kiersch, 1982) the cohesive strength of quartzite is approximately twice as high as that of monzonite. Unfortunately, there

6.0.W

17.0.N

EPICENTRE PROBABILITY

(events per km per eight - year interval )

0.0100 - 0.0150

0.0090 - 0.0100

0.0070 - 0.0090

0.0060 - 0.0070

,jj i G


0.0 I

I I

0.002 0.011 0.020

POSTERIOR PROBABILITY

Fig. 11. comparison of posterior probability density distributions for the binary and variable-weight models.

are very few data (5 values for quartzite; 8 values for monzonite) but the suggestion is that there may be an inverse relationship between the in- herent strength of the rock and the observed seismic activity.

This is the sort of behaviour predicted by Campbells (1978) ho-dimensional model of strong/weak zones in the upper crust but it is important to note that seismic activity in the study area, rather than occuring within a particular geological feature or adjacent to it, is generally occurring beneath the geological formations. Most geological inte~retations of gravity and magnetic data arrive at structural models which extend only to depths of 5 to 10 km (e.g., Gibb and van Boeckel, 1970). On the other hand, most seismic activity in the study area occurs at depths ranging from 5 to 20 km. Such depths are typical for intra-plate seismicity (Meissner and Strehlau, 1982) and are seen elsewhere in eastern Canada (e.g., Hasegawa et al., 1985). It is thought that below about 20 km crustal rocks are plastic due to the elevated temperature and cannot support long-term, non-hydrostatic stresses. Lack of seismic&y in the uppermost part of the crust may be due, in part, to the presence of fractures, at all scales, in the rocks and/or to insufficient intensity of differential stress (e.g., Das and Scholz, 1983). What may be happening in our study area is that, given the presence of a pervasive regional

horizontal compressive stress which is in excess of the lithostatic value, the inherently weaker near- surface geological formations cannot transmit this regional stress horizontally and so the underlying mid-crustal rocks need to withstand an additional stress. In other words, the heterogeneous nature of the upper crust causes stress concentrations and, hence, seismicity in the subjacent mid-crustal rocks.

Pre-existing faults or other zones of weakness in the upper crust, because they cannot efficiently transmit stress under some situations, would also be expected to cause stress ~ncentrations at mid-crustal depths (in much the same way that a surface scratch controls where a piece of glass under stress will break) even if the upper crust were homogeneous. Our result that a significant proportion of the seismicity in the study area is spatially associated with NNE drainage features, coupled with (a) the tacit assumption that the zones of weakness are nearly vertical and (b) the observation that there appears to be a regional northeast-southwest oriented compressive stress (Richardson et al., 1979; Adams, 19891, suggests that the mid-crustal rocks are often failing by strike-slip motion in a NNE direction. There are some fault-plane solutions (Wahlstriim, 1987; Adams et al., 1988, 1989b; Mareschal and Zhu, 1989) in the study area which are consistent with this sort of behaviour. Given the presence of a regional northeast-southwest compressive stress field, one would also expect near-vertical zones of weakness which are oriented east-northeast (and conjugate to the North-no~heast features) to be reactivated. In fact such east-northeast features do not seem to be present. There are, however, other fault-plane solutions in the same area which indicate the quite different mechanism of thrust faulting along faults which dip at angles of approximately 45 and whose surface traces are oriented in an approximately north-northwest direction. Noting the difficulty in relating the directions of principle stresses to seismic fault-plane solutions (McKenzie, 19691, these thrust faulting events are broadly consistent with the idea of a regional northeast-southwest compressive stress. We may be picking up events related to this latter type of mechanism in the secondary peak in the


126 direction noticed in Figure 5 but, as mentioned previously, our two-dimensional treatment does not accommodate the three-dimensional situation where zones of weakness dip at relatively shallow angles to the horizontal.

Mohajer (19871, after relocating some 56 small-magnitude, well recorded events in western Quebec, noted two dominant trends in the way the individual epicenters are aligned. The more dominant trend is directed 310-130, corresponding to our secondary peak while the second, less dominant, trend was oriented approximately 40-220 about 20 clockwise from our primary peak. Both Mohajers study and our analysis sug- gest that zones of weakness with either of these two orientations tend to be preferentially reactivated. In this context, it would be of interest to apply single-link cluster analysis (Friihlich and Davis, 1990) to seismicity in the study area.

We would like to emphasize that our results relating seismicity to geology, aeromagnetic anomalies and drainage, although encouraging, may not be universally applicable. We would also like to reiterate that our study does not explain why the northeast portion of the map area (e.g., Fig. 2) is presently aseismic and regard this as a problem yet to be solved.

Acknowledgments

We would like to thank Mr. B. Grover for approximating the drainage pattern by straight- line segments. We also thank Mr. M. Lamon- tagne and Mrs. J. Drysdale of the Seismicity Group (Geophysics Division) for their assistance in editing out quarry blasts, etc. from the seismic data and the preparation of Figure 1. Finally, we would like to thank the reviewers, Drs. M. Kul- dorff and J. van Eck for their many helpful com- ments.

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Documents

GOODACRE - A Statistical Analysis of the Spatial Association of Seismicity With Drainage