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Near-ridge-axis volcanism affected by hotspot: insights from effective elastic thickness and topography of the Ojin Rise Seamounts, east of Shatsky Rise in the northwest Pacific Ocean


We used recently collected bathymetric data and published gravity data to examine the effective elastic thickness of the lithosphere and the crustal thickness beneath the Ojin Rise Seamounts, located east of Shatsky Rise in the northwest Pacific Ocean. An admittance analysis of the bathymetric and gravity data indicates that the effective elastic thickness of the Pacific plate under the Ojin Rise Seamounts is 2.7 ± 0.1 km, implying that the seamounts were formed on or near the spreading ridge between the Pacific and Farallon plates. The mean crustal thickness beneath the seamounts estimated from the mantle Bouguer anomaly is 10.1 ± 1.7 km, which is thicker than the surrounding crust. The thick crust was probably formed by the interaction between the Pacific–Farallon ridge and a hotspot forming Shatsky Rise. Our results indicate that late-stage volcanism after the formation of the main edifices of Shatsky Rise spread widely beyond the eastern side of the rise, forming the Ojin Rise Seamounts.


The formation of oceanic plateaus is an important unresolved problem in Earth science. Oceanic plateaus are thought to be emplaced by rapid, voluminous eruptions over a surfacing mantle plume head (e.g., Duncan and Richards 1991). However, secondary (late-stage or post-plateau) volcanism also plays an important role in the formation of oceanic plateaus (e.g., Ito and Clift 1998; Pietsch and Uenzelmann-Neben 2015). Late-stage volcanism includes volcanism along the hotspot track and rejuvenated-stage volcanism. According to the plume model, hotspot-track volcanism represents activity of the plume tail (e.g., Hawaiian–Emperor volcanic chain; Clague and Dalrymple 1987). Rejuvenated-stage volcanism may occur as a result of melting of lithospheric mantle beneath the plateau (e.g., Tejada et al. 2015). Late-stage volcanism produced volcanic cones on the Manihiki Plateau (Pietsch and Uenzelmann-Neben 2015) and may have thickened the crust of the Ontong Java Plateau (Ito and Clift 1998). Thus, a comprehensive understanding of the formation of oceanic plateaus requires adequate knowledge of late-stage volcanism.

Shatsky Rise is proposed to have formed by the emergence of a mantle plume head at the ridge–ridge–ridge triple junction among the Pacific, Izanagi, and Farallon plates (Nakanishi et al. 1999). It consists of three major volcanic edifices, the Tamu, Ori, and Shirshov massifs, and the bathymetric high of Papanin Ridge (Fig. 1a). Drilled samples have yielded radiometric dates of ~ 145 Ma for the Tamu Massif and ~ 134 Ma for the Ori Massif (Mahoney et al. 2005; Geldmacher et al. 2014; Heaton and Koppers 2014). The maximum crustal thickness of the Tamu Massif is estimated to be 30 km on the basis of seismic refraction surveys (Korenaga and Sager 2012). Several studies have proposed that the thick crust of the massif was produced by deeper melting, with a higher degree of partial melting, than is typical at normal mid-ocean ridges (e.g., Sano et al. 2012). Previous studies have also suggested that late-stage volcanism occurred on Shatsky Rise (e.g., Sager et al. 2016; Shimizu et al. 2013; Tejada et al. 2016).

Fig. 1

Bathymetry of the study area. a Bathymetric map around the Ojin Rise Seamounts and Shatsky Rise. Bathymetric data are from Smith and Sandwell (1997); contour interval is 500 m. Shatsky Rise is outlined in red at the 5000 m bathymetric contour. Thin black lines represent magnetic anomaly lineations (Nakanishi et al. 1999). The white-edged black line at lower center is the seismic reflection survey line of Ohira et al. (2017). The two dashed rectangles are the areas shown in b and c. The inset shows the locations of Shatsky Rise, Japan, and present plate boundaries (dashed lines). b Bathymetric map based on data collected during cruise KR14-07. c Bathymetric map of the study area

The Ojin Rise Seamounts (ORS) lies east of Shatsky Rise and consists of approximately 80 volcanic edifices. Torsvik et al. (2019) devised an absolute Late Jurassic–Cretaceous Pacific plate model and showed that the ORS is a hotspot track connected to Shatsky Rise. Nakanishi et al. (1999) speculated that part of the ORS (around 37° 00′ N and 165° 30′ E) was formed near a spreading ridge because the elongation of the seamounts and the magnetic anomaly lineations have similar orientations (Fig. 1a). The crustal structure under the ORS is unknown. Tejada et al. (2016) indicated that the ORS was formed by late-stage volcanism related to the formation of Shatsky Rise and proposed two models of formation based on the geochemical data. One is that the ORS was formed by the interaction between volcanism of a spreading ridge and a hotspot. The other is that the ORS was formed only by deformation-related shallow-mantle volcanism. Age information for the ORS is indispensable for testing these models.

The effective elastic thickness (Te) value of the lithosphere under a seamount is an indicator of its tectonic setting (Watts 1978). The Te value, the thickness of the lithosphere behaving as an elastic body, can be estimated from bathymetric and gravity data. The relationship between Te and the age of the lithosphere at the time of loading was first proposed by Watts (1978). Small Te values (0–8 km) suggest that the seamounts were formed on or near a spreading ridge. For example, Te value of the lithosphere under the Foundation Seamounts near the Pacific–Antarctic Ridge is 0–5 km, suggesting an age difference of 0–10 Myr between the seamounts and the lithosphere under them (Maia and Arkani-Hamed 2002), and Te of the lithosphere under the Hawaiian Islands is 30–40 km, indicating an age difference of 70–80 Myr between the islands and the adjacent seafloor (Watts 1978). In this study, we determined the crustal thickness and the Te value of the lithosphere under the ORS to estimate its formation age, tectonic setting, and crustal structure.

Theory and method

We estimated the Te value of the lithosphere under the ORS by an admittance analysis, a method of spectral analysis of the bathymetry and free-air gravity anomaly (FGA) in the wavenumber domain. We used the admittance function (McKenzie and Bowin 1976),

$$ \begin{array}{*{20}c} {Z\left( k \right) = \frac{{C_{\text{C}} \left( k \right)}}{{E_{\text{t}} \left( k \right)}},} \\ \end{array} $$

where k is the wavenumber and Z(k) is the gravitational admittance between the bathymetry and the FGA. \( C_{\text{C}} \left( k \right) \) is a cross spectrum of FGA and bathymetry, and \( E_{\text{t}} \left( k \right) \) is a power spectrum of bathymetry:

$$ \begin{array}{*{20}c} {C_{\text{C}} \left( k \right) = \Delta g\left( k \right)H^{ *} \left( k \right),} \\ \end{array} $$
$$ \begin{array}{*{20}c} {E_{\text{t}} \left( k \right) = H\left( k \right)H^{*} \left( k \right),} \\ \end{array} $$

where ∆g(k) and H(k) are the Fourier transforms of the observed FGA and bathymetry, respectively, and the asterisk denotes the complex conjugate.

The Te value can be estimated by comparing the admittance function of an elastic plate model with observational admittances (Watts 2001). The elastic plate model used in this study is one in which the load of a seamount is compensated by flexure of a plate. The admittance function of this model is defined by

$$ \begin{array}{*{20}c} {Z\left( k \right) = 2\pi G\left( {\rho_{\text{c}} {-} \rho_{\text{w}} } \right){\text{e}}^{ - kd} \left( {1 - \varPhi_{\text{e}} \left( k \right){\text{e}}^{ - kt} } \right),} \\ \end{array} $$

where d is the mean water depth, G is the universal gravitational constant, t is the mean crustal thickness, and \( \rho_{\text{w}} \) and \( \rho_{\text{c}} \) are the densities of seawater and crust, respectively. The flexural response function of the lithosphere \( \varPhi_{\text{e}} \left( k \right) \) is (Walcott 1976)

$$ \begin{array}{*{20}c} { \varPhi_{\text{e}} \left( k \right) = \left[ {\frac{{Dk^{4} }}{{\left( {\rho_{\text{m}} - \rho_{\text{w}} } \right)g}} + 1} \right]^{ - 1} ,} \\ \end{array} $$

where g is the average gravitational acceleration, \( \rho_{\text{m}} \) is the density of the mantle, and D is the flexural rigidity of the lithosphere defined by

$$ \begin{array}{*{20}c} {D = \frac{{ET_{\text{e}}^{3} }}{{12\left( {1 - \nu^{2} } \right)}},} \\ \end{array} $$

where E is Young’s modulus and \( \nu \) is Poisson’s ratio. These and other parameters used in this study are listed in Table 1.

Table 1 Parameters used in this study

The most suitable Te value was determined by minimizing the root-mean-square (RMS) misfit between theoretical and observational admittances for various Te values (Kalnins and Watts 2009; Hu et al. 2015). Kalnins and Watts (2009) noted that use of a very small spatial window (≤ 400 km) produces spuriously low Te values by truncating the signals of features on stronger lithosphere. Our study area encompassing the ORS consisted of a 550 km × 550 km window that did not include any major topographic features of the Shatsky Rise and Emperor Seamount Chain (Fig. 1c; 35° N to 39° 56.98′ N and 163° 30′ E to 169° 47.16′ E). We extended the grid by line symmetry to avoid the Gibbs phenomenon.

The mean crustal thickness, which is required to calculate admittances with Eq. 4, can be estimated from the mantle Bouguer anomaly (MBA; Kuo and Forsyth 1988). The MBA can be calculated by subtracting the predicted attractions of the seawater–sediment, sediment–crust, and crust–mantle interfaces from the FGA under the assumption of a constant crustal thickness. When the crustal density is assumed to be constant, the MBA represents the spatial variation of crustal thickness, that is, undulations of the Moho. To calculate that spatial variation, we determined the constant reference crustal thickness for the ORS. To find a reasonable ORS reference crustal thickness, we calculated the crustal thickness within the area bounded by 27° N and 45° N and 152° E and 175° E (Fig. 1a), which is much larger than our study area. We chose the larger area because the crustal thickness in its southern part is known from a seismic reflection survey to range from 6.8 to 7.3 km (Ohira et al. 2017). We then calculated reference crustal thicknesses in steps of 0.1 km between 1 and 15 km and chose the value that minimized the RMS difference between the crustal thicknesses determined by Ohira et al. (2017) and our MBA calculation.

To determine the range of wavenumbers used to fit the observed and theoretical admittances, we used the coherence γ2(k), a measure of the portion of the FGA that is caused by bathymetry. McKenzie and Bowin (1976) defined coherence as

$$ \begin{array}{*{20}c} {\gamma^{2} \left( k \right) = \frac{{C_{\text{C}} \left( k \right)C_{\text{c}}^{*} \left( k \right)}}{{E_{\Delta g} \left( k \right)E_{\text{t}} \left( k \right)}},} \\ \end{array} $$

where \( E_{\Delta g} \left( k \right) \) is a power spectrum of the FGA. The coherence can range from 0 to 1, and a high coherence indicates that most of the FGA is caused by bathymetry. Kalnins and Watts (2009) suggested that wavenumbers with coherence greater than a threshold value of 0.4 are suitable for admittance analysis, and we adopted that threshold for our admittance analysis.

Bathymetric and gravity data

Research cruise KR14-07 of R/V Kairei was carried out in summer 2014 to investigate the origin of the ORS and its relationship with Shatsky Rise (Sano 2014). Bathymetric data were collected using the vessel’s SeaBeam 3012 multibeam echo sounder (Fig. 1b). Because the survey covered only a small fraction of the study area, we filled the gaps using gridded bathymetric data with a 1′ × 1′ grid spacing made by Sager et al. (1999) using the spline-under-tension gridding algorithm of Smith and Wessel (1990), shown in Fig. 1c.

Because the coverage of shipboard gravity data by cruise KR14-07 and previous research cruises was insufficient for admittance analysis, we used the satellite-derived FGA gridded data of Sandwell et al. (2014), with a grid spacing of 1′ × 1′ (Fig. 2). The sediment thickness was obtained from the gridded data of sediment thickness of Straume et al. (2019).

Fig. 2

Free-air gravity anomaly map of the study area (location in Fig. 1c). The data are from Sandwell et al. (2014); contour interval is 5 mGal


The seamounts of the ORS, distributed within the area defined by latitude 36° 30′ N and 39° N and longitude 164° E and 168° E, are ~ 1000–2000 m high and ~ 10–20 km in diameter (Fig. 1c). An elongated ridge, parallel to Hawaiian magnetic lineations, is situated between 36° 40′ N and 37° 20′ N and 165° E and 166° E and is 126 km long, 67 km wide, and 1800 m high (Fig. 1b). Four seamounts on top of this ridge have diameters of 16–18 km and elevations of ~ 800–1400 m above the ridge.

The FGA is positive over the seamounts of ORS, ~ 30 mGal, and negative over the abyssal plain around the seamounts, less than –20 mGal (Fig. 2). The wavelengths of these gravity features are ~ 20–30 km.

The optimum reference crustal thickness determined from our MBA analysis is 8.5 ± 0.1 km; at this thickness the RMS difference between the result of Ohira et al. (2017; see Fig. 3c) and the best-fit crustal thickness reaches a minimum of 0.26 km (Fig. 3a). The crustal thickness variations along the survey line of Ohira et al. (2017) is shown with the best-fit crustal thickness in Fig. 3b, and the crustal thickness variations in the area of the survey line based on the 8.5 km reference thickness is shown in Fig. 3c. The crust beneath the ORS study area is everywhere thicker than 7 km, reaching 14 km at 37° 25′ N, 166° 50′ E, and it has a mean thickness of 10.1 ± 1.7 km (Fig. 3d). We used this value in Eq. 4 to calculate the theoretical admittances. The mean water depth d and crustal density \( \rho_{\text{c}} \) used in this calculation were derived from the slope of a plot of log10 admittance vs wavenumber and its intersection at k = 0 (Fig. 4a; Watts 2001). The best-fit straight line for an admittance of 0.08 < k < 0.4 km−1 gave estimates of d = 5838 m and \( \rho_{\text{c}} \) = 2811 kg m−3.

Fig. 3

Crustal thickness results. a RMS misfit between crustal thicknesses by our analysis and by Ohira et al. (2017) for an area of normal oceanic crust (location in Fig. 1a). The dashed line represents the crustal thickness at the RMS minimum. b Crustal thickness along the survey line of Ohira et al. (2017) as determined by Ohira et al. (2017) (dashed line) and by our calculations using a constant reference crustal thickness of 8.5 km (solid line). c Map of crustal thickness around the survey line of Ohira et al. (2017) calculated for a reference crustal thickness of 8.5 km; contour interval 1 km. The thick white-edged line is the survey line of Ohira et al. (2017); the red portion was used for fitting crustal thickness (see the text). d Map of crustal thickness in the ORS study area for a reference crustal thickness of 8.5 km; contour interval 1 km

Fig. 4

Results of admittance analysis. a Admittance amplitude vs wavenumber k (red line) with dashed line indicating the best fit to the observed admittance for 0.08 < k < 0.4. b Coherence of the observation admittance values (red line). The gray area is the range of wavenumbers where coherence exceeds the threshold of 0.4. c Observational admittances (black circles with standard deviations) and the theoretical admittance for Te = 2.7 km (red line). d RMS misfit between observational and theoretical admittances (red line). The vertical dotted line represents the Te value at the minimum RMS. Dashed lines represent RMS misfits between observational and theoretical admittances for crustal thicknesses of 8.4 and 11.8 km

The coherence of bathymetry and gravity exceeds the threshold of 0.4 for wavenumbers between 0.04 and 0.22 km−1 (Fig. 4b). The coherence for the wavenumbers greater than 0.4 km−1 is almost zero. We therefore used only the data for the wavenumber band of 0.04 to 0.22 km−1 for the admittance analysis.

Figure 4c compares the observational admittances and the best-fitting admittance model. The Te value of this model is 2.7 ± 0.1 km, and the RMS is 4.4 mGal km−1 (Fig. 4d). Watts et al. (2006) showed that seamounts with Te values less than 8 km formed on young lithosphere, that is, on or near a spreading ridge. On this basis, we propose that the ORS was formed on or near a spreading ridge.

We determined Te values for several different cases to confirm the robustness of our analysis. To estimate the influence of the error in crustal thickness, we calculated Te values for crustal thicknesses between 8.4 and 11.8 km. These ranged from 2.3 to 3.2 km (Fig. 4d), implying that Te value is fairly constant within the tolerance interval of crustal thickness. The Te value for a crustal thickness of 8 km, typical of the normal oceanic crust around Shatsky Rise (e.g., Ohira et al. 2017; Zhang et al. 2016), was 3.6 ± 0.1 km. Given a window size of 600 km × 600 km, Te was 2.8 ± 0.1 km, which is within the error range of Te value with our 550 km × 550 km window. In all cases, the Te values around the ORS were less than 4 km, implying that our analysis is appropriate to address the formation of the ORS.


Te values less than 8 km for the underlying lithosphere imply that the seamounts of the ORS formed on a young and weak plate (Watts et al. 2006). Thus, the Te value of 2.7 ± 0.1 km for the seafloor around the ORS indicates that the seamounts formed on or near the spreading ridge between the Pacific and Farallon plates (Pacific–Farallon ridge). Similarly, with Te value less than 8 km, the age of the lithosphere at the time of seamount loading is less than 30 Myr (Watts et al. 2006), suggesting that the age of the seafloor in the western (older) margin of the ORS is about 134 Ma (Nakanishi et al. 1999) and that the ORS formed between 104 and 134 Ma. Our result is consistent with the ~ 120–124 Ma 40Ar/39Ar ages of the seamounts on top of the ridge (Sano et al. 2016; around 36° 45′ N and 166° 00′ E).

Tejada et al. (2016) raised the possibility that the ORS was formed by late-stage volcanism of Shatsky Rise and is a hotspot track representing the “plume head to tail” stage of hotspot development. The plate reconstruction model of Torsvik et al. (2019) also suggests that the ORS represents the track of the hotspot that formed Shatsky Rise from 135 to ~ 120 Ma. This age range is close to that of the seafloor around the ORS determined from magnetic anomaly lineations (125–134 Ma) and the radiometric ages of the seamounts. These lines of evidence support our inference that the ORS was formed on or near the Pacific–Farallon ridge.

The mean crustal thickness beneath the ORS is 10.1 ± 1.7 km, which is ~ 3 km thicker than that of the oceanic crust around Shatsky Rise. Some of the Foundation Seamounts near the East Pacific Rise, which are similar to the ORS in topography, size, and shape, are parallel or subparallel to the Pacific–Antarctic Ridge (O’Connor et al. 2004). The Foundation Seamounts, which were formed by the interaction between a spreading ridge and a hotspot (Maia and Arkani-Hamed 2002; O’Connor et al. 2001), have Te values of 0–5 km (Maia and Arkani-Hamed 2002), and the crust beneath them is 6 km thicker than the surrounding normal oceanic crust (Maia et al. 2000). These similarities between the ORS and Foundation Seamounts suggest that they were formed by the same mechanism. Thus, we conclude that the ORS was formed by the interaction between the Pacific–Farallon ridge and the hotspot forming Shatsky Rise, consistent with the model proposed by Tejada et al. (2016). The ORS does not show a clear hotspot track like the Hawaiian–Emperor volcanic chain, perhaps because interactions with the spreading ridge produced scattered near-ridge volcanoes and led to a diffuse hotspot track.

Tejada et al. (2016) proposed that the volcanic edifices on and around Shatsky Rise, such as Toronto Ridge and Cooperation Seamount, formed by late-stage volcanism related to the formation of Shatsky Rise that took place far from plate boundaries (Fig. 1a). The ages of Toronto Ridge and Cooperation Seamount, 129.4 ± 0.3 Ma and ~ 122 Ma, respectively (Tejada et al. 2016), are close to the age of the ORS estimated by our study. Several other volcanic cones on Shatsky Rise are also thought to have formed by late-stage volcanism (Zhang et al. 2017). Ohira et al. (2017) proposed late-stage volcanism beneath the abyssal basin southeast of Shatsky Rise to explain the thick crust–mantle transition layer there. These studies as well as our results indicate that late-stage volcanism related to the formation of Shatsky Rise not only occurred within the rise itself, but also extended to the abyssal basin to the east. Our results also indicate that the late-stage hotspot volcanism occurred not only within the Pacific plate, but also near a plate boundary, the Pacific–Farallon ridge.


Our analysis of bathymetric and gravity data provides new insight into the tectonic setting of the ORS, east of Shatsky Rise. Our study indicates that the effective elastic thickness of the lithosphere and the mean thickness of the crust beneath the ORS are 2.7 ± 0.1 km and 10.1 ± 1.7 km, respectively. The small effective elastic thickness suggests that the ORS formed on or near the Pacific–Farallon ridge, and the thick crust indicates that the ORS formed by the interaction between the Pacific–Farallon ridge and the hotspot forming Shatsky Rise. The volcanism forming the ORS was part of the late-stage volcanism associated with Shatsky Rise, which occurred on or near a spreading ridge. This late-stage volcanism extended beyond the rise itself to the abyssal basin to the east. Our conclusion should be tested by further sampling from the wide area of the ORS.

Availability of data and materials

The bathymetric dataset of cruise KR14-07 is available in the Data and Sample Research System of the Japan Agency for Marine-Earth Science and Technology,



Free-air gravity anomaly


Mantle Bouguer anomaly


Ojin Rise Seamounts



T e :

Effective elastic thickness


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We thank the crew and technical staff of cruise KR14-07 for collection of the geophysical data used in this study and M.L.G. Tejada for discussion and comments on this manuscript. We are grateful for the constructive reviews of the editor and two anonymous reviewers that significantly improved this manuscript. Funding was provided by the Japan Society for the Promotion of Science under KAKENHI Grants no. 26302010, 18H03746, and 18K03772.


Funding was provided by the Japan Society for the Promotion of Science under KAKENHI Grants no. 26302010, 18H03746, and 18K03772.

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The KR14-07 cruise was planned by TS and MN. Analyses were performed by SS and MN, and the manuscript was written by SS with extensive input and discussion from MN and TS. All authors read and approved the final manuscript.

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Correspondence to Shoka Shimizu.

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Shimizu, S., Nakanishi, M. & Sano, T. Near-ridge-axis volcanism affected by hotspot: insights from effective elastic thickness and topography of the Ojin Rise Seamounts, east of Shatsky Rise in the northwest Pacific Ocean. Earth Planets Space 72, 11 (2020).

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  • Effective elastic thickness
  • Ojin Rise Seamounts
  • Shatsky Rise