The depth of the seafloor on the flanks of a
mid-ocean ridge
A mid-ocean ridge (MOR) is a undersea mountain range, seafloor mountain system formed by plate tectonics. It typically has a depth of about and rises about above the deepest portion of an ocean basin. This feature is where seafloor spreading ...
is determined mainly by the ''age'' of the
oceanic lithosphere
A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the lithospheric mantle, the topmost portion of the upper mantle that behaves elastically on time sc ...
; older seafloor is deeper. During
seafloor spreading
Seafloor spreading, or seafloor spread, is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge.
History of study
Earlier theories by Alfred Wegener ...
,
lithosphere
A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the lithospheric mantle, the topmost portion of the upper mantle that behaves elastically on time ...
and mantle cooling, contraction, and
isostatic adjustment with age cause seafloor deepening. This relationship has come to be better understood since around 1969 with significant updates in 1974 and 1977. Two main theories have been put forward to explain this observation: one where the mantle including the lithosphere is cooling; the cooling mantle model, and a second where a lithosphere plate cools above a mantle at a constant temperature; the cooling plate model. The cooling mantle model explains the age-depth observations for seafloor younger than 80 million years. The cooling plate model explains the age-depth observations best for seafloor older that 20 million years. In addition, the cooling plate model explains the almost constant depth and heat flow observed in very old seafloor and lithosphere. In practice it is convenient to use the solution for the cooling mantle model for an age-depth relationship younger than 20 million years. Older than this the cooling plate model fits data as well. Beyond 80 million years the plate model fits better than the mantle model.
Background
The first theories for seafloor spreading in the early and mid twentieth century explained the elevations of the mid-ocean ridges as upwellings above
convection currents
Convection is single or multiphase fluid flow that occurs spontaneously through the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convect ...
in
Earth's mantle
Earth's mantle is a layer of silicate mineral, silicate rock between the Earth's crust, crust and the Earth's outer core, outer core. It has a mass of and makes up 67% of the mass of Earth. It has a thickness of making up about 46% of Earth's ...
.
The next idea connected seafloor spreading and
continental drift
Continental drift is a highly supported scientific theory, originating in the early 20th century, that Earth's continents move or drift relative to each other over geologic time. The theory of continental drift has since been validated and inc ...
in a model of
plate tectonics
Plate tectonics (, ) is the scientific theory that the Earth's lithosphere comprises a number of large tectonic plates, which have been slowly moving since 3–4 billion years ago. The model builds on the concept of , an idea developed durin ...
. In 1969, the elevations of ridges was explained as
thermal expansion
Thermal expansion is the tendency of matter to increase in length, area, or volume, changing its size and density, in response to an increase in temperature (usually excluding phase transitions).
Substances usually contract with decreasing temp ...
of a lithospheric plate at the spreading center.
This 'cooling plate model' was followed in 1974 by noting that elevations of ridges could be modeled by cooling of the whole
upper mantle
The upper mantle of Earth is a very thick layer of rock inside the planet, which begins just beneath the crust (geology), crust (at about under the oceans and about under the continents) and ends at the top of the lower mantle (Earth), lower man ...
including any plate.
This was followed in 1977 by a more refined plate model which explained data that showed that both the ocean depths and ocean crust
heat flow
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
approached a constant value for very old seafloor.
These observations could not be explained by the ''earlier '' 'cooling mantle model' which predicted increasing depth and decreasing heat flow at very old ages.
Seafloor topography: cooling mantle and lithosphere models
The depth of the seafloor (or the height of a location on a mid-ocean ridge above a base-level) is closely correlated with its age (i.e. the age of the lithosphere at the point where depth is measured). Depth is measured to the top of the
ocean crust
Oceanic crust is the uppermost layer of the oceanic portion of the Plate tectonics, tectonic plates. It is composed of the upper oceanic crust, with pillow lavas and a dike (geology), dike complex, and the lower oceanic crust, composed of troct ...
, below any overlying sediment. The age-depth relation can be modeled by the cooling of a lithosphere plate
or mantle half-space in areas without significant
subduction
Subduction is a geological process in which the oceanic lithosphere and some continental lithosphere is recycled into the Earth's mantle at the convergent boundaries between tectonic plates. Where one tectonic plate converges with a second p ...
.
The distinction between the two approaches is that the plate model requires the base of the lithosphere to maintain a constant temperature over time and the cooling is of the plate above this lower boundary. The cooling mantle model, which was developed after the plate model, does not require that the lithosphere base is maintained at a constant and limiting temperature. The result of the cooling mantle model is that seafloor depth is predicted to be proportional to the square root of its age.
Cooling mantle model (1974)
In the cooling mantle half-space model developed in 1974,
the seabed (top of crust) height is determined by the
oceanic lithosphere
A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the lithospheric mantle, the topmost portion of the upper mantle that behaves elastically on time sc ...
and mantle temperature, due to thermal expansion. The simple result is that the ridge height or seabed depth is proportional to the square root of its age.
In all models, oceanic lithosphere is continuously formed at a constant rate at the
mid-ocean ridge
A mid-ocean ridge (MOR) is a undersea mountain range, seafloor mountain system formed by plate tectonics. It typically has a depth of about and rises about above the deepest portion of an ocean basin. This feature is where seafloor spreading ...
s. The source of the lithosphere has a half-plane shape (''x'' = 0, ''z'' < 0) and a constant temperature ''T''
1. Due to its continuous creation, the lithosphere at ''x'' > 0 is moving away from the ridge at a constant velocity
, which is assumed large compared to other typical scales in the problem. The temperature at the upper boundary of the lithosphere (''z'' = 0) is a constant ''T''
0 = 0. Thus at ''x'' = 0 the temperature is the
Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Differen ...
. The system is assumed to be at a quasi-
steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
, so that the temperature distribution is constant in time, i.e.
By calculating in the frame of reference of the moving lithosphere (velocity
), which has spatial coordinate
and the
heat equation
In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quanti ...
is:
:
where
is the
thermal diffusivity
In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive ...
of the mantle lithosphere.
Since ''T'' depends on ''x and ''t'' only through the combination
:
:
Thus:
:
It is assumed that
is large compared to other scales in the problem; therefore the last term in the equation is neglected, giving one-dimensional diffusion equation:
:
with the initial conditions
:
The solution for
is given by the
error function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a function \mathrm: \mathbb \to \mathbb defined as:
\operatorname z = \frac\int_0^z e^\,\mathrm dt.
The integral here is a complex Contour integrat ...
:
:
.
Due to the large velocity, the temperature dependence on the horizontal direction is negligible, and the height at time ''t'' (i.e. of sea floor of age ''t'') can be calculated by integrating the thermal expansion over ''z'':
:
where
is the effective volumetric
thermal expansion
Thermal expansion is the tendency of matter to increase in length, area, or volume, changing its size and density, in response to an increase in temperature (usually excluding phase transitions).
Substances usually contract with decreasing temp ...
coefficient, and ''h
0'' is the mid-ocean ridge height (compared to some reference).
The assumption that
is relatively large is equivalent to the assumption that the thermal diffusivity
is small compared to
, where ''L'' is the ocean width (from mid-ocean ridges to
continental shelf
A continental shelf is a portion of a continent that is submerged under an area of relatively shallow water, known as a shelf sea. Much of these shelves were exposed by drops in sea level during glacial periods. The shelf surrounding an islan ...
) and ''A'' is the age of the ocean basin.
The effective thermal expansion coefficient
is different from the usual thermal expansion coefficient
due to
isostasic effect of the change in water column height above the lithosphere as it expands or contracts. Both coefficients are related by:
:
where
is the rock density and
is the density of water.
By substituting the parameters by their rough estimates into the solution for the height of the ocean floor
:
:
we have:
:
where the height is in meters and time is in millions of years. To get the dependence on ''x'', one must substitute ''t'' = ''x''/
~ ''Ax''/''L'', where ''L'' is the distance between the ridge to the
continental shelf
A continental shelf is a portion of a continent that is submerged under an area of relatively shallow water, known as a shelf sea. Much of these shelves were exposed by drops in sea level during glacial periods. The shelf surrounding an islan ...
(roughly half the ocean width), and ''A'' is the ocean basin age.
Rather than height of the ocean floor
above a base or reference level
, the depth of the seabed
is of interest. Because
(with
measured from the ocean surface) we can find that:
:
; for the eastern Pacific for example, where
is the depth at the ridge crest, typically 2500 m.
Cooling plate model (1977)
The depth predicted by the square root of seafloor age found by the 1974 cooling mantle derivation
is too deep for seafloor older than 80 million years.
Depth is better explained by a cooling lithosphere plate model rather than the cooling mantle half-space.
The plate has a constant temperature at its base and spreading edge. Derivation of the cooling plate model also starts with the heat flow equation in one dimension as does the cooling mantle model. The difference is in requiring a thermal boundary at the base of a cooling plate. Analysis of depth versus age and depth versus square root of age data allowed Parsons and Sclater
to estimate model parameters (for the North Pacific):
:~125 km for lithosphere thickness
:
at base and young edge of plate
:
Assuming isostatic equilibrium everywhere beneath the cooling plate yields a revised age-depth relationship for older sea floor that is approximately correct for ages as young as 20 million years:
:
meters
Thus older seafloor deepens more slowly than younger and in fact can be assumed almost constant at ~6400 m depth. Their plate model also allowed an expression for conductive heat flow, ''q(t)'' from the ocean floor, which is approximately constant at
beyond 120 million years:
:
Parsons and Sclater concluded that some style of mantle convection must apply heat to the base of the plate everywhere to prevent cooling down below 125 km and lithosphere contraction (seafloor deepening) at older ages.
Morgan and Smith showed that the flattening of the older seafloor depth can be explained by flow in the
asthenosphere
The asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between c. below the surface, and extends as deep as . However, the lower boundary of the asthenosphere i ...
below the lithosphere.
The age-depth-heat flow relationship continued to be studied with refinements in the physical parameters that define ocean lithospheric plates.
Impacts
The usual method for estimating the age of the seafloor is from marine
magnetic anomaly
In geophysics, a magnetic anomaly is a local variation in the Earth's magnetic field resulting from variations in the chemistry or magnetism of the rocks. Mapping of variation over an area is valuable in detecting structures obscured by overlying ...
data and applying the
Vine-Matthews-Morley hypothesis. Other ways include expensive
deep sea drilling and dating of core material. If the depth is known at a location where anomalies are not mapped or are absent, and seabed samples are not available, knowing the seabed depth can yield an age estimate using the age-depth relationships.
Along with this, if the seafloor spreading rate in an ocean basin increases, then the average depth in that ocean basin decreases and therefore its volume decreases (and vice versa). This results in global
eustatic sea level rise
The sea level has been rising from the end of the last ice age, which was around 20,000 years ago. Between 1901 and 2018, the average sea level rose by , with an increase of per year since the 1970s. This was faster than the sea level had e ...
(fall) because the Earth is not expanding. Two main drivers of sea level variation over geologic time are then changes in the volume of continental ice on the land, and the changes over time in ocean basin average depth (basin volume) depending on its average age.
See also
*
Sea level
Mean sea level (MSL, often shortened to sea level) is an mean, average surface level of one or more among Earth's coastal Body of water, bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical ...
*
Sea-level curve
*
Sea level equation
*
Sea level rise
The sea level has been rising from the end of the last ice age, which was around 20,000 years ago. Between 1901 and 2018, the average sea level rose by , with an increase of per year since the 1970s. This was faster than the sea level had e ...
References
Further reading
{{Cite journal, last=McKenzie, first=Dan, date=2018-05-30, title=A Geologist Reflects on a Long Career, journal=Annual Review of Earth and Planetary Sciences, language=en, volume=46, issue=1, pages=1–20, doi=10.1146/annurev-earth-082517-010111, bibcode=2018AREPS..46....1M, issn=0084-6597, doi-access=free
Coastal and oceanic landforms
Physical oceanography
Basalt
Geological processes
Plate tectonics
Volcanic landforms
Oceanographical terminology
Vertical distributions