Digital Isochrons of the World's Ocean Floor
R. Dietmar Müller
Department of Geology and Geophysics, University of Sydney, Australia
Walter R. Roest
Geological Survey of Canada, Ottawa, Canada
Jean-Yves Royer
Lab. de Géodynamique, Villefranche Sur Mer, France
Lisa M. Gahagan
Institute for Geophysics, University of Texas, Austin, Texas
John G. Sclater
Scripps Institution of Oceanography, La Jolla, California
Abstract
Introduction
Ocean Floor Isochrons and Plate Boundaries
Interpolation of Isochrons and Gridding
Accuracy
Conclusions
Acknowledgments
References
Addresses and e-mail of authors
Abstract
We have created a digital age grid of the ocean floor with a grid node interval
of 6 arc-minutes using a self-consistent set of global isochrons and associated
plate reconstruction poles. The age at each grid node was determined by
linear interpolation between adjacent isochrons in the direction of spreading.
Ages for ocean floor between the oldest identified magnetic anomalies and
continental crust were interpolated by estimating the ages of passive continental
margin segments from geological data and published plate models. We have
constructed an age grid with error estimates for each grid cell as a function
of (1) the error of ocean floor ages identified from magnetic anomalies
along ship tracks and the age of the corresponding grid cells in our age
grid, (2) the distance of a given grid cell to the nearest magnetic anomaly
identification, and (3) the gradient of the age grid, i.e. larger errors
are associated with high age gradients at fracture zones or other age discontinuities.
Future applications of this digital grid include studies of the thermal
and elastic structure of the lithosphere, the heat loss of the Earth, ridge-push
forces through time, asymmetry of spreading, and providing constraints for
seismic tomography and mantle convection models.
Introduction
The age of the ocean floor is an important parameter in the study of plate
tectonic processes. An accurate digital age grid is essential for many studies,
including plate kinematics, studies of plate driving forces, mantle dynamics,
ocean floor roughness and paleoceanography. Several analog maps of the age
of the ocean floor have been compiled using magnetic anomaly data [e.g.,
Sclater et al., 1981; Larson et al., 1985]. A digital version of the latter
map was produced by Cazenave et al. [1988], at a grid interval of half a
degree (approx. 55 km). Recent improvements in identifications of magnetic
anomalies and plate kinematic models, especially aided by dense gravity
data from satellite altimetry, permit a more detailed description of the
spreading process, and have initiated the construction of a more detailed
age grid.
Ocean Floor Isochrons and Plate Boundaries
We have constructed a global set of isochrons for the ocean basins corresponding
to magnetic anomalies 5, 6, 13, 18, 21, 25,31, 34, M0, M4, M10, M16, M21,
and M25 based on a global plate reconstruction model, magnetic anomaly identifications
and fracture zones [see also Royer et al., 1992]. The geomagnetic time scale
of Cande and Kent [1995] was used for anomalies younger than chron 34 (83
Ma), the time scale from Gradstein et al. [1994] for older times. Isochrons
were constructed by plotting reconstructed magnetic anomaly and fracture
zone picks, as well as selected small circles computed from stage rotation
poles for each isochron time, keeping one plate fixed. Then best-fit continuous
isochrons were constructed, connected by transforms, in the framework of
one fixed plate [see also Müller et al., 1991]. A complete set of isochrons
for all conjugate plate pairs was derived by rotation of every isochron
to their present day position.
Construction of a complete age grid also requires knowledge of the present
day plate boundary geometry. The boundaries shown in Figure 1 have been
compiled based on a marine gravity grid from Geosat exact repeat mission,
Geodetic Mission, and ERS-1 satellite altimetry data [Sandwell et al., 1994],
bathymetric data, and Earthquake epicenters. There is a significant area
of ocean floor that is older than the oldest mapped isochrons. In order
to estimate ages for the oldest ocean floor in ocean basins bounded by passive
margins, we assigned ages to continental margin segments based on geological
data and published plate models. The regional boundaries between continental
and oceanic crust have been compiled in Müller and Roest [1992] (North
and central North Atlantic), Nürnberg and Müller [1992] (South
Atlantic), and Royer et al. [1992] (Indian Ocean). South of 60°S a
dense grid of Geosat Geodetic Mission data [Sandwell et al., 1994] has been
used to better locate boundaries between continental and oceanic crust in
remote areas such as the Antarctic continental margin.
Interpolation of Isochrons and Gridding
In order to create a smooth grid of ocean floor ages that maintains all
sharp age discontinuities at fracture zones, we first create a set of densely
interpolated isochrons. We assume that the spreading direction between two
adjacent isochrons is given by a constant stage pole of motion, derived
from our plate kinematic model. We also assume that the spreading velocity
between two adjacent isochrons is constant, and that consequently the age
varies linearly in the direction of spreading on a given ridge flank. To
simplify the calculations, each pair of adjacent isochrons is transformed
to a coordinate system in which the stage pole of motion between the two
isochrons is moved onto the geographic north pole [Roest et al.,1992]. Then
intermediate isochrons were linearly interpolated along plate flow-lines.
This is equivalent to interpolation along small circles about the stage
pole. The complete set of isochrons for each stage was subsequently rotated
back into the geographic reference frame. This was done for each isochron
pair on each plate pair.
To interpolate the ages onto a regular grid, we assume that the isochrons are
continuous, which is implemented by densely interpolating between observation
points along each isochron. A minimum curvature routine is used to obtain age
values on a regular grid at a resolution of 0.1 degrees, equivalent to 6 arc-minutes.
Areas of the ocean floor with insufficient data coverage were blanked out in the
grid. We included data from selected back-arc basins, where data coverage is sufficient
and available to us. The resolution of our grid for these areas is typically reduced
by a factor of 10 with respect to the oceanic grid, i.e. the resolution in back-arc
basins does not exceed 1 degree, and provides merely a rough estimate of the age
distribution in these basins. The resulting grid is shown in Figure
1a.
Accuracy
The accuracy of the age grid varies considerably due to the spatially irregular
distribution of ship track data in the oceans. Other sources of errors are
given by our chosen spacing of isochrons as listed before, between which
we interpolated linearly. These stages are especially long during long time
intervals without changes in the polarity of the Earth's magnetic field
such as the Cretaceous Magnetic Quiet Zone from about 118 to 83 Ma. We assume
that age grid errors depend on the distance to the nearest data points and
the proximity to fracture zones. In order to estimate the accuracy of our
age grid, we construct a grid with age-error estimates for each grid cell
dependent on (1) the error of ocean floor ages identified from magnetic
anomalies along ship tracks and the age of the corresponding grid cells
in our age grid, (2) the distance of a given grid node to the nearest magnetic
anomaly identification, and (3) the gradient of the age grid, i.e. larger
errors are associated with high age gradients across fracture zones or other
age discontinuities. The latter also reflects that, due to the interpolation
process, uncertainty in the magnetic anomaly will induce larger age errors
in regions of slow spreading rates than in regions of fast spreading rates.
We first compute the age differences between ~30000 interpreted magnetic
anomaly ages and the ages from our digital age grid, and investigate the
size and distribution of the resulting age errors. We find that the majority
of errors are smaller than 1 m.y. and errors larger than 10 m.y. are mostly
due to erroneously labeled or interpreted data points. Therefore we set
an upper limit for acceptable errors as 10 m.y. As a lower limit we arbitrarily
choose 0.5 m.y., since we do not expect to resolve errors smaller than 0.5
m.y. given the uncertainty in the timescales used. We grid the remaining
age errors by using continuous curvature splines in tension.
The constraints on the ages in our global age grid generally decrease with
increasing distance to the nearest interpreted magnetic anomaly data point.
Areas without interpreted magnetic anomalies include east-west spreading
mid-ocean ridges in low latitudes such a the equatorial Atlantic ocean,
where the remanent magnetic field vectors are nearly parallel to the mid-ocean
ridge and cause very small magnetic anomalies, and areas with sparse data
coverage such as some remote areas in the southern ocean. In order to address
the "tectonic reconstruction uncertainties" for these areas, we
create a grid containing the distance of a given grid cell to the nearest
data point, ranging from zero at the magnetic anomaly data points to 10
at distances of 1000 km and larger. We smooth this grid using a cosine arch
filter (5° full width) and add the result to the initial splined grid
of age errors.
Fracture zones are usually several tens of km wide, containing highly fractured
and/or serpentinized ocean crust. Age estimates may be uncertain especially near
large-offset fracture zones, which are more severely affected by changes in spreading
direction than small-offset fracture zones. Consequently, our age estimates along
large-offset fracture zones may be more uncertain than at small-offset fracture
zones or on "normal" ocean crust. Large-offset fracture zones are easily
identified in the age grid by computing the gradient of the age grid. We identify
the age gradients associated with medium- to large offset fracture zones, set
the gradients of "normal" ocean crust to zero, smooth the result with
a 3x3 moving average filter, and scale the grid to range from one to two. After
multiplying the error grid with the smoothed age gradients along fracture zones,
we have not altered the errors associated with "normal" ocean floor,
and increased the errors at fracture zones by a factor between one and two, depending
on the magnitude of the age gradient. The resulting grid of age uncertainties
is shown in Figure 1b.
Conclusions
The digital age grid presented here is the first of its kind, because (1)
in the past ages of the ocean floor have only been available on analog maps,
with the exception of a digitized version of Larson et al.'s [1985] age
map produced by Cazenave et al. [1988] at a relatively coarse grid interval
of 0.5°, (2) our grid is based on a self-consistent global plate model,
and (3) it is accompanied by a grid estimating the uncertainties of the
gridded ages. A shortcoming of our error analysis at present is that it
does not include the uncertainties of the plate rotations. We hope to include
this parameter in the next age grid generation.
Acknowledgments
This work was made possible by the contributors to the former Paleoceanographic
Mapping Project (POMP, University of Texas, Austin) who released data that
served as partial input for constructing the isochrons, POMP industry sponsors
for financial support to RDM, LMG and JYR, and by the PLATES industry sponsors
through support to LMG. Construction of the age grid was started at the
Scripps Institute of Oceanography while the senior author was supported
by a graduate and a post-doctoral fellowship. JYR acknowledges support by
the CNRS (Centre National de la Recherche Scientifique). CONOCO/Canada provided
funds for publishing color figures. The GMT software system from P. Wessel
and W.H.F. Smith was invaluable in performing the age error analysis, and
for producing the Figures.
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Addresses and e-mail of authors
L. M. Gahagan, Institute for Geophysics, University of Texas, 8701 Mopac
Boulevard, Austin, TX 78759-8345 (e-mail: lisa@utig.ig.utexas.edu)
R. D. Müller, Department of Geology and Geophysics, Building F05, University
of Sydney, N.S.W. 2006, Australia (e-mail: dietmar@es.su.oz.au)
W. R. Roest, Geological Survey of Canada, 1 Observatory Crescent, Ottawa
ON, K1A 0Y3, Canada (e-mail: roest@agg.emr.ca)
J.-Y. Royer, Lab. de Géodynamique, O.O.V., La Darse, B.P. 48, 06230
Villefranche Sur Mer, France (e-mail: royer@es.su.oz.au)
J. G. Sclater,, Scripps Institution of Oceanography, UCSD, 9500 Gilman Drive,
La Jolla, CA 92093-0215 (e-mail: sclater@bullard.ucsd.edu)