The Meaning of Global Ocean Ridge Basalt Major Element Compositions

Mid-ocean ridge basalts (MORB) are arguably the most abundant and also the simplest igneous rocks on the Earth. A correct understanding of their petrogenesis thus sets the cornerstone of igneous petrogenesis in general and also forms the foundation for studying mantle dynamics. Because major element compositions determine the mineralogy, phase equilibria and physical properties of rocks and magmas, understanding global MORB major element systematics is of prime importance. The correlated large MORB major element compositional variations are well understood as the result of cooling-dominated crustal-level processes (e.g. fractional crystallization, magma mixing, melt–rock assimilation or reaction, and other aspects of complex open-magma chamber processes), but it remains under debate what messages MORB major elements may carry about mantle sources and processes. To reveal mantle messages, it is logical to correct MORB melts for the effects of crustal-level processes to Mg# 0 72 to be in equilibrium with mantle olivine of Fo90. Such corrected MORB major element (e.g. Si72, Ti72, Al72, Fe72, Mg72, Ca72 and Na72) compositional variations thus reflect fertile mantle compositional variation, composition-controlled mantle physical property variation (e.g. density and solidus), variation in the extent and pressure of melting, and uncertainties associated with the correction. The correction-related uncertainties can be removed through justified heavy averaging. Because ridge axial depth variation ( 0 to 6000 m below sea level) and plate spreading rate variation (<10 to >150 mm a) are the two largest known physical variables along the global ocean ridge system, possible correlations of MORB major element compositions at Mg# 0 72 with these two physical variables are expected to reveal intrinsic controls on global MORB petrogenesis and ocean ridge dynamics. Indeed, global MORB major element data averaged with respect to both ridge axial depth intervals and ridge spreading rate intervals show significant first-order correlations. These correlations lead to the conclusion that the ridge axial depth variation and MORB chemistry variation are two different effects of a common cause, induced by fertile mantle compositional variation. The latter determines (1) variation in both composition and mode of mantle mineralogy, (2) variation of mantle density, (3) variation of ridge axial depth, (4) source-inherited MORB compositional variation, (5) density-controlled variation in the maximum extent of mantle upwelling, (6) apparent variation in the extent of melting, and (7) the correlated variation of MORB chemistry with ridge axial depth. These correlations also confirm the recognition that the extent of mantle melting increases with, and is caused by, increasing plate spreading rate. Mantle temperature variation could play a part, but its overstated role in the literature results from a basic error (1) in treating ridge axial depth variation as solely caused by mantle temperature variation by ignoring the intrinsic control of mantle composition, (2) in treating mantle plume-influenced ridges (e.g. Iceland) as normal ridges of plate spreading origin, and (3) in treating seismic low velocity at great depths (>300 km) beneath these mantle plume-influenced ridges as evidence for hot ridge mantle. There is no evidence for large mantle temperature variation beneath ridges away from mantle plumes. The suggested conclusions of this study may continue to be VC The Author 2017. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 2081 J O U R N A L O F P E T R O L O G Y Journal of Petrology, 2016, Vol. 57, No. 11&12, 2081–2103 doi: 10.1093/petrology/egw073


INTRODUCTION
Mid-ocean ridge basalts (MORB) are arguably the most abundant igneous rocks on the Earth because they cover much of the global ocean floor and continue to form along the $60 000 km long globe-encircling ocean ridges. They are also arguably the simplest igneous rocks on the Earth because they have relatively uniform chemical and isotopic compositions and because their origin is well understood as a straightforward consequence of plate tectonics; that is, plate separation induced passive mantle upwelling, decompression melting, melt extraction and cooling-dominated crustal-level differentiation (e.g. Klein & Langmuir, 1987;McKenzie & Bickle, 1988;Niu & Batiza, 1991a;Sinton & Detrick, 1992;Niu, 1997). Nevertheless, MORB compositional variations do exist on all scales and have been recognized from the early days of MORB studies (e.g. Sun et al., 1975Sun et al., , 1979Bryan & Moore, 1977;Langmuir & Hanson, 1980;Schilling et al., 1983). The correlated large major element compositional variation has been correctly explained as resulting from low-pressure crustal-level differentiation (O'Hara, 1968a(O'Hara, , 1968bWalker et al., 1979;Stolper, 1980;Perfit & Fornari, 1983;Christie & Sinton, 1986;Langmuir et al., 1986;Langmuir, 1989;Sinton et al., 1991;Sinton & Detrick, 1992;Batiza & Niu, 1992;Rubin et al., 2009;O'Neill & Jenner, 2012;Coogan & O'Hara, 2015). Variations in abundances and ratios of incompatible elements and radiogenic isotopes have been logically interpreted as reflecting fertile mantle source compositional variation (e.g. Frey et al., 1974;Sun et al., 1975Sun et al., , 1979Zindler et al., 1984;Mahoney et al., 1994;Niu et al., 1996Niu et al., , 1999Niu et al., , 2001Castillo et al., 1998Castillo et al., , 2000. In addition to these repeatedly verified and generally accepted interpretations, MORB melts, in particular their major element compositions, are predicted also to carry information on both mantle sources and processes as shown by the correlated variations among major element abundances, incompatible element ratios and radiogenic isotopes (e.g. Langmuir & Hanson, 1980;Christie & Sinton, 1986;Natland, 1989;Niu & Batiza, 1991a, 1997Mahoney et al., 1994;Shen & Forsyth, 1995;Niu et al., 1996Niu et al., , 1999Niu et al., , 2001Niu et al., , 2002aLecroart et al., 1997;Rubin et al., 2009) and by experimental petrology (e.g. Jaques & Green, 1980;Green & Falloon, 1998, 2015Green, 2015). On the basis of ample observations and many studies, it is reasonable to state that MORB major element compositional variation must be inherited from the fertile mantle source compositional variation while also recording the physical conditions of magma generation as a result of plate spreading rate variation (Niu & Hé kinian, 1997a, 1997b and possibly mantle potential temperature variation (see Niu et al., 2001). In this regard, the work by Klein & Langmuir (1987), after , offered an unprecedented insight. It showed correlated variations of MORB Fe 8 and Na 8 (i.e. FeO and Na 2 O values corrected for fractionation to a constant MgO value of 8 wt %) with ridge axial depth on a global scale. These correlations have been interpreted, following the experimental data of mantle peridotite melting (Jaques & Green, 1980), as reflecting varying extent and pressure of mantle melting in response to mantle solidus temperature variation of up to 250 K on a global scale. Langmuir et al. (1992) further elaborated quantitatively that the global MORB Fe 8 variation can be effectively used to calculate the mantle solidus temperature (T [solidus] ) and pressure (P [solidus] ) and mantle potential temperature (T P ) from the single MORB Fe 8 parameter: P [solidus] ¼ 6Á11Fe 8 À 34Á5 (kbar), T [solidus] ¼ 1150 þ 13P [solidus] ( C), and hence T P ¼ T [solidus] À P [solidus] Â 1Á8 ( C) by using the experimentally determined dry mantle solidus curve and by assuming an adiabatic thermal gradient of 1Á8 K kbar -1 (see McKenzie & Bickle, 1988; also see Niu & O'Hara, 2008).
Because of its convenience, Fe 8 has been popularly and axiomatically used in basalt studies. Given the welldocumented mantle compositional heterogeneity for all major elements including FeO (e.g. Langmuir & Hanson, 1980;Niu et al., 1999Niu et al., , 2002a, and to conscientiously inform readers of the inevitable errors when indiscriminately using Fe 8 in MORB studies, Niu & O'Hara (2008) demonstrated in detail in terms of straightforward petrological concepts, physical principles and logical arguments that Fe 8 is a misguiding parameter and cannot be used to infer mantle conditions and processes. In defence of the 'usefulness' of Fe 8 , Langmuir and his group recently published two papers Gale et al., 2014) to refute the demonstrations by Niu & O'Hara (2008).
In commemoration of Michael J. O'Hara in this thematic O'Hara volume, and given the fundamental importance of understanding MORB petrogenesis as the foundation for igneous petrology in particular and global mantle dynamics in general, there is a pressing need to demonstrate explicitly and objectively that using Fe 8 in MORB studies can be misleading and must be treated with caution. The first-order global MORB major element compositional variation is largely source inherited and the signal of varying extent of melting as a function of plate spreading rate variation is also conspicuous as demonstrated previously (Niu & Hé kinian, 1997a). A more comprehensive and thorough demonstration on the origin of global MORB chemical systematics will be presented elsewhere.
In Fig. 1 the Klein & Langmuir (1987) data show that the MORB melts with varying Fe 8 values have Mg# $0Á55-0Á68, which is significantly lower than the Mg# ! 0Á72 required to be in equilibrium with mantle olivine. Hence, in terms of the straightforward petrological concept, Fe 8 cannot be used to infer mantle processes simply because it records dominantly the highly evolved signature of MORB melts that have ascended across the Moho and left the mantle. The mantle solidus temperatures (T [solidus] ) and potential temperatures (T P ) calculated by using Fe 8 following Klein & Langmuir (1987) and Langmuir et al. (1992) thus have no significance. The varying low Mg# values exhibited by MORB melts with varying Fe 8 (as in Fig. 1) are consistent with varying extents of crustal-level MORB melt evolution (O'Hara, 1968a(O'Hara, , 1968bWalker et al., 1979;Niu, 1997).
In this context, it is important to note that the popular emphasis on mantle pyroxenites as sources of OIB and some alkali basalts (e.g. Sobolev et al., 2007) has led some to consider that mantle melts generated by pyroxenite melting should have low Mg# (e.g. Yang & Zhou, 2013). This is wrong in concept and incorrect in practice, for the following reasons: (1) melting of pyroxenites with Mg# ! 0Á90 would still produce primitive melts with Mg# ! 0Á72 constrained by the Fe-Mg exchange Kd (i.e. Kd clinopyroxene/melt % Kd orthopyroxene/melt % Kd olivine/melt % 0Á30 6 0Á03 (e.g. Grove et al., 1992;Niu et al., 2002b); (2) partial melts of pyroxenites with low Mg# values (e.g. subducted ocean crust) will readily reach chemical equilibrium with the ambient mantle mineralogy to gain Mg# ! 0Á72, because pyroxenites are volumetrically minor; (3) the melts generated by pyroxenite total melting will have the same Mg# as the pyroxenites and will again reach equilibrium with the ambient mantle mineralogy to gain Mg# ! 0Á72, regardless of the actual pyroxenite compositions. Hence, ascending mantle melts prior to crossing the Moho should all be in equilibrium with mantle mineralogy and have Mg# ! 0Á72 unless  Klein & Langmuir (1987) (KL87) indicating the first-order MORB major element Fe 8 variation (weight per cent FeO corrected for fractionation effect to MgO ¼ 8Á0 wt %) as a function of ocean ridge axial depth (water depth). Klein & Langmuir used Fe 8 to infer mantle temperature variation (see Langmuir et al., 1992). Niu & O'Hara (2008) demonstrated that this Fe 8 usage is erroneous because to reveal mantle melting conditions and processes, MORB melts must have Mg# ¼ Mg/(Mg þ Fe 2þ ) (10% total Fe is assumed to be Fe 3þ in the Mg# calculation) ! 0Á72 to be in equilibrium with mantle olivine of Fo ! 90. However, MORB Fe 8 values correspond to Mg# ¼ 0Á54-0Á68 as in (b), which are too evolved to be in equilibrium with mantle olivine and thus cannot be used to infer mantle melting conditions and processes, but largely tell us about crustal-level differentiation processes. (c) combines (a) and (b) to illustrate the variably evolved nature of MORB melts corrected to Fe 8 . This figure is simplified from Niu & O'Hara (2008). significant cooling and olivine crystallization has taken place during melt ascent through the cold thermal boundary layer beneath ridges (or lithospheric mantle elsewhere) as seen in abyssal peridotites (Niu, 1997;. Therefore, if one wants to unmistakably decipher mantle processes from MORB major element compositions, it is required to correct for the effects of crustal-level processes to Mg# ! 0Á72 (e.g. Si 72 , Ti 72 , Al 72 , Fe 72 , Mg 72 , Ca 72 and Na 72 ), which must be constrained by the most primitive MORB glass samples with Mg# ! 0Á72 (see Niu et al., 1999;Niu & O'Hara, 2008).
The Klein & Langmuir (1987) correction to Fe 8 has no significance Figure 2 is modified from Niu & O'Hara (2008) to compare the fractionation-corrected data of Klein & Langmuir (1987) with fractionation-uncorrected average MORB data with MgO ! 7 wt %. This illustrates that the apparently meticulous correction procedure of Klein & Langmuir (1987) is an unnecessary data manipulation because the corrected Fe 8 and Na 8 values have no geological difference from the uncorrected data. This is true for Na 2 O and largely true also for FeO and Mg# because the Klein & Langmuir (1987) interpretations were largely based on the large range (i.e. in Fe 8 ) defined by samples from the shallowest and deepest ridges (see Niu, 1997). This evident problem remains despite the apparently exhaustive arguments in defence of the Fe 8 parameter by Gale et al. (2014) as discussed below.
The Gale et al. (2014) justification of Fe 8 correction is unjustified Gale et al. (2014) made a commendable effort in providing an updated MORB dataset for improved studies. They discussed global MORB systematics and their origin. However, the very heart of the study by Gale et al. (2014) is to refute the Niu & O'Hara (2008) criticism against using Fe 8 and to defend the Fe 8 -based interpretations by Klein & Langmuir (1987) and Langmuir et al. (1992). The Niu & O'Hara (2008) criticism of using Fe 8 has three specific points: (1) Fe 8 , representing highly and variably evolved MORB compositions, cannot be used to decipher mantle processes as discussed above; (2) MgO and FeO are both sensitive and proportional to the pressure of melting in primitive melts in equilibrium with mantle mineralogy (see Niu & O'Hara, 2008, fig. 1), but the use of the Fe 8 parameter with constant MgO ¼ 8 wt % has ignored MgO as a potential pressure indicator; (3) SiO 2 is also sensitive to pressure of melting, but is inversely proportional to MgO and FeO in primitive melts in equilibrium with mantle mineralogy (see Niu & O'Hara, 2008, fig. 12a), but MORB SiO 2 shows no pressure signature (see Niu & O'Hara, 2008, fig. 12b and c). Gale et al. (2014) skilfully replied to these critical points through an apparently painstaking effort, which is in fact unjustified and has an additional misguiding effect.
The Gale et al. (2014) global MORB data in the MgO-FeO space are illustrated in Fig. 3a. It is evident that the corrected Fe 8 values must be equal to or greater than the range of 7-12Á5 ($5Á5 Fe units) as indicated for FeO at MgO ¼ 8 wt %. To argue for Fe 8 to be useful in reflecting mantle-melting conditions as claimed, Gale et al. (2014) also corrected MORB melts to be in equilibrium with mantle olivine of Fo 90 , denoted as Fe 90 . As shown  Niu & O'Hara (2008) (NOH08) to show that the apparently meticulous correction procedure of Klein & Langmuir (1987) (KL87) has little significance because both corrected and uncorrected data are essentially the same, dominated by a variably evolved nature with Mg# ¼ 0Á54-0Á68. This figure is simplified from Niu & O'Hara (2008), where details of depth-interval averages are explained in their fig. 3 and accompanying text.
in Fig. 3b their calculated Fe 8 and Fe 90 are essentially the same, with the calculated Fe 8 (or Fe 90 ) in the range of 6-13 ($7 Fe units). The significant Fe 8 -Fe 90 correlation with the same range of values looks convincing, but is curiously incomprehensible. It is puzzling and confusing why MORB melts are in equilibrium with mantle olivine Fo 90 if expressed with Fe 90 (i.e. horizontal-axis Mg# melt $0Á72-0Á73), whereas these same MORB melts are not in equilibrium with mantle olivine if expressed with Fe 8 (i.e. vertical-axis Mg# melt $0Á70 -< 0Á54) despite the simple fact that Fe 8 % Fe 90 (Fig. 3b). I leave this petrological impossibility to readers to comprehend, but only offer my personal understanding of the Gale et al. (2014) correction in terms of a simple mathematic treatment.
It is obvious that the only way to produce the correlated values in Fig. 3b is to set a given Fe 8 value as the target to produce Fe 90 ! Fe 8 . This can be done by raising MgO while lowering FeO as much or as little as needed. This is illustrated in Fig. 3c, where MgO must be raised, on average, by a factor of two (e.g. Mg 90 ) higher than the actual data (the horizontal-axis values), whereas FeO must be lowered from the range of 7-16 (horizontal-axis value of Fig. 3a) to Fe 90 $5-12 (Fig. 3c). This may be assumed to be equivalent to adding olivine Fo 90 (or other Fo values) until Fe 90 % Fe 8 , by adding more olivine (hence more MgO) to samples with higher Fe 8 and less olivine (hence less MgO) to samples with lower Fe 8 . In doing so, the primary melt in the mantle source region parental to each of the MORB samples would have Mg# $0Á72-0Á73 in equilibrium with the mantle mineralogy (see Fig. 3d).
There has been a long history in petrology of adding olivine to evolved basaltic melts to infer their primary magma compositions in equilibrium with the mantle mineralogy. Despite the various uncertainties in doing so, this is nevertheless a useful approach. The question is if this approach by Gale et al. (2014) is appropriate here. The answer is simply 'No' because (1) adding varying amounts of olivine with the purpose of making Fe 90 ! Fe 8 is an unjustified exercise, and (2) the so calculated FeO (Fe 90 , same as Fe 8 ) and MgO (Mg 90 ) in equilibrium with mantle olivine of Fo 90 shown by the stacked red open circles with large MgO ($8-19 wt %) and FeO ($6-12 wt %) variations ( Fig. 3d) are remotely removed from, and having no relevance to, the actual That is, the Gale et al. (2014) correction to Fe 90 is entirely unconstrained and is petrologically unlikely -way beyond the data and beyond petrologically possible and permitted interpolation and extrapolation range.
Their 'olivine addition' procedure apparently answered the criticisms by Niu & O'Hara (2008) (see above) because olivine controls the positive Fe 90 -Mg 90 correlation (red circles in Fig. 3d) and negative Si 90 -Mg 90 and Si 90 -Fe 90 correlations (not shown here) as if the varying Fe 90 , Mg 90 and Si 90 values were consistent with mantle melting pressure effects. It is objectively correct to state that MORB melts preserve no melting pressure signature at all in terms of SiO 2 as demonstrated in fig. 12 of Niu & O'Hara (2008) [also see Niu et al. (2011) and further illustration below]. The correlated Fe 90 -Mg 90 -Si 90 variations by Gale et al. (2014) have no pressure significance, but are the artefact of making Fe 90 ! Fe 8 (Fig. 3b). can be used to discuss mantle sources and processes because primitive melts having Mg# ! 0Á72 are in equilibrium with mantle olivine of Fo ! 0Á90 (Fo 90 ).

THE EFFICACIES OF MORB MAJOR ELEMENTS
However, MORB melt FeO contents corrected to MgO ¼ 8 wt % (i.e. Fe 8 with Mg# ¼ 0Á56-0Á68) are too evolved to be in equilibrium with mantle olivine and cannot be used to discuss mantle processes as elaborated above. The Gale et al. (2014) corrected Fe 90 cannot be used either because Fe 90 ¼ Fe 8 (Fig. 3b).
Petrological effectiveness of Fe 72 versus misguiding Fe 8 Gale et al. (2014) asserted that their new data are not in agreement with the presentation of Niu & O'Hara (2008), 'whose results relied on an inaccurate fractionation correction procedure, which led them to large errors for high-and low-FeO magmas' (p. 1051). This is an incorrect statement as further demonstrated below in terms of basic petrological concepts and elementary illustrations. Figure 4a is a familiar diagram showing global MORB melt (glass) major element oxide abundance variations as a function of MgO. Because MgO is proportional to the liquidus temperature, the data trend for each of the oxides with decreasing MgO is to a first order consistent with the liquid line of descent (LLD), which is conceptually the residual melt compositional variation as the result of fractional crystallization of olivine þ spinel ! plagioclase þ olivine ! plagioclase þ , assuming Fe 2þ /total Fe ¼ 0Á9 for simplicity]. As MgO is linearly proportional to the liquidus temperature (e.g. Weaver & Langmuir, 1990;Danyushevsky, 1998;Niu et al., 2002b;Niu & O'Hara, 2009), all the oxide variations with decreasing MgO define first-order liquid lines of descent (LLD) during cooling-dominated MORB melt cooling and evolution. In detail, however, these trends are not simple LLD, but the combined effect of LLD, magma mixing, melt-rock reactions and complex open-magma chamber processes (O'Hara, 1977). In other words, these trends are the net effect of all these natural processes. Mg# is not strictly linearly proportional to the liquidus temperature, but is convincingly close for MORB melts with MgO > $ 4 wt % (see Niu et al., 2002b;Stone & Niu, 2009), with deviation caused by varying FeO content. Hence, to a first order, MORB major element oxide abundance variations versus Mg# in (b) are also a net effect of the combined MORB melt evolution trends. As indicated by the vertical gray dashed lines, the band width for each oxide would be the values and ranges at MgO ¼ 8Á0 wt % in (a) or at Mg# ¼ 0Á72 in (b), respectively. clinopyroxene 6 olivine prior to reaching MgO $4Á0 wt %, after which crystallization of titanomagnetite (Ti-Fe oxides) depletes FeO and TiO 2 while increasing SiO 2 , entering the basaltic-andesite stage of basaltic magma evolution (e.g. Niu et al., 2002b;Niu, 2005a;Niu & O'Hara, 2009;Stone & Niu, 2009). Strictly speaking, the data trends in Fig. 4a are not simple LLD, but the net effect of cooling-dominated crustal-level processes combined (e.g. fractional crystallization, magma mixing, melt-rock assimilation and, or, reaction and other aspects of complex open-magma chamber processes). The Klein & Langmuir (1987) and Langmuir et al. (1992) method of calculating Fe 8 and Na 8 was to assume a common LLD slope for FeO-MgO and Na 2 O-MgO, respectively, to project individual data points onto the plane of MgO ¼ 8 wt % as indicated, by backtracking (for samples with MgO < 8 wt %) and forwardtracking (for samples with MgO > 8 wt %). To avoid correction errors, Klein & Langmuir (1987) and Langmuir et al. (1992) chose samples with MgO ! 5Á5 wt %. One can do the same to obtain Ti 8 , Al 8 , Ca 8 and Ca 8 /Al 8 (Niu & Batiza, 1991a. The only difference of the Gale et al. (2014) approach from that of Klein & Langmuir (1987) and Langmuir et al. (1992) was to obtain separate sets of LLD for MORB samples from each ridge segment with the belief that samples from different ridge segments have different LLD trends as discussed by Niu & Batiza (1993). This philosophical consideration is reasonable, but has unavoidable problems: (1) MORB samples from most ridge segments do not have enough MgO variation coverage to obtain suitable LLD (if they were LLD); hence, assumptions must be made to justify the chosen LLD slopes that in practice cannot be constrained; (2) natural MORB sample suites do not define pure LLD, but show the combined effects of complex crustal-level processes (see above).
The same data as a function of Mg# are plotted in Fig. 4b. The data trends are again not simple LLD, but the net effect of compound crustal-level processes (see above). To correct for such net effect for the global dataset, it is logical to find a common set of correction coefficients for each oxide, applicable to the global dataset in this Mg# variation diagram. Obviously, the most objective, logical and simplest method is to obtain a set of polynomial regression coefficients for each oxide based on the entire global dataset (see Niu et al., 1999;Niu & O'Hara, 2008) and to project each sample along the polynomial curves to Mg# ¼ 0Á72 as indicated by the vertical gray dashed line in Fig. 4b. To avoid unnecessary errors, Niu & O'Hara (2008) used MORB samples with MgO ! 7Á0 wt %, thus the polynomial coefficients mostly give rise to linear coefficients, especially for FeO and MgO [see Appendix of Niu & O'Hara (2008)]. This method of correction is objective, logical and simple for the following reasons.
1. We follow the data (Fig. 4b) without making any unnecessary assumption that cannot be justified.
2. Regardless of how evolved and how complex the histories each MORB sample may have experienced through crustal-level processes, its parental melt must have once had Mg# ! 0Á72 within the range constrained by the data as indicated by the gray dashed line at Mg# ¼ 0Á72 (Fig. 4b). 3. The method corrects for the net effect of compound crustal-level processes expressed by the global data trends without having to know exactly what LLD for a single sample suite may be (Fig. 4b). 4. Mg# ¼ 0Á72 is the best reference point: (a) the most primitive MORB samples have Mg# % 0Á72-0Á73 (corresponding to some of the samples with MgO % 10Á5 wt % in Fig. 4a) so that the correction is well constrained within the known dataset ( Fig. 4b) without having to make assumptions that cannot be justified; (b) Mg# ¼ 0Á72 is about the minimum value for a basaltic melt required to be in equilibrium with mantle olivine. 5. The key difference of the Niu & O'Hara (2008) correction method is not an 'inaccurate fractionation procedure' as incorrectly stated by Gale et al. (2014), but the use of the petrologically and logically best reference of Mg# ¼ 0Á72 ( Fig. 5b) rather than the problematic reference of MgO ¼ 8Á0 wt % (Fig. 5a).
We should note that correction to MgO ¼ 8 wt % or Mg# ¼ 0Á72 has less effect on the relative abundances and systematics of Ti 72 (vs Ti 8 ), Al 72 (vs Al 8 ), Ca 72 (vs Ca 8 ) and Na 72 (vs Na 8 ), as well as Ca 72 /Al 72 (vs Ca 8 /Al 8 ), but has large effects on Fe 72 (vs Fe 8 ) and Mg 72 (vs Mg 8 ¼ 8) because of the FeO-MgO-Mg# interrelationships as further illustrated below.
More on the effectiveness of Fe 72 versus misguiding Fe 8 (and Fe 90 ) The variation of FeOt against MgO and Mg# respectively ( Fig. 5a and b) explicitly shows that Fe 72 is objective and more logical than Fe 8 , and why Fe 72 values must have a significantly smaller range ($1Á0 Fe unit) than Fe 8 ($4Á5 Fe units) without any correction. With decreasing MgO (or Mg#), the upper bound of FeOt reaches the maximum at MgO % 4 wt % (or Mg# % 0Á30) as a result of combined fractional crystallization of spinel þ olivine þ plagioclase þ clinopyroxene before Fe-Ti oxide (titanomagnetite) appears on the liquidus at MgO $4 wt % to cause FeOt depletion. By considering samples with MgO > 5Á5 wt % only, this can certainly avoid potential errors caused by highly evolved samples in correcting to Fe 8 (Klein & Langmuir, 1987;Langmuir et al., 1992;Gale et al., 2014). However, the actual data, with no correction, show that at MgO ¼ 8 wt %, FeO ¼ Fe 8 $7Á2 À $11Á7 wt % has an Fe 8 range of $4Á5 Fe units as indicated (Fig. 5a). This is the very minimum Fe 8 spread because correction for samples with MgO > 5Á5 wt % and < 8Á0 wt % onto the MgO ¼ 8Á0 wt % plane can only make the Fe 8 spread larger (i.e. > $4Á5 Fe units). On the other hand, it is evident that FeO at or projected to Mg# ¼ 0Á72 has a limited variation of  (2008) (NOH2008) used samples with MgO ! 7Á0 wt %, so the obviously scattered FeO values below these chosen cut-off MgO values will not affect the calculated Fe 8 or Fe 72 . However, those samples below the main trend in the broad shaded region cannot simply be evolved MORB melts, but are most consistent with being 'snapshots' of magma mixing in open magma chamber (or something equivalent) systems, largely resulting from mixing of newly replenished primitive melts with already highly evolved melts having low MgO and low FeO. There is no doubt that many samples towards the lower bound of the main data band at a given MgO or Mg# have resulted from such mixing, although it is not possible to precisely quantify this process. It is reasonable to infer that such mixing is more obvious in FeO-MgO space (a) than in the FeO-Mg# space (b) because of the significantly fatter lower bound at a given MgO in (a). The key message here is as follows: for this same dataset, Fe 8 $7-11Á5 wt % with variation of $4Á5 Fe units, corresponding to Mg# ¼ 0Á68 -0Á57, far too evolved to be used for discussing mantle melting conditions and processes. On the other hand, Fe 72 $7-8Á0 wt % with $1Á0 Fe unit variation at a constant Mg# ¼ 0Á72, which is in equilibrium with mantle olivine of Fo 90 and thus can be logically used to discuss mantle melting conditions and processes. It is straightforward that the small Fe 72 range of $1 Fe unit [versus the large Fe 8 range of >4Á5 Fe units found by Gale et al. (2014)] is a property of the actual data, and is not the result of an inaccurate correction procedure as incorrectly stated by Gale et al. $7-8 wt % with an Fe 72 range of $1 Fe unit as illustrated. Given the narrow FeO band at a given Mg#, and because all the samples, regardless of how they evolved, were modified through complex crustal-level processes, their parental melts must have once passed through Mg# ¼ 0Á72 with an Fe 72 spread that cannot be significantly greater than that observed. This is a straightforward demonstration based on the actual data without applying any correction, in contradiction to the incorrect statement by Gale et al. (2014).

THE MEANING OF MORB MAJOR ELEMENTS AT Mg# 5 0Á72
We can now use MORB major element compositions at Mg# ¼ 0Á72 to infer mantle processes. Because ridge axial depth variation ($0 to $6000 m) and plate spreading rate variation (<10 to >150 mm a -1 ) are the only two largest known physical variables along the global ocean ridge system, our task is to examine whether MORB major element compositions respond to these two physical variables. Klein & Langmuir (1987)   Ti 72 , Al 72 , Mg 72 , Ca 72 , Ca 72 /Al 72 as well as Na 72 and Fe 72 all correlate with ridge axial depth and offered different explanations for the cause of such correlations. Niu & Hé kinian (1997a) demonstrated the significant correlations of Al 8 and Ca 8 /Al 72 (also K 8 /Ti 8 as shown below) with plate spreading rate, which, together with the then available global abyssal peridotite data, were interpreted to reflect the extent of mantle melting, which increases with increasing plate spreading rate as expected in terms of straightforward physics (Reid & Jackson, 1981;Niu & Hé kinian, 1997a). However, Gale et al. (2014) denied the existence of such a correlation by stating: 'There is no correlation between the chemical parameters and spreading rate' (p. 1080). In this section, I discuss these correlations, but it is conceptually important first to clarify that spreading rate variation and ridge depth variation are two genetically unrelated variables (except for extremely slow-spreading ridges; see below) and we need to separate the effects of the two variables for a better understanding of ridge processes.
The origin of plate spreading rate variation and ridge axial depth variation Plate spreading rate here refers to the separation rate of the two plates with respect to each other on both sides of the ridge, which is also called the 'full spreading rate' or 'total opening rate' of the ridge, and is determined by the absolute motion speeds of the two plates relative to some hotspot reference framework (e.g. DeMets et al., 1990). The absolute motion speed of a given plate has been well understood as resulting from subducting slab pull (e.g. Forsyth & Uyeda, 1975;McKenzie & Bickle, 1988;Davies & Richards, 1992), which is straightforward to understand for plates connected with subduction zones such as those in the Pacific, but not so obvious for plate motion in the Atlantic. Nevertheless, Niu (2014Niu ( , 2016 illustrated that (1) seafloor spreading in ocean basins with passive margins (e.g. the Atlantic type) and (2) continental drift are simply passive movements in response to trench retreat of active seafloor subduction in ocean basins like the Pacific with subduction zones. Hence, the varying speeds of plate motion determine the plate spreading rates of the ridges concerned. Because ocean ridge magmatism results from plate separation, it is expected that the effect of plate separation rate variation must be recorded in the MORB chemistry. To deconvolve the effect of plate spreading rate variation from the effects of all other probable or possible variables involves averaging MORB chemistry with respect to spreading rate intervals, so as to average out all other possible effects (Niu & Hé kinian, 1997a). This is mathematically the same as seeking the partial derivatives of a quantity with respect to a particular variable, with all other variables held constant (Niu & O'Hara, 2008).
The above elaboration demonstrates that globally the large ridge axial depth variation is unrelated to spreading rate (see below for very slow spreading ridges). This is because ridge axial depth variation is largely controlled isostatically by sub-ridge material density variations owing to varying thermal or compositional buoyancy variations that are unknown to slab pulls in remote subduction zones. For example, the pulling of the subducting slabs in the western Pacific or beneath the Andes does not know the sub-ridge buoyancy and ridge axial depth variation at the southern East Pacific Rise. Nevertheless, it has been known for decades that ridge spreading rate differences do control across-ridge morphology and along-ridge topography on local and ridge segment scales, especially at slow-spreading ridges (e.g. Macdonald, 1982;Macdonald et al., 1988;Sempere et al., 1990;Sinton et al., 1991;Grindlay et al., 1991;Niu & Batiza, 1993;Niu et al., 2001;Dick et al., 2003). These local and segment-scale variations of ridge depth and morphology are most probably of lithospheric origin and isostatically uncompensated (i.e. dynamic topography or morphology). The effects of these features, if any, thus must be removed to reveal the origin of the correlated variations of MORB chemistry with ridge axial depth on a global scale. Klein & Langmuir (1987) and Gale et al. (2014) used regionally smoothed ridge axial depth to obtain an average depth value for a given ridge segment. This requires assumptions on how to smooth and how to choose a segment depth value. Instead, Niu & O'Hara (2008)  The meaning of MORB chemistry-ridge depth correlation As above for elucidating the spreading rate effect, to effectively deconvolve the effect of processes that lead to ridge axial depth variations from the effects of all other probable or possible variables, it is desirable to average MORB chemistry with respect to ridge axial depth intervals. The averaging is not arbitrary, but follows basic principles (Niu & O'Hara, 2008), as listed here.

A 250 m depth interval is chosen because this depth
interval size approximates the ridge depth variation over $500 km regional scale-lengths. This gives >20 average data points with which to work. This number of data points is large enough to be statistically significant without compromising first-order systematics, but small enough to smooth out secondary effects while making the first-order global systematics prominent. 2. The averaging uses actual sample depths regardless of geographical location and ocean basin (i.e. the Pacific, Atlantic and Indian Oceans). 3. Such heavy averaging averages out the effects of (a) spreading rate variation, (b) local-scale fertile source compositional heterogeneity [including the arbitrary normal (N-) and enriched (E-)type MORB division], and (c) dynamic topography on regional and ridge segment scales (see above) to objectively observe the significance of MORB chemistry variation with respect to ridge axial depth. MORB data with MgO ! 7 wt %, corrected to Mg# ¼ 0Á72 within each of the 22 depth intervals (bins) of 250 m from actual ridge depths of $250 to 5750 m below sea level (see Niu & O'Hara, 2008, fig. 3). Figure 7a and b shows significant correlations of MORB Ti 72 , Al 72 , Fe 72 , Mg 72 , Ca 72 , Na 72 and Ca 72 /Al 72 with ridge axial depth. Such correlations suggest a genetic relationship between MORB chemistry and ridge axial depth. However, this relationship, cannot be a 'cause and effect' one because ridge axial depth (water depth) cannot physically control MORB chemistry. I consider that the correlated variations of MORB chemistry with ridge axial depth in Fig. 7a and b are two different effects of a common cause. What is this common cause?
MORB chemistry-ridge depth correlation results from mantle compositional variation Niu & O'Hara (2008) demonstrated explicitly that the intrinsic cause is the fertile mantle major element compositional variation. This is because fertile mantle major element compositions determine (1) variation in both composition and mode of mantle mineralogy, (2) variation of mantle density, (3) variation of ridge axial depth because of the mantle density variation, (4) sourceinherited MORB compositional variation, (5) densitycontrolled variation in the maximum extent of mantle upwelling, (6) apparent variation in the extent of melting, and (7) the correlated variation of MORB chemistry with ridge axial depth. These physically straightforward, logically sound and geologically simple demonstrations are summarized in Fig. 7c.
The physical significance of the correlation between MORB chemistry and ridge axial depth is shown in Fig. 7 in the form of schematic illustrations, which are convenient for conceptual clarity [see Niu & O'Hara (2008) for quantitative analysis; their figs 13-19 and related discussion]. It has long been recognized that source rock compositions exert a key control on the resulting magmas, as summarized by Cox (1992): 'the most fundamental thing to understand is that the spectrum of compositions we see is controlled in the first place by the composition of the Earth itself. Just as in the simplest phase diagram the course of evolution of residual liquids by fractionation, or the course of liquid evolution during partial melting, is controlled by the starting composition, so in the Earth the range of igneous rocks is constrained by the original materials'. This simple concept of source control has been repeatedly demonstrated experimentally (see Jaques & Green, 1980;Green, 2015;Green & Falloon, 2015), and also well documented observationally (e.g. Mahoney et al., 1994;Niu et al., 1996Niu et al., , 1999Niu et al., , 2001Niu et al., , 2002aCastillo et al., 1998Castillo et al., , 2000. Furthermore, on the basis of their detailed petrology and geochemistry study of several ridge segments along the northern Mid-Atlantic Ridge, Niu et al. (2001) recognized the dynamic role of mantle source compositional variation: 'Mantle compositional control on the extent of mantle melting, crust production, gravity anomaly, ridge morphology, and ridge segmentation'. Indeed, as demonstrated by Niu & O'Hara (2008), the simplest interpretation is that the MORB major element compositional systematics illustrated in Fig. 7a and b largely derive from the fertile mantle compositional systematics. That is, with increasing ridge axial depth, MORB Ti 72 , Al 72 and Na 72 increase whereas Fe 72 , Mg 72 , Ca 72 and Ca 72 /Al 72 decrease, reflecting variations in the fertile mantle source composition. In other words, corresponding to the increasing ridge axial depth, the subridge mantle source increases in TiO 2 , Al 2 O 3 and Na 2 O, and decreases in FeO, MgO, CaO and CaO/Al 2 O 3 , becoming progressively less depleted (or more enriched) in a basaltic melt component. This correspondence becomes physically straightforward if we consider the source mineralogy as a function of the major element compositions (Niu, 1997). Correlated with increasing ridge depth, the mantle source region is progressively (1) enriched in pyroxene over olivine (or higher pyroxene/olivine ratio) because of decreasing FeO and MgO, (2) enriched in jadeite over diopside (or higher jadeite/diopside ratio) in clinopyroxene because of increasing Na 2 O and Al 2 O 3 and decreasing CaO and MgO, and (3) enriched in garnet because of increasing Al 2 O 3 . These mineralogical systematics consistently indicate increasing asthenospheric mantle density from beneath shallow ridges to beneath deep ridges (see Niu & Batiza, 1991b, 1991cNiu et al., 2003), which explains in terms of isostasy why the progressively deeper ridge is underlain by progressively more enriched (or less depleted) denser mantle and why there is such MORB chemistry-ridge depth correlation as demonstrated quantitatively by Niu & O'Hara (2008) (see their figs 13-19 and detailed discussion) with the compensation depth probably in the mantle Transition Zone (Niu & O'Hara, 2008).
This fertile mantle compositional variation controlled mantle density variation can in turn have a physical feedback on ridge dynamics. Because the sub-ridge mantle upwelling is a passive response to plate separation (McKenzie & Bickle, 1988), and because the extent of the upwelling (i.e. P o ÀP f in Fig. 7c) determines the extent of decompression melting (F / P o ÀP f ), the dense fertile mantle beneath deep ridges thus has restricted upwelling (isostatic control), which gives way to conductive cooling to a deep level, forces melting to stop at such a deep level, leads to a short melting interval, and thus produces less melt and probably a thin magmatic crust relative to the less dense (more refractory) fertile mantle beneath shallow ridges as illustrated in Fig. 7c (see Niu & O'Hara, 2008). This increased final depth of melting (P f ), the increased thickness of the 'cold thermal boundary layer' (CTBL), and hence the reduced extent of decompression melting (F / P o ÀP f ) in response to the increased fertility and density of the MORB mantle source beneath deep ridges collectively result from a direct physical control; that is, the well-understood 'lid effect' (Niu et al., 2011). The effect of this physical  Niu & O'Hara (2008) to emphasize that, except for SiO 2 , all the major element oxides (TiO 2 , Al 2 O 3 , FeO, MgO, CaO, Na 2 O and CaO/Al 2 O 3 ), not just FeO and Na 2 O, of the global MORB data after correction for the effects of cooling-dominated crustal-level processes to Mg# ¼ 0Á72, show significant intercorrelations and systematic correlations with ocean ridge axial depth. Such correlations are most consistent with fertile MORB mantle source compositional variation. The fertile mantle source is progressively more enriched (or less depleted) from beneath shallow ridges than beneath deep ridges, pointing to increasing modal garnet, jadeite/diopside ratio in clinopyroxene, and pyroxenes/olivine ratio, and thus a progressively denser mineral assemblage towards deep ridges as shown in (c). This explains straightforwardly why deep ridges are deep-fertile asthenospheric mantle is denser than more depleted mantle (see Niu et al., 2003), thus resulting in deeper ridges. Shallower ridges are underlain by more depleted asthenospheric mantle and controlled by isostasy (see Niu & O'Hara, 2008, figs 13 and 14 and accompanying discussion). In addition, dense fertile mantle beneath deep ridges upwells reluctantly in response to plate separation, which leads to a limited extent of upwelling, allowing conductive cooling to penetrate to a great depth, making a thickened cold thermal boundary layer (CTBL; the gray triangular region labeled '2' in the illustration), forcing melting to stop at a deep level (P f ), resulting in a short melting interval (P o ÀP f ) and less melting, and probably producing a thin magmatic crust relative to the more refractory fertile mantle beneath shallow ridges. The shaded triangular areas in the P-T diagrams illustrate conceptually the difference in melt production that is proportional to the height of the decompression melting intervals (P o ÀP f ). Thus, deep ridge MORB have signatures of apparently lower extents of melting than shallow ridge MORB [see (a) and (b)] superimposed on the fertile mantle compositional inheritance [see details given by Niu & O'Hara (2008)]. An important point here is that globally the solidus depth (P o ) beneath ocean ridges away from mantle plumes (or anomalous mantle with abundant volatiles and alkalis) is essentially constant or varies little (e.g. T o < $ 50 K if any; see Niu & O'Hara, 2008). In contrast, the final depth of melting (P f ) can vary because of varying thickness of the CTBL, termed the 'lid effect', which is conspicuous for intra-plate ocean island basalts (see Niu et al., 2011), but is also detectable beneath ocean ridges as the result of plate spreading rate variation as demonstrated by Niu & Hé kinian (1997a) and further illustrated in Fig. 8 using the new global dataset of Gale et al. (2014). feedback on MORB chemistry is expected to be small, but produces the same systematics as those inherited from fertile source compositions and thus amplifies the MORB chemistry correlation with ridge axial depth as in Fig. 7b and c. Hence, the global MORB compositional systematics ( Fig. 7b and c) are the net effect of (1) fertile mantle source inheritance and (2) varying extents of melting controlled by the varying extent of upwelling and decompression melting as the result of mantle density variations ultimately still controlled by fertile mantle compositional variation. Dick and co-workers have recently offered supporting case studies on the effect of fertile mantle compositional control on MORB chemistry and ridge depth (Zhou & Dick, 2013;Dick & Zhou, 2015).
The overstated mantle temperature variation is secondary or has negligible effect on the MORB chemistry-ridge depth correlation Klein & Langmuir (1987), Langmuir et al. (1992) and Gale et al. (2014) used the large Fe 8 variation (on average $5 Fe units; Figs 1-6) to argue for large mantle temperature variations of $250 K beneath global ocean ridges (this refers to mantle solidus depth variation, DP o , and corresponding solidus temperature variation, DT o ) as the cause of the MORB chemistry-ridge depth correlation. Because Fe 8 (and their Fe 90 ¼ Fe 8 ; Fig. 3b) is not a mantle signature, but a highly and variably evolved crustal-level signature with Mg# ¼ 0Á56-0Á68 that cannot be used to infer mantle conditions in the first place, there is no petrological evidence for large mantle potential temperature variations along the global ocean ridges. Given the small thermal expansion coefficient of 3 Â 10 -5 K -1 under upper mantle conditions, the effect of mantle temperature variation on ridge axial depth variation, if any, is negligible as vigorously demonstrated by Niu & O'Hara (2008) (e.g. 1% density reduction owing to compositional depletion is equivalent to temperature increase of $330 K). Hence, mantle temperature variation as the cause of ridge depth variation can be ruled out on the basis of simple mineral physics. To defend the interpretation of mantle temperature control, Langmuir & co-workers used ridge axial depth as a constraint for mantle temperature variation ; their supporting argument is the low seismic velocity in the deep mantle (>300 km) beneath Iceland and adjacent shallow ridges. Evidently, using ridge depth as a mantle temperature constraint is subjective and circular, rather than justified evidence, because this argument neglects the intrinsic control of fertile mantle compositional variation on the physical properties and dynamic role of the mantle, as well as on MORB compositional variation.
In this context, it is conceptually important not to confuse plate tectonics with mantle plumes because they have no genetic connection and represent different modes of Earth's cooling. It is well understood that plate tectonics is driven by the top cold thermal boundary layer (lithospheric plates) that cools the mantle, drives major aspects of mantle convection and explains seafloor subduction and ridge dynamics (McKenzie & Bickle, 1988;Davies & Richards, 1992), whereas mantle plumes are driven by the basal hot thermal boundary layer (core-mantle boundary) (e.g. Richards et al., 1989;Campbell & Griffiths, 1990;Davies & Richards, 1992) despite some debate (e.g. Davies, 2005;Foulger, 2005;Niu, 2005b). However, when mantle plumes rise to reach the lithospheric plates, interaction between the two can take place. Because the lithosphere is the thinnest at ridges, such interaction is best expressed as plume-ridge interactions (e.g. Ito et al., 2003;Niu & Hé kinian, 2004). To study ridge processes of plate tectonic origin, we should study ridges uninfluenced by hotspots or mantle plumes. Hence, to use the seismic low V s anomaly at >300 km depth beneath Iceland Gale et al., 2014) that is absent elsewhere beneath global ocean ridges as evidence of a hot ridge of plate spreading origin and as evidence of large mantle temperature variations beneath global ocean ridges is inappropriate. In fact, the invoked large mantle temperature variation disappears when data from plume-influenced ridges are removed (see Niu & Hé kinian, 1997a;Niu & O'Hara, 2008;Regelous et al., 2016; also see below). There is no evidence of any kind for large mantle temperature variation beneath ridges away from mantle plumes.
I will specifically discuss in a later section why MORB melts do not preserve the solidus conditions (i.e. P o and T o ) as previously elaborated (Niu, 1997).

The meaning of MORB chemistry-spreading rate correlation
Because ocean ridges are of plate tectonic origin, and because sub-ridge mantle upwelling is a passive response to plate separation, the rate of mantle upwelling must be positively related to plate spreading rate (e.g. Reid & Jackson, 1981;Phipps Morgan, 1987;Niu, 1997). This means that the sub-ridge mantle thermal structure and extent of decompression melting must also vary as a function of plate spreading rate. Indeed, Niu & Hé kinian (1997a) used the then available global MORB data (Niu & Batiza, 1993) together with the available abyssal peridotite data Dick, 1989;Johnson et al., 1990;Niu & Hé kinian, 1997b) to demonstrate that the extent of sub-ridge mantle melting increases with increasing spreading rate as anticipated, and as recently confirmed with an updated dataset (Regelous et al., 2016). Figure 8a-c is reproduced from the spreading rate interval (bin width 20 mm a -1 ) averaged MORB data of Niu & Hé kinian (1997a), plotted as a function of full spreading rate. As above, heavy averaging is required to remove the effects of ridge axial depth variation and location-related mantle source heterogeneity variation on varying scales (including the arbitrary N-and E-type MORB  Niu & Hé kinian (1997a); that is, that decreasing Al 72 (d) and Al 8 (a), increasing Ca 72 /Al 72 (e) and Ca 8 /Al 8 (b), and decreasing K 2 O/TiO 2 (f) and K 8 /Ti 8 (c) with increasing spreading rate are simply and straightforwardly the result of increasing extent of melting. This spreading rate dependent extent of melting is a consequence of the spreading rate controlled lid effect as illustrated in (g), where notations are the same as in Fig. 7c. The numerals next to the data points in (a) and (d) denote '20 mm a -1 ' spreading rate intervals for averaging. Details for (a) and (b) have been given by Niu & Hé kinian (1997a). Details in (d)-(f) (the insets show all the data and averages) are as follows: 1, <20 mm a -1 , n ¼ 891 samples; 2, 20-40 mm a -1 , n ¼ 2163; 3, 40-60 mm a -1 , n ¼ 1923; 4, 60-80 mm a -1 , n ¼ 1228; 5, 80-100 mm a -1 , n ¼ 1406; 6, 100-120 mm a -1 , n ¼ 1130; 7, 120-140 mm a -1 , n ¼ 7; 8, 120-140 mm a -1 , n ¼ 236. The heavy averaging is necessary to examine objectively the presence and significance of any spreading rate effect by averaging out all other non-spreading rate factors (e.g. effects of fertile source variation, including the arbitrary N-and E-type MORB, ridge axial depth variation and uncertainties associated with the correction procedures). Samples with seawater depth <1500 m are excluded, as are those from plumes and plume-influenced ridges (these are samples from Iceland, near-Iceland ridges and the Red Sea) as indicated in Fig. 9a. The reason for choosing <1500 m depth is because most normal ridges have axial depths >2000 m, but there are ridges far away from plumes or hotspots that can be as shallow as $1500 m; for example, the ridge OH-1 south of the Oceanographer Fracture Zone at $35 N MAR (Niu et al., 2001). division) to reveal if there indeed exists any genuine correlation between MORB chemistry and plate spreading rate. As Al is an incompatible element and K is more incompatible than Ti during sub-ridge mantle melting, the decreasing Al 8 and K 8 /Ti 8 and increasing Ca 8 /Al 8 with increasing spreading rate are a straightforward expression of an extent of mantle melting that increases with increasing spreading rate. Figure 8g provides a straightforward illustration in terms of the lid effect (i.e. the CTBL thickness) as to why the extent of mantle melting increases with increasing spreading rate. Because the rate of mantle upwelling increases with increasing plate spreading rate (see above), fast upwelling beneath fast-spreading ridges allows the adiabat to extend to a shallower level against conductive cooling to the surface. By contrast, with slower upwelling beneath slowspreading ridges, conductive cooling to the surface extends to a greater depth against the adiabat. Hence, the depth of P f decreases and the decompression interval (P o ÀP f ) increases with increasing spreading rate, hence the extent of melting F (/ P o ÀP f ) increases with increasing plate spreading rate.
However, Gale et al. (2014) refuted the demonstration and interpretation by Niu & Hé kinian (1997a) by stating: 'There is no correlation between the chemical parameters and spreading rate' (p. 1080). Figure 8d-f is based on the Gale et al. (2014) data and argues against their unfounded statement, confirming the findings and demonstration by Niu & Hé kinian (1997a) that the extent of sub-ridge mantle melting increases with increasing spreading rate. It is important to compare Fig. 8a-c with Fig. 8d-f. The conclusion based on the 20 years older MORB dataset remains valid and is seen in the newest data.

FURTHER INSIGHTS FROM OBSERVATIONS AND BASIC PETROLOGY
The above has illustrated that to understand the physical controls on ocean ridge processes and MORB petrogenesis, the logical approach is to isolate the effects of different physical observables. This is conceptually the same as mathematically seeking partial derivatives for a particular variable while keeping all other variables held constant (Niu & O'Hara, 2008). For example, to evaluate the effects of plate spreading rate variation on MORB petrogenesis, it is best to average petrological parameters with respect to spreading rate intervals so that the potential effects of other variables (e.g. ridge depth variation, mantle source heterogeneity on varying scales within and between ocean basins) can be largely or effectively averaged out. Likewise, to decipher the effects of processes that lead to global ridge axial depth variation on MORB petrogenesis, it is best to average petrological parameters with respect to ridge axial depth intervals so that possible effects by other variables (e.g. spreading rate variation, dynamic topography on regional and ridge segment scales as well as mantle compositional heterogeneity on all scales within and between ocean basins) can be effectively averaged out. This approach offers us new insights.

Effects of spreading rate variation on ridge axial depth and mantle melting
We have demonstrated in Fig. 8a-f that the extent of mantle melting decreases with decreasing spreading rate (see Niu & Hé kinian, 1997a), which is a straightforward consequence of the 'lid effect' as illustrated in Fig.  8g. Because the sub-ridge mantle upwelling rate is, in an ideal situation, half of the full spreading rate (Phipps Morgan, 1987;Niu, 1997), the subdued upwelling beneath a slow-spreading ridge should lead to a deep ridge depth because conductive cooling (1) overcomes adiabatic upwelling, (2) thickens the cold (and dense) thermal boundary layer (CTBL), (3) deepens P f , (4) reduces the P o ÀP f interval, (5) lowers the extent of decompression melting, and predictably (6) produces thinner magmatic crust. This is correct in terms of basic petrology and straightforward physics. However, this anticipated correlation between ridge depth and spreading rate is not obvious in Fig. 9a. The data points are still scattered even after plume-or hotspotinfluenced shallow ridges (<1500 m) are removed. However, as done for MORB chemistry, if we average ridge depth values with respect to the same spreading rate intervals, an expected trend emerges as indicated by the red filled circles. Figure 9b plots only the spreading rate interval averages with 2s error bars. The topology of the power-law fitting curve is essentially the same as those of the petrological parameters in Fig. 8, with a flatter trend at spreading rates >50 mm a -1 and a rapid change at <40 mm a -1 . This is the first-time revelation of the otherwise long anticipated systematics, and points to the first-order genetic connections among spreading rate, ridge depth and petrological parameters. However, for ridges with spreading rates >50 mm a -1 , the ridge depth is essentially constant, but the petrological parameters define first-order trends that are not horizontal, and have slopes consistent with a spreading rate dependent extent of melting (Fig. 8). The average depth for ridges with spreading rates <40 mm a -1 progressively and significantly deepens with decreasing spreading rate. Because of the fact that all the average ridge depth values are spreading rate interval averages with the potential effects of all other variables being averaged out, the $1100 m depth difference may be the maximum (with uncertainties to be verified) ridge depth deepening as the result of reduced spreading rate alone, as indicated in Fig. 9b.
A recent study by Regelous et al. (2016), using an updated abyssal peridotite dataset and the Gale et al.
(2014) MORB dataset, confirmed the recognition by Niu & Hé kinian (1997a;also Niu & O'Hara, 2014) that the extent of ridge mantle melting decreases with decreasing spreading rate, especially beneath slow-spreading ridges as demonstrated above (Fig. 8). Regelous et al. further concluded, however, that this rules out the effect of fertile mantle compositional variation. This latter statement is imprecise and incorrect. Let us examine why this statement needs correction. In Fig. 7 the correlations of MORB chemistry with ridge depth are best interpreted as mantle major element compositional variation as per Niu & O'Hara (2008), and provide no information on spreading rate effect because this effect is averaged out in these plots. The Fig. 8 correlations of MORB chemistry with spreading rate are consistent with spreading rate-dependent varying extent of melting (as shown by these authors), but yield no information on ridge depth effects because these are again averaged out. Hence, on the basis of Fig. 8 we cannot rule out the effect of ridge depth and mantle source effects. Now, we can see by comparing Fig. 8 and Fig. 9 that the largest MORB compositional variation occurs at slow spreading rates of <40 mm a -1 , which corresponds, conservatively, to a ridge axial depth variation of $3200 m to $4200 m. Within this depth range, we see no constant, but a significantly systematic MORB compositional variation in Fig. 7.
Therefore, it is conceptually important and correct to state that globally primitive MORB major element compositions (i.e. MORB melts with Mg# > 0Á72) are largely controlled by both fertile mantle compositional variation (e.g. Fig. 7) and plate spreading rate variation ( Fig. 8) with the spreading rate effect being especially prominent at very slow-spreading ridges (Figs 8 and 9).
MORB melts preserve no signature of P o and T o , but signature of P f and T f By stating that global MORB major element compositional variations (e.g. Fe 8 , Fe 90 ) result from mantle (potential) temperature variations of $250 K (Klein & Langmuir, 1987;Langmuir et al., 1992;Dalton et al., 2014;Gale et al., 2014), this specifically refers to variation of the depth at which upwelling mantle intersects the solidus; that is, the initial depth of melting P o and the corresponding T o , as schematically shown in Fig. 10. Prior to the introduction of the final depth of melting P f and the corresponding T f (Niu & Batiza, 1991a), the ridge mantle decompression melting was thought to continue up to the base of the crust (Klein & Langmuir, 1987;McKenzie & Bickle, 1988). It follows that a hotter parcel of upwelling mantle would intersect the solidus deeper, have a longer melting column and produce more melt with the signature of higher pressure (high Fe 8 ) and higher extent (low Na 8 ) of melting, whereas a cooler parcel of upwelling mantle would intersect the solidus shallower, have a shorter melting column and produce less melt with the signature of a  Fig. 8). Hence, we cannot simply state that ocean ridge depth increases with decreasing spreading rate. The red filled circles are ridge depth interval averages as described in the Fig. 8 caption. (b) As (a), but showing only the depth interval averages with 2r error bars. The topology of the power-law fitting curve is essentially the same as those of the petrological parameters in Fig. 8 with a flatter trend at spreading rates >50 mm a -1 and a rapid change with further spreading rate decrease. This points to the first-order genetic connections between spreading rate, ridge depth and petrological parameters. However, for the ridges with spreading rates >50 mm a -1 , the ridge depths define an essentially horizontal band ($0 slope; the purple band), but the petrological parameters define firstorder trends that are not horizontal, and have slopes all consistent with a spreading rate dependent extent of melting (Fig. 8). The average depths for ridges with spreading rates <40 mm a -1 are progressively and significantly deeper with decreasing spreading rate (light blue rectangle). Because of the fact that all the depth averages result from ridge depth interval averages with the potential effects of all other variables averaged out, the $1100 m depth difference may be the maximum (within uncertainties) ridge depth deepening as the result of reduced spreading rate alone. lower pressure (low Fe 8 ) and lower extent (high Na 8 ) of melting.
Niu and co-authors (Niu, 1997(Niu, , 2004Niu & Hé kinian, 1997a,b;Niu & O'Hara, 2008) have emphasized that there is no evidence for large mantle potential temperature variation beneath global ocean ridges. The petrological parameter Fe 8 (now also Fe 90 ) as a pressure indicator collapses (see above). Dalton et al. (2014) used ridge axial depth variation as evidence for large mantle potential temperature variation, but this is a circular argument and has no foundation (see above and below) because fertile mantle density variations owing to compositional variations (compositional buoyancy variation) are much more effective in causing ridge axial depth variation. Niu and co-authors advocate the presence and significance of the cold thermal boundary layer (CTBL) beneath ocean ridges because this is consistent with physical analysis (Reid & Jackson, 1981) and petrological observations (Niu, 1997(Niu, , 2004Niu & Hé kinian, 1997a,b;Niu & O'Hara, 2008) as elaborated above (Figs 7 and 8). The thickness of the CTBL determines the final depth of melting or meltsolid re-equilibration, P f , hence affecting the decompression melting interval P o ÀP f and the extent of melting. This is called the 'lid effect' (Niu et al., 2011) as elaborated above as functions of fertile mantle compositional / density variation and plate spreading rate variation with correlated variations of MORB chemistry with ridge axial depth (Fig. 7) and plate spreading rate (Fig. 8).
The key message of Fig. 10 concerns the very fundamental question as to whether the erupted MORB melts can preserve the signature of P o and T o . The answer is simply 'No'. The melt formed by decompression (in the depth interval P o ÀP f ) will ascend because of buoyancy and melt segregation caused by matrix compaction (McKenzie, 1984). This occurs as soon as the initial porosity exceeds the permeability threshold, the value of which has varied from up to 10% (e.g. Maaloe, 1982), to $3% (McKenzie, 1984), and to several orders of magnitude less than 1% (McKenzie, 1985;Spiegelman & Elliott, 1993) to explain the observed Th-Ra excess in MORB. However $1% porosity may be more consistent with physical analysis (Turcotte & Phipps Morgan, 1992) and petrological constraints (Johnson et al., 1990). Melt migration and ascent may occur as diffuse porous flow or network-like channeling on millimeter scales (e.g. McKenzie, 1984;Turcotte & Phipps Morgan, 1992). Therefore, recognizing that (1) porous flow is the primary means of melt transport, (2) the time scale for melt transport from the melting region to the crust is of the order of thousands of years (e.g. McKenzie, 1984McKenzie, , 1985Spiegelman & McKenzie, 1987;Rubin & Macdougall, 1988, and (3) a time of no more than tens of hours is sufficient for attaining solid-melt The plate separation induced decompression melting begins when the upwelling mantle intersects the solidus at P o (at corresponding T o ) and continues until the upwelling mantle reaches P f (at corresponding T f ), the final depth of melting or melt-solid equilibration, which is the base of the cold thermal boundary layer beneath the ridge. Because of its buoyancy, the melt (red-arrowed thin dashed lines) ascends faster than the residual solids (blue-arrowed thick lines). The melt is extracted to form the ocean crust whereas the residue contributes to the lithospheric mantle beneath the crust (shallow portions sampled as abyssal peridotites). The globally large mantle (potential) temperature variation of $250 K claimed by Klein & Langmuir (1987) and Gale et al. (2014) to be preserved in MORB chemistry refers to large T o and P o variation. The 'lid effect' argued by Niu & O'Hara (2008) to be preserved in MORB chemistry here refers to T f and P f , either because of mantle density and related decompression melting (Fig. 7;Niu & O'Hara, 2008) or because of plate spreading rate variations and related decompression melting ( Fig. 7; Niu & Hé kinian, 1997a,b). It should be noted that because of melt-solid re-equilibration during decompression melting (P o ÀP f ) on a time scale of thousands of years (re-equilibration is achieved in tens of hours experimentally), the MORB melts do not record the signature of P o and T o ; hence there is no petrological evidence for large mantle potential temperature variation of $250 K beneath global ocean ridges. equilibrium in peridotite melting experiments, lowpressure melt-solid equilibration is inevitable during melt ascent (Niu, 1997). Hence, the erupted melts will not preserve the signature of the initial depth of melting (P o , T o ), nor the signatures of any condition in the decompression interval P o ÀP f . The pressure signature the erupted MORB melts can retain would be the final depth of melting or melt-solid equilibration of P f and T f , which is the condition at the base of the CTBL (¼ 'lid'). The MORB compositional variation as a function of ridge depth variation (composition-controlled density variation; Fig. 7) and plate spreading rate variation (Fig. 8) is the manifestation of the 'lid effect'; that is, the P f and T f signature preserved in MORB melts (Figs 7, 8 and 10).
Because the erupted MORB melts have lost the signature of the initial depth of mantle melting (i.e. P o and T o ) owing to the inevitable melt-solid re-equilibration, how can we use MORB chemistry to say that large mantle potential temperature variations ($250 K) exist beneath global ocean ridges? How can we logically establish primary magmas parental to MORB with MgO as high as 19 wt % (corrected to Fe 90 ; see Fig. 3d)? In Fig. 10 it is shown explicitly that the melt produced will ascend in the form of porous flow (< $2%) through the solid peridotite matrix (>$98%) and undergo continuous melt-solid re-equilibration. The re-equilibration is expected to be complete during decompression melting (P o ÀP f ) because of the close melt-solid contact and because the thousands of years of melting and melt segregation is long enough compared with the tens of hours required to reach equilibrium in experimental charges, especially for elements such as Si, Fe and Mg controlled by olivine, which is the dominant mantle peridotite mineral. Niu (1997) presented this argument explicitly, but I ask readers to judge objectively whether MORB melts can preserve the signature of P o and T o in terms of Si, Fe and Mg as presumed by Klein & Langmuir (1987), Langmuir et al. (1992), Dalton et al. (2014) and Gale et al. (2014).
A point that should be remembered: the meaning of the correlated compositional variations of MORB and abyssal peridotites We should note the nature of the compositional correlation between abyssal peridotites and spatially associated MORB  and the petrological interpretations of this correlation (Dick et al., 1983;Klein & Langmuir, 1987). This correlation was effectively summarized in fig. 1 of , showing a scattered but statistically significant positive linear correlation between the modal clinopyroxene (vol. %) content of abyssal peridotites and the Na 8 of spatially associated MORB (18 site averages with R 2 ¼ 0Á74).  proposed that when sample locations approach 'hotspots' with shallowed ridge depths, both Na 8 and modal clinopyroxene decrease, which is consistent with an increasing extent of mantle melting, influenced by hotter mantle beneath hotspots. This observation is simple and powerful. The interpretation is logical also, but may not be correct. Following a detailed bulk-rock major and trace element study of global abyssal peridotites, Niu (2004Niu ( , p. 2452 could not avoid the conclusion that: 'there is no clear justification that Na 8 in MORB or cpx mode in abyssal peridotites genuinely reflects the extent of mantle melting beneath mid-ocean ridges, nor that such an inferred extent of melting reflects subridge mantle potential temperature variations. The complementarity could very well be inherited from the fertile mantle sources.' This was echoed by Dick et al. (2007), who stated: 'As the previously analyzed peridotites are from fracture zone walls 0Á5 to 14 Ma. old, and the "spatially associated basalts" are largely from the modern ridge axis, this argues for a long-term stability in magma composition and therefore mantle composition as well.' Indeed, despite the compositional complementarity between MORB (melts) and abyssal peridotites (residues), it is unlikely for the $14 Myr old abyssal peridotites to be melting residues of the present-day MORB. Mantle thermal anomalies may be long-lived, but can decay away with time. However, compositional anomalies (and buoyancy) should be long-lasting. For this, Zhou & Dick (2013) provided a good case study.
The geodynamic significance of compositional buoyancy contrast is best manifested by the largest topographic contrast on the Earth: the compositionally buoyant continental lithosphere (the crust and mantle lithosphere) and the compositionally dense oceanic lithosphere (despite the contribution of the 'coldness' of the latter) (Niu et al., 2003;Niu, 2014Niu, , 2016. SUMMARY 1. The popular petrological parameter Fe 8 devised by Klein & Langmuir (1987) and advocated by Langmuir et al. (1992) and Gale et al. (2014) in studying MORB mantle melting conditions is misleading, as demonstrated by Niu & O'Hara (2008), because Fe 8 represents variably evolved melts with Mg# ¼ 0Á56-0Á68 (Figs 1-3), which is a crustal signature and cannot be in equilibrium with mantle olivine. Recent work by Gale et al. (2014) showed that Fe 8 % Fe 90 (Fig. 3b), with the purpose of advocating Fe 8 to be the same as Fe 90 , and to reflect melts in equilibrium with mantle olivine Fo 90 . This is not true. Because melts with Fe 8 have Mg# ¼ 0Á56-0Á68, but those with Fe 90 are meant to have Mg# $0Á72-0Á73, how can Fe 8 % Fe 90 ? (Fig. 3b). The data treatment to make Fe 90 ! Fe 8 was achieved by adding varying amount of olivine, but can MORB melts have MgO as high as 19 wt % (Fig. 3d)? The most primitive MORB melts with Mg# ! 0Á72 have $10Á5 wt % MgO (data constrained). The Gale et al. (2014) corrected Fe 90 (¼ Fe 8 ) values have no relevance to actual data as they are compositionally remotely different from any MORB composition MORB chemistry with plate spreading rate variation cannot be used to rule out a fertile mantle compositional control. Both fertile mantle compositional variation (expressed as large ridge axial depth variations owing to composition-determined density variations) and spreading rate variation are two primary variables that control first-order ocean ridge processes in general and MORB petrogenesis in particular. 10. It has long been anticipated that ridge axial depth should increase with decreasing plate spreading rate, but the lack of correlation between the two has been puzzling. This correlation does indeed exist after removing hotspot-influenced ridges and after averaging ridge depth values within spreading rate intervals (Fig. 9). This correlation is best described by a non-linear power-law relationship that also best describes the relationship between MORB chemistry and spreading rate. All these observations are straightforward consequences of plate tectonics. 11. The meaning of the global MORB major element compositions may continue to be debated, but the conclusions offered here are the most objective and logical, and are most consistent with petrological, geochemical, geological and geophysical principles and observations. 12. To promote scientific debate, I end this paper here by sharing my philosophy: for the same data, there can be many different interpretations, but reasonable interpretations are limited and, strictly speaking, the correct interpretation must be openminded and objective.

FUNDING
This work was supported by Chinese NSF (Grants 41630968 and 91014003), Chinese NSF-Shandong (Grant U1606401), Chinese Academy of Sciences (Innovation Grant Y42217101L), Qingdao National Laboratory for Marine Science and Technology (Grant 2015ASKJ01), and grants from regional and local authorities (Shandong Province and City of Qingdao).

ACKNOWLEDGEMENTS
I write this paper in commemoration of Mike O'Hara for his friendship, for our scientific exchanges and for the memorable times we had over the previous $18 years before his passing through emails, phone calls, lunchtime chats and extended visits. His constructive review of my abyssal peridotite paper for this journal (Niu, 1997) began our productive research collaboration and led to my migration from the University of Queensland to Cardiff and to Durham. We published 10 papers together on topics including subduction initiation, continental crust accretion, petrogenesis of intra-plate ocean island basalts, ocean ridge basalts and lunar rocks. Our friendly discussion and scientific debates benefited me tremendously. It may surprise some, but we actually disagreed more often than agreed and he was extremely happy when he was convinced that I was correct. An anonymous journal reviewer is thanked for the very detailed and thorough constructive comments on an early version of the paper. The comments and editorial efforts by Marjorie Wilson and Alastair Lumsden have improved the paper, for which, and for their exceptional patience, I am grateful.