# The Malpelo Plate Hypothesis and implications for nonclosure of the Cocos-Nazca-Pacific plate motion circuit

## Abstract

Using global multiresolution topography, we estimate new transform-fault azimuths along the Cocos-Nazca plate boundary and show that the direction of relative plate motion is 3.3° ± 1.8° (95% confidence limits) clockwise of prior estimates. The new direction of Cocos-Nazca plate motion is, moreover, 4.9° ± 2.7° (95% confidence limits) clockwise of the azimuth of the Panama transform fault. We infer that the plate east of the Panama transform fault is not the Nazca plate but instead is a microplate that we term the Malpelo plate. With the improved transform-fault data, the nonclosure of the Nazca-Cocos-Pacific plate motion circuit is reduced from 15.0 mm a^{−1} ± 3.8 mm a^{−1} to 11.6 mm a^{−1} ± 3.8 mm a^{−1} (95% confidence limits). The nonclosure seems too large to be due entirely to horizontal thermal contraction of oceanic lithosphere and suggests that one or more additional plate boundaries remain to be discovered.

## Key Points

- Transform fault azimuths from multibeam sonar show that the direction of Cocos-Nazca plate motion is ~3 degrees clockwise of prior estimates
- The plate east of the main part of the Panama transform fault is not the Nazca plate but the Malpelo plate
- Pacific-Nazca-Cocos plate circuit nonclosure is less than that found before but large enough that more undiscovered plate boundaries may exist

## Plain Language Summary

The central tenet of plate tectonics is that the tectonic plates are rigid. In sharp conflict with this assumption is the prior result that the relative motions between the Cocos, Nazca, and Pacific tectonic plates, which lie in the Pacific Ocean basin, do not sum to zero as expected if the plates are indeed rigid. From an analysis of plate-motion data, we show that part of the traditionally defined Nazca plate, which lies off the west coast of South America, is really a separate tectonic plate, which we refer to as the Malpelo plate. Recognition of this new tectonic plate reduces the inconsistency in the plate-motion circuit, but a large and significant inconsistency remains. This remaining inconsistency suggests that there may be one or more plate boundaries still remaining to be discovered within these three plates.

## 1 Introduction

The central tenet of plate tectonics is that the plates are rigid. In sharp conflict with this assumption is the result that the Cocos-Nazca-Pacific plate-motion circuit fails to close by 14 ± 5 mm a^{−1} (95% confidence limits) [*DeMets et al.*, 2010]. Absent serious errors in the plate-motion data (spreading rates and the azimuths of transform faults), the magnitude of this misfit is difficult to explain from known processes of intraplate deformation, such as horizontal thermal contraction [*Collette*, 1974; *Kumar and Gordon*, 2009; *Kreemer and Gordon*, 2014; *Mishra and Gordon*, 2016] or movement of plates over a nonspherical Earth [*McKenzie*, 1972; *Turcotte and Oxburgh*, 1973]. Alternatively, there may be one or more unrecognized plate boundaries in the circuit, but no such boundary has been found or hypothesized to date.

To make progress on this problem, herein we report three new Cocos-Nazca transform fault azimuths from multibeam data now available through GeoMapApp's global multiresolution topography data sets [*Ryan et al.*, 2009], but unavailable to *DeMets et al*. [2010].

## 2 Cocos-Nazca Transform Fault Azimuths

Figure 1 shows the location of the transform faults with useful azimuths along the conventionally defined Cocos-Nazca plate boundary. *DeMets et al*. [2010] used an azimuth from the Inca transform fault (at 85.3°W) and the easternmost transform fault, the Panama transform fault, to estimate the direction of Cocos-Nazca plate motion (Figures 1 and 2). From a combination of precision depth recorder data and limited multibeam data, *DeMets et al*. [2010] estimated the azimuth of the Inca transform fault to be 002.0° ± 0.8° (±1σ). Using the more extensive multibeam data now available through GeoMapApp [*Ryan et al.*, 2009], we estimate the strike to be 005.0° ± 0.7° (±1σ) (Figure S1 in the supporting information), which is 3° clockwise of the estimate of *DeMets et al*. [2010]. We also obtain a new well-constrained estimate of the strike of the 84.7°W transform fault of 003.0° ± 1.2° (±1σ) and a new less well-constrained strike for a short portion of the 84.3°W transform fault of 003.0° ± 3.3° (±1σ) (Figures 2 and S1). Azimuths for these faults were not available to *DeMets et al*. [2010]. We retain the azimuth (358.0° ± 1.2°) of the Panama transform fault adopted by *DeMets et al*. [2010] based on satellite altimetry and crossings of precision-depth-recorder profiles (Figure S2).

We determined a new Cocos-Nazca best-fitting angular velocity from the three new transform-fault azimuths (while excluding the transform-fault azimuths of *DeMets et al*. [2010]) combined with the spreading rates of *DeMets et al*. [2010]. (We take the term best-fitting angular velocity to be the angular velocity determined only from data along the mutual boundary of a plate pair.) The three new azimuths are mutually consistent and fit well (Figure 2). Azimuths calculated from the new best-fitting angular velocity are 3.3° ± 1.8° (95% confidence limits) clockwise of those calculated from the best-fitting angular velocity of *DeMets et al*. [2010] and agree better with the earlier results of *DeMets et al*. [1990] and of *Wilson and Hey* [1995] than they do with the results of *DeMets et al*. [2010]. Moreover, the azimuth predicted for the Panama transform fault, which we did not use as input to the new best-fitting angular velocity, is 4.9° ± 2.7° (95% confidence limits) clockwise of the observed value (Figure 2), demonstrating that the Panama transform fault does not parallel Nazca-Cocos plate motion.

## 3 Malpelo Plate Hypothesis

While we still assume that the Cocos plate lies west of the Panama transform fault, we hypothesize that the lithosphere east of it moves independently of the Nazca plate and constitutes a microplate, which we term the Malpelo plate (Figure 3). We further hypothesize that a diffuse plate boundary separates the Malpelo plate from the much larger Nazca plate (Figure 3). In most diffuse oceanic plate boundaries, the pole of rotation lies in the diffuse boundary [*Gordon*, 1998; *Zatman et al.*, 2001, 2005; *Cande and Stock*, 2004; *Jellinek et al.*, 2006], and we speculate that is also the case for the Malpelo-Nazca boundary (Figure 3).

We assume that the Malpelo plate extends only as far north as ≈6°N where seismicity marks another boundary with a previously recognized microplate, the Coiba plate [*Pennington*, 1981; *Adamek et al.*, 1988] (Figure 3).

Figure 4 shows a velocity space representation of the Nazca, Cocos, and Malpelo plates at a point (4.15°N, 82.6°W) along the Panama transform fault, which separates the Cocos and Malpelo plates. The Cocos-Nazca velocity is determined from the best fitting angular velocity described above. The strike of the Panama transform fault is known. To estimate the direction of motion between the Malpelo and Nazca plates, we assume that their pole of relative rotation lies where it is shown in Figure 3. With these assumptions, the speed of the Malpelo plate relative to the Nazca plate at this point is 5.9 mm a^{−1}.

## 4 Nonclosure of the Cocos-Nazca-Pacific Plate Motion Circuit

We re-estimate the nonclosure of the Cocos-Nazca-Pacific plate motion circuit with our new best- fitting angular velocity for Cocos-Nazca plate motion. If the plates were rigid and if there were no errors in the data, then the sum of the three best-fitting angular velocities would be zero. When we sum the Cocos-Pacific, Pacific-Nazca, and Nazca-Cocos best-fitting angular velocities of *DeMets et al*. [2010], however, we obtain an angular velocity of nonclosure of 0.34° Ma^{−1} (± 0.12° Ma^{−1}; 95% confidence limits) about a pole at 24.8°N, 96.5°W (Figure 5a), which differs significantly from zero. Evaluated at the approximate location of the triple junction of 2.3°N, 102.0°W (Figures 5a and S3), we obtain a linear velocity of nonclosure of 15.0 mm a^{−1} (± 3.8 mm a^{−1}; 95% confidence limits) 283° clockwise of north (Figure 5b). (This differs slightly from that found by *DeMets et al*. [2010], perhaps because we use a different reference point.) In comparison, our new angular velocity of nonclosure is 0.33° Ma^{−1} (± 0.12° Ma^{−1}; 95% confidence limits) about a pole at 19.8°N, 96.9°W (Figure 5a) and the new linear velocity of nonclosure is 11.6 mm a^{−1} (± 3.8 mm a^{−1}; 95% confidence limits) toward 286° clockwise of north (Figure 5b). By replacing the two transform fault azimuths from *DeMets et al*. [2010] with the improved set of three new transform fault azimuths, the nonclosure is reduced by 3.4 mm a^{−1}.

The new angular velocity of nonclosure still differs significantly from zero, however. Using the *F* ratio test for plate circuit closure [*Gordon et al.*, 1987], we obtain a value of *F* of 19.5 with 3 versus 205 degrees of freedom from the best-fitting angular velocities of *DeMets et al*. [2010] and a value of *F* of 16.9 with 3 versus 206 degrees of freedom from our new best-fitting angular velocities (Table S2). Reference values of *F* are *F*_{0.05} = 2.7 (5% significance level of 95% confidence level) and *F*_{0.01} = 3.9 (1% significance level of 99% confidence level); thus, the nonclosure, while reduced, remains significant.

## 5 Discussion

When we reanalyze the closure of the Cocos-Nazca-Pacific plate circuit using our new set of Cocos-Nazca transform fault azimuths and make no other changes, the nonclosure of the circuit is reduced from 15.0 ± 3.8 mm a^{−1} to 11.6 ± 3.8 mm a^{−1}, thus reducing but not eliminating the nonclosure of the Pacific-Cocos-Nazca plate circuit. The sense (i.e., sign) of the velocity of nonclosure seems consistent with an explanation in terms of horizontal thermal contraction of oceanic lithosphere [*Kumar and Gordon*, 2009], but the magnitude of nonclosure is almost surely too large to be caused only by known processes of intraplate deformation including thermal contraction.

Specifically, the work of *Kreemer and Gordon* [2014] indicates that the displacement rates across the Pacific plate due to thermal contraction are 1–2 mm a^{−1}, which are consistent with intraplate strain rates due to horizontal thermal contraction inferred by *Mishra and Gordon* [2016]. If all three of the Cocos, Nazca, and Pacific plates are characterized by intraplate displacements of 1–2 mm a^{−1} due to horizontal thermal contraction, and if we assume that the orientations and magnitudes of these are uncorrelated between plates, a nonclosure of ≈2–4 mm a^{−1} (1–2 mm a^{−1} × √3) might be expected, which is much smaller than the 11.6 ± 3.8 mm a^{−1} (95% confidence limits) of nonclosure that we find. Thus, the cause of at least part of the nonclosure remains unknown and we suggest that one or more plate boundaries remain to be discovered.

If the nonclosure is due to deformation of one of the plates or to an undiscovered plate boundary within that same plate, the Cocos plate seems the best candidate because of its proximity to the pole of rotation of nonclosure. Larger displacement rates would be required for an undiscovered plate boundary in the Pacific or Nazca plate simply because any hypothetical deformation zone would lie farther from the pole of rotation of nonclosure. Furthermore, the absence of significant nonclosure about the Nazca-Pacific-Antarctica plate motion circuit suggests that the Pacific and Nazca plates are not highly nonrigid [*DeMets et al.*, 2010].

## 6 Conclusions

The lithosphere east of the Panama transform fault moves independently of the Nazca plate, constituting a microplate that we term the Malpelo microplate. The new transform fault azimuths result in nonclosure about the Galapagos triple junction that is 3.4 mm a^{−1} smaller than that found by *DeMets et al*. [2010], but remains large (11.6 ± 4 mm a^{−1}). While the sense of the observed nonclosure is consistent with horizontal thermal contraction of oceanic lithosphere, the indicated magnitude of deformation remains too large to be explained only by thermal contraction. Thus, we suggest that one or more plate boundaries remain to be discovered.

## Acknowledgments

This work was supported by NSF grant OCE-1559316. Some of the figures were made with Generic Mapping Tools software [*Wessel and Smith*, 1991]. The data supporting the conclusions can be obtained in the references, tables, and supporting information.