A Statistical Correlation Between Ridge Crest Offsets and Spreading Rate

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 results 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 offsets 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 bathymetric 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]. offset B-value. Arrow points to shortest length On the intermediate spreading rate Juan de used. Line is offset B-value. The log-log scale Fuca ridge system, A - 26.6 per 1000 km of ridge increases the apparent errors of the longer off- length, B - 0.81 +/- 0.32. On this ridge crest, sets. The distance between the observed and pre- we predict 31 offsets > 4 km long every 1000 km dicted number of offsets is always less than one with an average distance between offsets of 32 offset on the right side of each plot. (left) km and a range of 30-34 km. Given the error MAR: 81 offsets observed, 43 used. (Middle) JdF: limits, the theoretical models predict a 30-62 25 observed, 22 used. (right) EPR: 28 observed, km average ridge length at a whole spreading 18 used. Abbott' Statistical Correlation 159

M A R - 2øs-- 57' N the mode which has the longest ridge crest •o1:' -r'-I---,' •3us •o-• JdF length is the mode predicted by the model. On the Juan de Fuca ridge, the most dominant mode uJ • :• 41,N-.50•N • TRANSFORM is associated with ridge crests within transform Z Z faults. On the east Pacific rise, the two domi- ...... • nant modes are both caused by ridge crest off- RIDGELENGTH, Km RIDGELENGTH, Km sets. The modal peak at ridge crest lengths of EPR 48-64 km agrees with our theoretical prediction of 58-95 km. The average of the two dominant modes of ridge crest length on the East Pacific rise is around 80 km. A simple average of all z of the ridge lengths is 73 km, a value which is 0 16 •. 4• 64 •0 9• 112128144 within the errors of other simple averages RIDGE LENGTH, Krn [Schouten et al., 1985]. Consequently, our Fig. 2b. Histograms of ridge segment lengths. results agree with other observations, but the (left) MAR. Striped zones- ridge segments in the btmodal distribution of modal ridge lengths FAMOUSand TAG areas. (middle) JdF, (right) EPR. indicates that the processes may be more complex Hachures- ridge segments within transforms. Bold than previously assumed. point with error bar is mean ridge length estimated from offset data. Conclusions

The modal values of ridge length are in on slow spreading ridges roughly defines the agreement with the predictions of ridge crest width of the zone of active intrusion. Ridge offsets for all three spreading centers' the crest offsets which are contained within the Mid-Atlantic ridge, the Juan de Fuca ridge', and zone of active intrusion may appear and disap- the East Pacific rise. The B-values and as- pear during different magmatic episodes. Con- sociated constants change in a fashion which is sequently, the processes controlling the abun- consistent with independent observations of an dance of these short offsets are likely to be increase in the number of ridge crest offsets as somewhat different and they should not be in- the spreading rate decreases. Therefore, the eluded in a ridge crest offset B-value relation- B-value distributions of ridge crest offset ship. lengths are reasonable in light of the present knowledge of ridge crest morphology. Further- Distribution of Ridge Crest Lengths more, because the topographic relief of fracture zones is largely determined by the age offset of The distribution of ridge crest lengths is the fracture zone, these offset length B-values shown in Figure 2b. We assume that the modal are an important step in quantifying the contri- ridge lengths, as measuredfrom these distribu- bution of fracture zones to the basement mor- tionS, are estimates of the mean ridge lengths. pho!ogy of oceanic lithosphere created at dif- This relationship would hold if the true dis- ferent spreading rates. tribution were symmetical and peaked at some These offset length 'B-values' could contri- non-zero ridge length, an assumption supported bute to several types of studies. They can be by theoretical models [Schoutenet al., 1985]. used to estimate sea floor roughnessand thus (We attribute the asymmetryof the observed have a bearing on models of tides and tsunamts distributiom to the Skewing effect of missing [Fox and Hayes, 1985]. The techniquecan aiso offsets). Having estimated a mean ridge length, be used to extrapolate low spatial resolution we can then compare it to the mean ridge length data, such as is collected by the SEASAT satel- implied by the ridge crest offset distribution, lite altimeter. The offset distribution also evaluated at 4 km. predicts variations in seafloor morphology as a On the slow spreading mid-Atlantic ridge, the function of spreading rate. This spreading- modal ridge length is 32-48 km, which is within rate-dependent morphology implies that this the range of the theoretically predicted 12- relationship might ultimately lead to a method 74 km average ridge length. This modal ridg e of estimating the paleo-spreadtng rate of mag- lengthappears in boththe iargerdata set and netically quiet seafloor. i n the two areas of detailed surveys, FAMOUSand TAG. The appearance of this modal ridge length Acknowledgements. We thank B. Brandsdottir, V. in the FAMOUSand TAG areas is particularly Kulm, and W. Menke for critical reading of the encouragingbecause none of the ridge crest manuscript. offset s from these detailed survey areas are References longer than 42 km. Consequently, the modeof this Subset of the ridge lengths was derived Aki, K., Maximum likelihood estimate of b in the from a completely independent data set. This formula 16g N = a bM and the confidence limits, mode confirms the basic validity of the BUll, Earthquake Res.• Inst., 43, 237-239, 1965. offset length B-value for the northern Mid- Atwater, T. M., Constraints from the FAMOUSarea Atlantic ridge. concerning the structure of the oceanic sec- On the east Pacific rise and the Juan de Fuca tion, Deep Drilling Results in the Atlantic: ridge, the ridge crest lengths are not complete- Ocean Crust, eds. M. Talwani, C. G. Harrison, ly independent from the offset length B-value. and D. E. Hayes, 2, 33-42, 1979. Nevertheless, the ridge crest length distribu- Belderson, R. H., E. J. W. Jones, M. A. Gorini, tion does provide a test of the relationship. and N.H. Kenyon, A long-range side-scan sonar Both the Juan de Fuca ridge and East Pacific (GLORIA) survey of the Romanthe active trans- rise show a bimodal distribution of ridge crest form in the Equatorial Atlantic, MariDe Geolo- lengths. Of the two dominantmodes (Figure 2b), gX, 55, 65-78, 1984. 160 Abbott' Statistical Correlation

Collette, B. J., J. M. Schouten, K. Rutten, and A. MacDonald, K., J.-C. Sempere, and P. J. Fox, East P. Slootweg, Structure of the Mid-Atlantic Pacific Rise from Sequieros to Orozco Fracture Ridge Province between12 and 18 N, Marine Zones' Along-strike continuity of axial neo- Geophys. Res., _2, 143-179, 1974. volcanic zone and structure and evolution of Crane, K., F. Ai.kmanIII, R. Embley, S. Hammond, overlapping spreading centers, J. Geophys. A. Malahoff, ahd J. Lupron, The distribution of Res., 89, 6049•6069, 1984. geothermal fields on the Juan de Fuca Ridge, J• Madsen, J. A., P. J. Fox, and K. C. MacDonald, The Geophys. Res., 90, 727-744, 1985. morphotectonic fabric of the Orozco transform Derrick, R. S., and G. M. Purdy, The crustal fault' Results from a Sea BeamInvestigation structure of th e Kane fracture zone from seis- in press, J. Ge•phys. Res., 1986. mic refraction studies, J. •eophys. Res,., 85, Malahoff, A., and R. Riddihough, Tectonics of the 3759-3777, 1980. Explorer Ridge and Soyanco Fracture zone, N. Derrick, R. S., M. M. Cormier, R. Prince, D.W. E. Pacific Ocean, EOS, 6_•5,1111, 1984. Forsyth and E. L. Ambos, Seismic constraints on Menard, H. W. and T. E. Chase, Fracture zones, in the crustal structure witl•i• the VemaFracture A.E. Maxwell(ed•), The Sea, Wiley-Inter- zone, J. Geophys. Res., 87, 10599-10612, 1982. science, New York, 4, 321-443, 1971. Embley, R. W., L. Kulm and D. Abbott, Kinematic OTTER seientific Team, The geology of the Oceano- and structural development of the Blanco trans- grapher transform: The ridge transform inter- form zone, EOS, •6_•5, 1110-1111, 1984. section, Mar. Geophys. Res., •, 109-142, 1984. Fox,C. G., and D. E. H•yes, Quantitative methods Perry, R. K., H. S. Fleming, P. R. Vogt, N. Z. for analyzing the roughness of the seafloor, Cherkis, R. H. Feden, J. Theide, J. E. Strand, Rev. Geophys., 23, 1-48, 1985. and B. J. Collette, North Atlantic Ocean: Fox, P. J., and D. G. Gallo, A tectonic model for Bathymetry and plate tectonic evolution, Geol. ridge-transform-ridge plate boundaries' Impli- Soc. Am., Map and Chart Series MC-35, 1981. cations for the structure of the oceanic litho- Ramberg,I. B., D. F. Gray, and R. G. M. Reynolds, sphere, Tectonophysics, 104, 205- 242, 1984. Tectonic evolution of the FAMOUSarea of the Fujita, K., and N. Sleep, Membrane stresses near Mid-Atlantic Ridge, latitude 35050 ' to 37ø20'N, mid-ocean ridge-transform intersections, Tec- Geol. Soc. Am. Bull., 88, 609-620, 1977. tonophysics, 50, 207-222, 1978. Rona, P. A., R. N. HarbiSon, B. G. Bassinger, R. Heezen, B.C., E. T. Bunce, and M. Tharp, Chain B. Scott, and A. J. Nalwalk, Tectonic fabric and Romanche fracture zones, Deep-Sea Res., 11, and hydrothermal activity of Mid-Atlantic Ridge 11-18, 1964. crest (lat 260 N), Geol. Soc. Am. Bull., 87, Johnson, H. P., J. L. Karsten, J. R. Delaney, E. 661-674, 1976. E. Davis, R. G. Currie, and R.L. Chase, A de- Salisbury, M. H., and R. D. Hyndman, Leg 78B' tailed study of the Cobb offset of the Juan de Background, objectives, and geological setting, Fuca Ridge: Evolution of a propagating rift, in Hyndman, R. D., Salisbury, M. H., et al., J. Geophys. Res., 88, 2297-2315, 1983. Init. Repts. DSDP, 78B' Washington (U.S. Govt. Juan De Fuca Ridge Atlas, Preliminary Seabeam Printing Office), 635-652, 1984. Bathymetry, producedby Energy, Mines and Re- Sandwell, D. T., and G. Schubert, Lithospheric sources, Canada, 1985. flexure at fracture zones, J. Geophys. Res., Laughton, A. S., and R. C. Searle, Tectonic pro- 87, 4657-4667, 1982. cesses on slow spreading ridges, in Deep Dril- Schouten, H., K. D. Klitgord and J. A. Whitehead, ling Results in the Atlantic Ocean: Ocean Segmentation of mid-ocean ridges, Nature, 317, Crust, Maurice Ewing Series 2, edited by M. 225-229, 1985. Talwani, C. G. Harrison and D. E. Hayes, Am. Sclater, J. G., R. N. Anderson, and M. L. Bell, Geophys• Union, 15-32, 1979. Elevation of ridges and evolution of the cen- Lonsdale, P., Regional shape and tectonics of the tral eastern Pacific, J. Geophys. Res., 76, Equatorial East Pacific Rise, Mar. Geophys. 7888-7915, 1971. Res., •, 295-315, 1977 Searle, R. C. and A. S. Laughton, Sonar studies of Lonsdale, P., Overlapping rift zones at the 5.50 S the mid-Atlantic ridge and Kurchatov Fracture offset of the East Pacific Rise, J. Geophys. Zone• J. Geophys. Res., 82, 5313-5328, 1977. Res., 88, 9393-9406, 1983. Searle, R. C., The active part of •he Charlie Lonsdale, P., Nontransform offsets of the Pacific- Gibbs fracture zone' a study using sonar and Cocos plate boundary and their traces on the other geophysical techniques, J. Geophys. Res., rise flank, Geol. Soc. Am. Bull., 96, 313-327, 8__6,243-262, 1981. 1985a Sleep, N.H. and S. Biehler, Topography and tec- Lonsdale, P., Linear volcanoes along the Pacific- tonics at the intersections of fracture zones Cocos plate boundary, 90 N to the Galapagos and central rifts, J. Geophys. Res., 7__5,2748- triple Junction, Tectonophysics, 1•6, 255-279, 2752, 1970. 1985b Van Andel, T. J., R. P. Von Herzen, and J. D. MacDonald, K. C., A geophysical comparison between Phillips, The Vema Fracture Zone and the tec- fast and slow spreading centers: constraints tonics of transverse shear zones in oceanic on magma chamber formation and hydrothermal crustal plates, Mar. Geophys. Res., !, 261-283, activity, in Hydrothermal Processes at SeaFloor 1971. Spreading Centers, edited by Peter A. Rona, K. Bostrom, and K. L. Smith, Jr., NATO Conference Series, Series IV: Marine Sciences, Vol. 12, D. Abbott, College of Oceanography, Oregon Plenum Press, New York, 27-51, 1983. State University, Corvallis, OR 97331. MacDonald, K. C. and P. J. Fox, Overlapping spreading centers: new accretion geometry on the East Pacific Rise, Nature, 302, 55-58, (Received November 19, 1985; 1983. accepted December 6, 1985.)