Global variation of seismic energy release with oceanic lithosphere age

Variations in Mid Ocean Ridge seismicity with age provide a new tool to understand the thermal evolution of the oceanic lithosphere. The sum of seismic energy released by earthquakes during a time, and for an area, is proportional to its lithospheric age. Asthenospheric temperatures emerge on ridge centers with new crust resulting in high seismic activity; thus, the energy released sum is highest on the young lithosphere and decreases with age. We propose a general model that relates the systematic variation of seismic energy released with the lithospheric age. Our analysis evaluates the main physical factors involved in the changes of energy released sum with the oceanic lithosphere age in MOR systems of different spreading rates. These observations are substantiated based on three cross-sections of the East Pacific Rise, six sections in the Mid Atlantic Ridge, and three profiles in the Central Indian Ridge. Our global model provides an additional tool for understanding tectonic processes, including the effects of seismicity and mid-plate volcanism, and a better understanding of the thermal evolution for the young oceanic lithosphere.

Transect considerations and energy release sum. We derived twelve perpendicular transects in different MOR areas, three transects located on the EPR, six on the MAR, and three on the CIR (Fig. 1). We selected areas with a special high density of earthquakes recorded in the ridge area located towards the flanks and ridge areas whose transforming boundaries were relatively spaced. Hence, areas with very few events and/or with significantly affected by transform boundaries were avoided. The transect longitudes, and the corridors, depended on the distribution and scatter of events, and longitudes vary between 3° to 5° (approx. 350-550 km), and the transect corridor widths range from 0.3º to 1°. Additionally, due to the fact that some study areas were located close to transforming zones, it was necessary to check the focal mechanisms to exclude the strike-slip mechanism and only to consider earthquakes associated with spreading centers. Also, the corridor is broad enough to prevent the relocation process. We divide the ocean basins into age intervals of 1 Ma, and then we computed the sum of seismic energy released by earthquakes located within each age interval along the transects.
Seismic energy calculations and global model. The seismic catalog used in this work has limited magnitude resolutions. It is due to the location of seismic networks and limitations for deployments of oceanbottom seismometers. Hence, the computation of seismic energy released by earthquakes, for each transect, would be restricted to the completeness magnitude (M c ), which varies from 4.8 to 4.5. Furthermore, the transect with the most number of events involved (Fig. 1D,L) has almost 70 earthquakes. Thus the low number of events try to estimate makes it challenging to use the b-value parameter for evaluating the number of earthquakes below the M c for each age interval. Then, it is important to note that we are not considering the energy released by microseismicity. However, we consider that the contribution of microseismicity to empirical relationships is not significant. Since the sum of seismic energy is calculated using the moment magnitude (M o ) formula, in this work, we use a series of empirical relationships to obtain the seismic energy released. First, knowing the bodywave magnitude (m b ) from the seismic catalog, we used the empirical approach given by Shapira and Hofstetter 25 to estimate M o from m b (Eq. 1) .
Then we used the model proposed by Hofstetter and Shapira 26 that relates the seismic energy with M o (Eq. 2), where M o is expressed in dyn⋅cm, and Log (E O ) is in ergs.
Once we computed the sum of seismic energy released for the age intervals along the twelve transects, we performed an average energy release sum for EPR, MAR, and CIR (Fig. 5). Finally, following the methodology proposed by Sclater et al. 8 and Stein & Stein 1 , we estimated a general relationship between the sum of seismic energy released and the oceanic lithosphere age based on a linear regression by least-squares fit between the binary combination of these parameters.

Results
MOR systems and seismic energy released. It is noticeable in the transects that, independent of the spreading rate, there are more seismic events along the ridge axis. The event count decreases towards the axial flanks. Also, scarce earthquakes of high and intermediate magnitude occur preferentially in the young oceanic lithosphere (Fig. 2). Interestingly, we observe that as the spreading rates increase, the number of spreading earthquakes reduces. In contrast, in slow-spreading centers like MAR and CIR ( Fig. 2D-L), we observed up to twenty events for the lithosphere younger than 1 Ma. In the EPR, for the same age interval, there occurred only five to ten events ( Fig. 2A-C). The EPR transect generally shows a higher frequency of seismic events of low and moderate magnitudes (m b < 5.5), mostly concentrated on the ridge axes. At the ridge axes, the 1200 °C isotherm emerges, and as the oceanic lithosphere gets colder, the seismicity production decreases.
Our results show that changes in spreading rates lead to changes in the seismic regime on MOR's and, therefore, calculating the sum of energy released for individual transects, we find that it is a little higher in fastspreading MOR's systems than for slow-spreading rates regimes (Fig. 3). Also, as the spreading rate decreases, the seismicity has a greater range with respect to the age of the lithosphere. In the EPR (Fig. 3A-C), the sum of  In the older lithosphere, between 3 to 10 Myr, the sum of seismic energy released decreases gradually to a value of Log(E o ) = 18.020 ± 0.765 erg (Fig. 4b).
On the CIR, we found that the sum of seismic energy released decrease rapidly for younger ages until 3 Myr approximately. Moreover, for the lithosphere older than 3 Myr, it decreases more gently until 6 Myr. For the lithosphere younger than 1 Myr, the sum of seismic energy released is Log(E o ) = 19.984 ± 0.665 erg, and it shows a rapid decay until 3 Myr. For lithosphere ages ranging between 3 and 6 Myr, the sum of energy released decreases gradually since Log(E o ) = 18.995 ± 0.583 erg to a value of Log(E o ) = 16.840 ± 0.339 ergs respectively (Fig. 4c).
Global model. The systematic decrease of the seismic energy released, in the young oceanic lithosphere, from the ridge axis towards the older flanks, is notable in each of the cross-sections made on EPR, MAR, and CIR (Figs. 3, 4). The same behavior according to global bathymetry and heat flow were related to the lithosphere age 1,8,27 . Similarly, we calculated the average of the energy released sum for all MOR systems and proposed a comprehensive model as a function of age and independently of the spreading rate (Fig. 5a). According to our results, the average of the sum of the seismic energy released for a lithosphere no older than 1 Myr is Log(E o ) = 20.344 ± 0.282 erg. We also found that this energy released decreases rapidly with the square root of age, and it occurs over a lithosphere age of about 3 Myr where the energy released sum is Log(E o ) = 18.899 ± 0.583 erg. In crusts older than 3 Myr, this relation breaks down, and the energy decreases exponentially to a constant value of Log(E o ) = 18.02 ± 0.765 erg for lithosphere ages of 10 Myr (Fig. 5b). The statistical adjustment for t ≤ 3Myr (see Equations on Fig. 5a) shows a correlation coefficient of R 2 = 0.970 , with a constant value K 1 = 20.344   Fig. 5a show that the seismic energy released over the axis (t = 0) is infinite. For this reason, we carry out the integration of the formulas to remove the singularity in the proposed system. The limits of the integration extending from t i−1 to t i , where t 0 is zero (see Eqs. 3 and 4), and the integral is given in erg⋅Myr. Thus, a finite value for the average energy released in a young lithosphere above the ridge's axis is found easily.
It is necessary to bear in mind that these expressions are restricted to the seismicity around the ridge. Thus, the main limitation to generate these empirical relations are aseismic zones in MOR's; hence, we considered only the most seismically active zones. According to the study areas, it was possible to compute the sum of seismic energy for the lithosphere no older to 10 Myr (Fig. 5a). Furthermore, we consider that to generate a more representative model, observations in more ridge systems must be rendered. In that case, the outcome of new scenarios may gradually modify the expressions proposed. furthermore, to the extent that digital signals are used to calculate energy, it is expected to have less uncertainty with respect to the models presented in this work.

Discussion
The results obtained for each MOR system show a variation of the sum of seismic energy released with the spreading rate. At slower spreading rates, the energy released would be expected to decrease (Fig. 4). However, for fast-spreading rates, the sum of seismic energy released could be computed only for very young oceanic lithospheres (EPR ≤ 4 Myr). Whereas for low spreading rates, it was possible to estimate the energy for slightly older oceanic lithospheres (MAR ≤ 10 Myr). One of the relevant factors that seems to determine the seismicity occurrence in young plates is the high thermal gradient in areas close to the axis of the spreading center 9,28 , which is governed by the isotherm 1200 °C 5 . Thus, we assume that for fast-spreading rates, the isotherm is near the surface and high temperatures due to the a steeper geotherm than on slow-spreading rate areas, where the isotherms would be flatter. These observations can be supported by taking into account some physical variables that have an effect on the behavior of the 1200 °C isotherm. Hydrothermal flow at oceanic spreading centers remove for about ten percent of all heat flux in the oceans and controls the thermal structure of young oceanic plates 2,29 . Additionally, hydrothermal cooling enhances cracking events in the upper crust of ridge environments 30 . Previous hydrothermal circulation studies on MOR's show deep, but perhaps more significant, heat sources at slower spreading ridges. They provide larger and longer-lived but sparser hydrothermal venting sites and cooling. The steady, near-continuous, shallow magma supply at the fast-spreading ridges leads to frequent but small-scale vent fields 31 . Hence, the upper crust is, therefore, sensitive to crustal inflation and/or heating. Still, another possibility to consider is that seismicity could vary as the stress concentrations change with the shallow heat source of the axial magma chamber 32,33 . If this is so, concentrations of stress near the slow-spreading ridge center would be greater than stresses on fast-spreading rates giving rise to increased seismicity on the last ones. A good way to verify this is through the spatio-temporal monitoring of b-value, and them analyses more careful the state of The frequency of the oceanic intraplate earthquakes shows an apparent variation for different spreading rates. The maximum number of events for an interval of less than 1 Myr occurs in slow-spreading centers and this quantity decrease with the spreading rate. On slow-spreading rate centers, such as MAR and CIR, the seismicity involved greater age ranges of the lithosphere than fast-spreading. It could be due to a high thermal gradient, variations in hydrothermal circulations, and increasing extensional stresses in the axial ridge.
Our results show a variation in the sum of seismic energy released with the age of the lithosphere, and globally it can be expressed according to the formulas in Fig. 5. In particular, our model predicts the energy released sum with age for young oceanic lithospheres (t ≤ 10 Myr). We suggest that the variations in the energy released with age are an expression of the thermal evolution of the young oceanic lithosphere. Hence we used the calculated data of energy released sum for the global model of the oceanic thermal evolution (Fig. 5b). Our model suggests that, probably due to a high thermal and highly stressed areas, the sum of energy released decreases steeply on a very young lithosphere (< 3 Myr approx). Thus, we assume that the 1200 °C isotherm has a steep descent to depths close to 30 km for the lithosphere age around 3 Myr. For crust older than 3 Ma, the isosurface could change its trend and begins an asymptotic flattening, where the thermal gradient should be lower and stable, resulting in a low rate of seismicity in the upper crust. The dramatic depth-changes in the general shape of the isosurface, between 2 and 3 Myr, can also be explained by variations in the elastic thickness of the oceanic lithosphere and by the effects of hydrothermal circulation that, together and in a delicate balance, control the thermal gradient of the lithosphere.