Geo736: Seismicity along mid-ocean ridges Course Notes: S. G. Wesnousky Spring 2018 Bathymetric maps show the ocean basins of the world are characteristically divided by a bathymetric ridge. The bathymetric ridges may reach to several or more kilometers above the absyssal sea floor, show relatively large values of heat-flow, and are marked by the occurrence of earthquakes (Figure 1). Figure 1. (upper) Schematic plot showing elevation and heat flow along mid-ocean ridges. (lower) Map of global seismicity shows mid-ocean ridges are marked by occurrence of seismicity and that these rates are less than observed along the world subduction zones (Figure from Barazangi and Dorman, 1969). Analysis of magnetic sea-floor lineations and the age of the sea-floor show that the ridges mark divergent plate boundaries where lithosphere is created and transported away from the ridge with time. Hence mid-oceanic ridges are commonly referred to as spreading centers. Earthquake seismology can be used to define the details or structure of the sea-floor spreading process. New lithosphere is created at the ridge and then moves away (Figure 2). The process is evidenced by the occurrence of normal faults along the ridge axis oriented to indicate extension perpendicular to the ridge crest. The transform faults are sites of relative plate motion between lithosphere moving in opposite directions. Depending on the sense of ridge offset, transform motion may be either right- or left-lateral, but reflect the same sense of relative plate motion. The relative motions defined by the transform fault mechanisms is not what is responsible for the offset of the ridges. The length of a transform fault will not change if the rate of spreading is equal on the offset ridges. This is very different than a transcurrent fault whereby offset is produced by motion on the fault and the length of offset between ridge segments would increase with time. Spring 2018 - wesnousky 1
Figure 2. Schematic illustration of seafloor spreading, types of boundaries (divergent and transform) observed along mid-ocean ridges, and types of focal mechanism expected along the boundaries. Solid quadrants of focal mechanisms encompass regions of compressional first-arrivals. Analysis of magnetic sea-floor lineations and the age of the seafloor shows that spreading rates along different ridges reach up upwards of 20 cm/yr whereas mid- Atlantic rates are no more than 4 cm /yr. both the morphology of mid-ocean ridges and the style and rate of seismicity along mid-oceanic ridges is a function of sea-floor spreading rate. Understanding of these relationships has developed with understanding the evolution of oceanic lithosphere. The major aspects of the relationship between seismicity, the morphology of the seafloor, and spreading rates has arisen from application of a simplified model of the formation of the seafloor, whereby lithosphere is created by introduction of hot material at the spreading centers which in turn cools as the plate moves away from the spreading center. Figure 3. Rates of seafloor spreading at mid-ocean ridges (arrows ~perpendicular to ridges) are greater in Pacific than Atlantic. (Figure I think from Le Pichon, 19?? Material from the mantle of temperature Tm is brought to the surface (ocean floor) at the ridge axis where the temperature is defined as Ts (Figure 4). It is generally taken that Tm is about 1100 C). The material is then transported away at a velocity V, while the upper surface remains at Ts. The horizontal component of heat conduction is neglected because is it negligible compared to the horizontal transport to heat due to sea-floor spreading at velocity V. In this manner the system may be considered Spring 2018 - wesnousky 2
analogous to a cooling half-space: assume the surface of the half-space is suddenly cooled to temperature Ts at time t=0. Figure 4. Schematic illustration of cooling of lithospheric plate as it moves away from ridge. T Because any column of lithosphere moves away from the ridge crest at a rate faster than heat is conducted in the horizontal direction, the mathematical description of plate cooling is treated as a problem of one dimension. Ts and Tm are the temperature at the surface and within the mantle, respectively. The velocity of plate motion is u. The right side shows schematically 3 columns of crust that have moved at 3 separate distances from the ridge. The heat flow is labeled q. (figure from Stein, 1991). The temperature as a function of depth and time is described by the 1-dimensional heat-flow equation. where is a property of the material call thermal diffusivity and measures the rate at which heat is conducted. Units of K are distance squared over time. The definition of is, where is the thermal conductivity, is the density, and is the specific heat at a constant pressure. The solution of the above equation is where is known as the error function and between limits s=0 and s= an exponentially increasing curve with limits between 0 and 1 (Figure 5). The behavior of a cooling halfspace as described by the equation is illustrated in Figure 6. Thus, in the right-hand side of Figure 4 one may envision that the seafloor is composed of a number of columns each of which progressively cool from the surface as they are translated away from the ridge. Figure 5. The behavior of the error function erf(s). Value is limited between zero and 1 for values of s = to to infinity. Spring 2018 - wesnousky 3
Figure 6. Schematic illustration of a half-space cooled from the top. At time t=0 one may envision magma from the mantle of temperature Tm being injected to the surface at which time the surface is exposed to temperature Ts. The isotherms for t =1, 2, and 3 show the expected pattern of cooling with time. The assumption is then made that the oceanic lithosphere cools in this manner and that Ts=0 C, so describes the temperature at a depth z for material of age time=t. Because the age of lithosphere is the distance x from the ridge divided by the halfspreading rate V the preceding expression may be rewritten as a function of position. The mechanical behavior of the lithosphere (rock) is largely dependent on the temperature profile or geothermal gradient and for this reason descriptions of the mechanical behavior of the seafloor are conveniently examined by study of the location of specific isotherms (lines of constant temperature). The utility of such a description follows from our earlier development of the strength envelope. For the preceding descriptive equation, an isotherm is a curve on which the argument of the error function remains constant. or equivalently and thus it is predicted the depth to a given temperature increases as the square root of the lithospheric age. The resulting pattern of isotherms is schematically illustrated in Figure 7. Figure 7. Individual isotherms increase with depth as a function of the square root of the plate age. Spring 2018 - wesnousky 4
The isotherm structure has been used to explain various aspects of the mechanical and geophysical characteristics of the oceanic lithosphere. Surface wave studies for example sow the existence of a low velocity zone beneath oceanic lithosphere. The depth of the low-velocity zone generally correlates to the 1100 isotherm of various models, and it is thus this isotherm that is often defined as the base of the lithosphere. According to the model then the thickness of the lithosphere increases as the square root of plate age, and this is observed in the findings of surface wave studies. As well, heat-flow is predicted to decrease as the square root of lithospheric age. The velocity of surface waves is a function of lithospheric age which may be attributed to the thickening of the lithosphere (deepening) of low-velocity zone) as a function of square root of lithospheric age. Figure 8. (left) Rayleigh wave group velocity dispersion curves plotted as function of age of seafloor through which they propagated. (right) Velocity of shear waves as function of depth plotted for waves propagating across seafloor of 10-20 my and 20-50 my. Each shows a pronounced decrease in velocites from the surface to a depth of about 100 km at which point they begin to increase. The zone of low-velocity is commonly referred to as the low-velocity zone. The velocities above the low-velocity zone are greater for the older lithosphere. (Figures taken from Forsyth, 1975; Figures taken from Forsyth, 1977). Observations of heat flow also support the model, again showing a decrease in heat flow as a function of the square root of age (Figure 9). Figure 9. Heat flow as function of age of seafloor in (left) Pacific, South Atlantic, Indian, and (right) the north Pacific oceans (Parsons and Sclater, 1977). The slope of -1/2 on log-linear plot at right shows decrease of heat flow is function of square root of age. Our mathematical description of the evolution of lithosphere thus far ignores the observation that spreading centers are characterized by a bathymetric ridge. The decrease in elevation away from the ridge may also be attributed to plate cooling, or as a function of the square root of the lithospheric age. The explanation has its roots in the Spring 2018 - wesnousky 5
idea of isostacy, which states the the mass of any 2 columns in the earth crust or lithosphere must balance. The approach thus begins with considering the mass of 2 columns of lithosphere: the first column located at the ridge where seafloor is of age 0 and the second column at some location where age = t (Figure 10). The additional assumption is made that the lithosphere is defined by the isotherm T = Tm and has zero thickness at the ridge and z = m(t), where the water depth is h(t). Figure 10. The assumption that the mass in a vertical column of the seafloor remains the same for all ages of seafloor can yield a mathematical description on the increase in ocean depth with age of the lithosphere. Summary of Boundary Conditions and assumptions: z = 0 at ridge z = m(t) at age t lithosphere of age t overlain by H20 Tm = base of lithosphere Isostatic equilibrium Temperature Asthenosphere = Tm Density Asthenosphere = Pm Temperature in cooler lithosphere at point (z,t) = T(z,t) and The density at point (z,t) can be described with the equation The change in density with temperature is given by the coefficient of thermal expansion or in terms of density ρ (and the minus because dp/dt is negative. Then the density perturbation at any point (z,t) can be written Spring 2018 - wesnousky 6
for the halfspace cooling model. Furthermore, if the density of water p w and the mass of the 2 columns of lithosphere are equal as isostacy requires, then which yields the isostatic condition for ocean depth Given that we have chosen the base of the lithospheric plate to correspond to a specific isotherm, the temperature and density in the plate are then defined for all values of z. Then allowing that z = z - h(t) and m(t) ---> the previous expression for h(t) can be rewritten Then making the substitution one arrives at the expression (after integrating by parts) that predicts that ocean depth increases as the square root of the plate age. Figure 9. (left) Depth of seafloor as function of age across north Pacific and Atlantic oceans. (Parsons and Sclater, 1977). Spring 2018 - wesnousky 7
To further show how heat flow varies as a function of plate age, we again consider the base of the lithosphere as defined by isotherm = Tm, and recall that lithospheric thickness increases with the square root of age. Also, we approximate the temperature gradient at the surface by the gradient averaged through the entire lithosphere. In this manner heat flow is defined as and the equations predict that heat flow decreases as a function of the square root of age (time) which is generally observed (Figure 9). The approximation does not account for the observation that ocean depths tend to become flatter at ~70 m.y. than predicted. All of this leads to a simplified model of sea-floor spending that explains to first order the thickening of lithosphere with distance from the ridge-axis, the decay in heatflow values with distance from ridge-axes, and the increase in depth with distance from the ridge axes of the seafloor. The character of seismicity along ridge crests and transform faults may also be explained in the context of this model of seafloor spreading. More specifically, source parameters for large earthquakes along rifts and transforms are limited or controlled by the depth of an isotherm marking the transition from seismic to aseismic slip. In turn, the depth to isotherms is a function of spreading rate. Recall that spreading rates along the mid-atlantic ridge are 2-4 cm/yr whereas spreading rates are 10-20 cm/yr along the mid-pacific rise (Figure 3). Study of earthquakes aligned along the mid-atlantic ridge (not the transforms) shows that the size of the largest events range only to about M6.3 (Mo = 1.0 x 10 25 dyne-cm) and that the depth of events beneath the seafloor is generally no more than 3 or 4 km (Figures 10 and 11), indicating the transition from seismic to aseismic conditions occurs at very shallow depth, in accord with the observation of high heat flow along the ridge. The relatively small size of earthquakes along the ridge may also be attributed to the high heat-flow and resulting shallow depth to the brittle-ductile transition. Focal mechanisms of the largest mid-atlantic ridge earthquakes are normal-type with T-axes oriented approximately perpendicular to the ridge crest (Figure 12). Spring 2018 - wesnousky 8
Figure 10. List magnitudes of moments and depths of earthquakes located along the mid-ocean ridge axes. Location of events shown in Figure 11. (Table 1 of Huang and Solomon, 1988). Figure 11. Locations of mid-ocean earthquakes listed in Figure 10. (Figure 1 of Huang and Solomon, 1988). Figure 12. Normal fault mechanisms of earthquakes along the axes of 3 different sections of the North Atlantic ridge plotted on bathymetric map (Figs 6, 8 and 10 of Huang et al., 1986). Spring 2018 - wesnousky 9
Earthquakes on oceanic transform faults reach to larger magnitudes than ridgetype earthquakes. Magnitudes and seismic moments of M7 and Mo>5 x 10 26 dyne-cm have been reported, respectively (Figure 13). Figure 13. Magnitude and moments of large ocean transform faults. ((Table 2 of Burr and Solomon, 1978). Focal mechanisms along the transform faults are typically strike-slip (Figure 14). Figure 14. Strike-slip focal mechansims of earthquakes along the Vema and Gibbs Fracture Zones (transform faults) in the mid-atlantic. (Figures 8 and 10 of Huang et al., 1986). The relationship of earthquake size to spreading rate for mid-oceanic ridge normal faulting earthquakes is illustrated in Figure 15. Ridge crests with slower spreading rates show relatively larger earthquakes. The observation is consistent with idea that slower spreading ridges are characterized by a cooler and thicker (albeit thin) lithosphere than faster spreading ridges. Spring 2018 - wesnousky 10
Figure 15. (left) Seismic Moment and (right) body wave magnitude of earthquakes on or near midoceanic ridge crests (not on transform fault). Transform Earthquakes Along transform faults, the temperatures should generally be less at any given depth than in the immediate vicinity of ridge crests which in itself provides simple qualitative explanation for the observation that oceanic transform earthquake reach larger magnidutes than do ridge-axis earthquakes. The thermal structure of a transform fault depends not only on the spreading rate but also the length of the transform offset L. The shaded area in the following figure represents the area along a transform fault that is less than some temperature To on both sides of the fault. If To is the isotherm that corresponds to the brittle-ductile transition, then the shaded region represents the maximum area of faulting for an earthquake on this transform. One then might expect that the maximum size Figure 16. Schematic illustration of how an isotherm may limit the area of a transform fault that susceptible to failure in earthquakes. The shaded region is the portion of the transform fault that is above some isotherm To which is assumed to limit the depth of brittle failure. (Figure 6 of Solomon and Burr, 1979). of earthquake expected on a transform fault is a function of both the spreading rate and the offset of the ridge (Figure 17). Spring 2018 - wesnousky 11
Figure 17. Seismic moment of earthuakes on oceanic transform faults versus (left) spreading velocity V and (right) L/V, where L is the length of the transform zone. The value of L/V provides a measure of the maximum age contrast of the lithosphere across the transform. The maximum observed size of the earthquakes decreases with spreading velocity and increases as a function of L/V, though earthquakes are too few to establish the latter relationship clearly. (Figs 8 and 9 of Solomon and Burr, 1979 (seems there should be a more recent study)) Comparison of isotherms predicted from a model similar to the model we earlier developed to the location of transform earthquakes shows that transform fault earthquake depths are generally limited to above the 400 C isotherm. Figure 18. Thermal models generally indicate that transform fault earthquakes occur above the 400 C isotherm. This is example from Romanche fracture zone in Atlantic (Fig 17 of Engeln et al., 1986). Earthquakes near Mid-Ocean Ridges (Intraplate) There are also a significant number of earthquakes that occur near mid-ocean spreading centers but not directly on the ridge crests or transform faults (Figure 19). The earthquake mechanisms show thrust, normal, and strike-slip faulting. The depth distribution of these earthquakes also reflects the cooling and hence thickening of the lithosphere with distance from the ridge crest. Spring 2018 - wesnousky 12
Figure 19. Map showing location of mid-oceanic ridge earthquakes that neither fall on the crest of the ridge or on transform faults (Bergman and Solomon, 1984). The depth of oceanic intraplate earthquakes also increases with age of seafloor, much like transform earthquakes (Figure 20). The deepest of the oceanic intraplate earthquakes characteristically show normal mechanisms, consistent with our earlier development of the strength envelope. However, the limiting isotherm for the intraplate earthquakes is apparently much greater (~750 C) than for transform faultl earthquakes (~400 C). This is the opposite of the effect we might expect since strain rates in the intraplate region must be orders of magnitude less than along transforms. The simple models thus do not explain everything and this latter conundrum remains an area of interest today. Figure 20. Depth of earthquake versus age of lithosphere for earthquakes in Figure19. The earthquakes are distinguished according to (left) location, (middle) seismic moment,and (right) focal mechanism. Not clearly evident in the figures I have provided, it is observed that earthquakes along the Mid-Pacific Rise occur more frequently along transform faults and very few earthquakes at all occur along the ridge crest itself, whereas seismicity is distributed along both the transform faults and mid-oceanic ridgecrests of the Atlantic. The morphology of the Mid-Pacific Rise also differs from the mid-atlantic ridge. The mid- Atlantic ridge is characterized by a graben at the summit whereas the Mid-Pacific Rise is not (Figure 21). Generally, spreading centers with rates >~6 cm/yr do not show midaxes grabens or rifts whereas spreading centers characterized by V< 6 cm/yr show a mid-axial rift. The difference in morphology and the lack of mid-axial earthquakes along fast spreading centers is thought to be due to the difference in spreading rates. Spreading ridges with axial highs (rather than grabens) do not have ridge crest faulting. Spring 2018 - wesnousky 13
Figure 21. Schematic illustration of ridge crest morphology for (left) slow spreading and (right) fast spreading ridges. Bibliography Barazangi, M., and J. Dorman (1969). World seismicity maps compiled from ESSA, Coast and Geodetic Survey, epicenter data, 1961-1967, Bulletin of Seismological Society of America, 59, 369-380. Bergman, E. A., and S. C. Solomon (1984). Source mechanisms of earthquakes near mid-ocean ridges from body waveform inversion - implications for the early evolution of oceanic lithosphere, Journal of Geophysical Research, 89, 1415-1441. Burr, N. C., and S. C. Solomon (1978). Relationship of source parameters of oceanic transform earthquakes to plate velocity and transform lenght, Journal of Geophysical Research, 83, 1193-1206. Engeln, J. F., D. A. Wiens, and S. Stein (1986). Mechanisms and Depths of Atlantic Transform Earthquakes, Journal of Geophysical Research-Solid Earth and Planets, 91(B1), 548-577. Forsyth, D. W. (1975). Early Structural Evolution and Anisotropy of Oceanic Upper Mantle, Geophysical Journal of the Royal Astronomical Society, 43(1), 103-162. Forsyth, D. W. (1977). Evolution of Upper Mantle beneath Mid-Ocean Ridges, Tectonophysics, 38(1-2), 89-118. Huang, P. Y., and S. C. Solomon (1988). Centroid Depths of Mid-Ocean Ridge Earthquakes - Dependence on Spreading Rate, Journal of Geophysical Research-Solid Earth and Planets, 93(B11), 13445-13477. Huang, P. Y., S. C. Solomon, E. A. Bergman, and J. L. Nabelek (1986). Focal Depths and Mechanisms of Mid-Atlantic Ridge Earthquakes from Body Wave-Form Inversion, Journal of Geophysical Research-Solid Earth and Planets, 91(B1), 579-598. Parsons, B., and J. G. Sclater (1977). Analysis of Variation of Ocean-Floor Bathymetry and Heat-Flow with Age, Journal of Geophysical Research, 82(5), 803-827. Solomon, S. C., and N. C. Burr (1979). Relationship of source parameters of ridge-crest and transform earthquakes to the thermal structure of oceanic lithosphere, Tectonophysics, 55, 107-126. Stein, S. (1991), Introduction to Seismology, Earthquakes, and Earth Structure, preprint ed., 553 pp., Department of Geological Sciences, Northwestern University. Spring 2018 - wesnousky 14