GEOPHYSICAL RESEARCHLETTERS, VOL. 13, NO. 1, PAGES 157-160, FEBRUARY 1986 A STATISTICAL CORRELATION BETWEEN RIDGE CREST OFFSETS AND SPREADING RATE D. Abbott Oregon State University, Corvallis, OR 97331 Abstract. Ridge crest offsets follow the which describes the probability of finding a statistical distribution, N - A exp [-BIn ridge crest offset of a given length. (L/L^)],. where N is the cumulative number of ridg• crest offsets with lengths greater than L, Measurement Technique L is the cutoff length, and A and B are con- s•ants. We measured A and B for the slow The data used to determine the spectral char- spreading mid-Atlantic ridge, the intermediate acter of the distribution of ridge crest offsets spreading Juan de Fuca Ridge, and the fast included multibeam (SEABEAM)and detailed single spreading east Pacific Rise. The predicted mean beam (PDR) bathymetric surveys of the ridge distances between offsets greater than 4 km long crest. Continuous sections of ridge crest are 30, 32, and 74 km on the slow, intermediate (Figure 1) were used, because detailed surveys and fast spreading ridge crests. These dis- are preferentially located on the longer off- tances are in agreement with observations of sets. The locations of the ends of a single other workers and calculations of modal ridge ridge crest segment were always determined from lengths. the same map, to minimize navigational errors and discrepancies between different maps. We Introduction used bathymetry from three ridge crests spanning a range of whole spreading rates: the slow Oceanic crust created at a fast spreading spreading (3 cm/yr) Mid-Atlantic ridge, the ridge has lower basement relief and fewer ridge intermediate spreading (6 cm/yr) Juan de Fuca crest offsets than crust created at a slow ridge, and the fast spreading (9-12 cm/yr) east spreading ridge [MacDonald, 1983]. In part, the Pacific rise. greater topographic roughness of oceanic crust We measured the maximum perpendicular offset created at a slow spreading ridge is due to a between ridge segments. This measurement dif- greater number of ridge offsets without a cor- fers from another common measure; the actual responding decrease in average offset length. fault length. We used the perpendicular offset Because of the slower spreading rate, the same because it more accurately reflects the age-off- length of offset on a slow spreading ridge re- set between the two ridge segments and it re- sults in a larger age difference between the duces the possibility of bias between different offset pieces of oceanic lithosphere. Because bathymetric data sets. the oceanic crust subsides as it ages [Sclater et al., 1971], this increased age difference Distribution of Offsets will increase the local topographic relief. Furthermore, the depth of the valley at ridge- Locations of the ends of the maximum perpen- transform intersections is proportional to the dicular offsets were used to generate two data age-offset between the two ridge-segments [Fox sets: the distribution of offset lengths and of and Gallo, 1984]. Although some of the relief ridge segment lengths. The offset lengths could is due to hydraulic head loss [Sleep and also be used to generate a distribution of age- Biehler, 1970], these fracture zone valleys are offsets, but for convenience in the comparison often preserved on older seafloor [Menard and with other data sets, the data has been kept in Chase, 1971]. Similarly, the size of the topo- the form of offset length distribution. On each graphic step across fracture zones is propor- ridge crest, the distribution of offset lengths tional to the age difference between the sea- was plotted as a cumulative distribution: the floor on either side of the fracture zone log of the length of offset versus the log of [Sandwell and Schubert, 1982]. Because ridge the cumulative number of offsets longer than a crest processes control most of the morphology given length (Figure 2a). We found that the of older oceanic basement, the offset length cumulative number of ridge offsets, N, which are distribution of ridge crests has many potential longer than a given length, L, is given by the applications in analyzing the basement topo- relationship' N - A exp [-BIn (L/Lo), whereL graphy of older oceanic crust. is the cutoff length, and A and B are constantS. Recent multibeambathymetric surveys of This formula is similar to one used in seis- spreading centers with slow, intermediate, and mology to describe the distribution of earth- fast total opening rates have shown that small quake magnitudes. In the seismic case the con- offsets of the ridge crest are more abundant stant B is called a 'B-value'. We will also use than large offsets [McDonald and Fox, 1983; this phrase, recognizing, of course, that there Ramberg et al., 1977]. Fox and Hayes [1985] need not be any physical connection between found that the basement relief of oceanic crust these two types of B-values. Formulas for esti- as a function of spatial frequency can be fit by mating B-values and their standard errors are a power law. We have derived a similar quantity given by Aki [1965]. As with earthquake B-value plots, the slope of the log normal line remains Copyright 1986 by the American Geophysical Union. constant only in the region of 100% detection, that is for L>L . Each of the three data sets Paper number 5L6762 can be fit by t•e exponentialdistribution, in 0094-8276/86/005L-6762503.00 the sense that they pass a chi-squared test. 157 158 Abbott' Statistical Correlation rate of 6 cm/yr [Schouten et al., 1985]. My results are consistent with these predictions 55 48 ,•41ø'*50•N I but are close to the maximum error limits. However, previous calculations indicate that the 5o MAR 46 stresses on the Juan de Fuca transform faults 0 • -.• 57ON may be increased by the subduction zone [Fujita 45 and Sleep, 1978]. This increase in stress might cause the longest transforms to break up into 132 130 128 IP_.6 shorter transforms separated by short ridges or LONG. pull apart basins. Consequently, the Juan de Fuca ridge may have more offsets per unit length than a 'typical' intermediate spreading rate :50 // ridge. Unfortunately, it is presently the only ridge crest with an intermediate spreading rate which has sufficiently detailed bathymetric 20 coverage to calculate an offset length B-value. On the fast spreading northern segment of the 15 east Facific rise, A = 8.21 per 1000 km of ridge crest, B = 1.07 +/-0.49. In this instance, we predict a mean distance of 74 km between offsets I0 > 4 km long and a range of 58-95 km, or 14 off- sets every 1000 km of ridge length. This range of distances between offsets brackets the 85-90 km distance predicted by some observations and ! theoretical models [McDonald, 1982; Schouten et 45 5 5O 25 al., 1985]. LONG. LONG. We estimate that these B-values are valid for Fig. 1. Location of offsets. Short offsets offsets longer than the width of the zone of (single triangle) and long offsets (two connected active intrusion, or approximately 4 km. Be- triangles). Data sources below not cited in text. cause cooling increases the thickness of the (left) Mid-Atlantic ridge (MAR): Laughtonand brittle layer, the rift valley floor on slow Searle, 1979; Perry et al., 1981; Searle, 1981; spreading ridges is narrowest where an active Searle and Laughton,1977; R. Bell, pers. comm., crustal magmachamber is present [Harper, 1985]. OTTER,1984; Ronaet al., 1976; Derrick and Purdy, Detailed studies also showthat magmaticactivi- 1980; Salisbury and Hyndman,1984; Collette et ty is confined to the floor of the rift valley al., 1974; Derrick et al., 1982; Van Andel et al., [Atwater, 1979]. Therefore, the minimumwidth 1971; Heezenet al., 1964; Beldersonet al., 1984. (2-4 km) of the inner floor of the rift valley (right top) Juan de Fuca ridge (JdF): Juan de Fuca Ridge Atlas, 1985; Crane et al., 1985; Embley et al.; 1984; A. Malahoff, pers. comm. (right iooo bottom) East Pacific Rise (EPR): Madsen et al., 1986; Lonsdale, 1977, 1983, 1985a, 1985b. • MAR AI i• + •. -2ø S -• 57øN AI J dF Deviations from the exponential distribution can • 10 o ,,u. •o be explained by random error. o On each spreading ridge, we choose an offset length above which there appears to be 100% i 2• 24 2G 2e 2•o 21 •$ 2s 27 detection of all offsets (Figure 2a). These OFFSET LENGTH, Km OFFSET LENGTH, Km lengths are respectively: L - 43 km on the Mid-Atlantic ridge, L - 4.• kmon the Juande Fucaridge and L - 6•4 kmon the East Pacific EPR rise. The east •acific rise and the Juan de 3øS • 16øN AI •oa Fuca ridge have nearly complete multibeam bathy- metric coverage and, consequently, a very low • I detection limit. • io o On the slow-spreading Mid-Atlantic ridge, A - 3.43 per 1000 km of ridge crest, B - 0.96 i ' +/0.39. We predict a cumulative number of 34 21 2 $ 2 $ 2 7 2 9 offsets >4 km long for every 1000 km of ridge OFFSET LENGTH, Km crest with an average of one offset every 30 km Fig. 2a. Loõ-Log plot of cumulative number of and a range of 12-74 km. This range overlaps offsets 1onõer than a given length versus the off- early estimates of one offset every 50-80 km set length, Crosses are a subset of actual data, [Schouten and White, 1980; McDonald, 1982], and Total number of offsets is given both as observed coincides with more recent estimates of one offsets and as the subset used to calculate the offset every 40 km [Schouten et al., 1985].