RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES4001, doi:10.2205/2007ES000218, 2008
[7] Qualitative approach to the solution of geodynamic problem can be based only on coherent definition of "geodynamics''. Comparison of experts' views with those of their opponents [Belousov, 1975; Pavlenkova, 1987; Zonenshein and Kuzmin, l993] shows the presence of a common pivot proceeds from the definition of dynamics used in physics. "Mechanics studies the simplest form of matter motion i.e. mechanical movement to change mutual arrangement of bodies and their parts in space and time. Bodies are macroscopic systems consisting of a very large number of molecules and atoms, so sizes of the systems many times higher than intermolecular distances. Kinematics studies mechanical motion of bodies without the connection defining the interaction between bodies. Dynamics studies the way in which force produces motion [Yavorsky and Detlaf, 1974]. Interaction means the analysis of forces and energy sources. Therefore, "geodynamics'' is considered as science that studies the interaction between geological object with time. The development of approaches to parametrization of complex properties of geological bodies to further use them in the quantative analysis is important for solution of geodynamic problems. A very similar to the above definition of "geodynamics'' was given in the work by Khain and Lomize [1995]. Objects in terms of geodynamic turn to be much more complicated than those in classical physics which makes this subject quite unique. Complexity of objects affects greatly the presence of adequate and efficient quantitative models describing processes of geodynamics.
[8] The above definition assumes that parameters describing a geodynamic object are to be delivered into three main groups:
[9] 1. Description of geometry and physical properties of the object.
[10] 2. Description of forces and energy release within the object.
[11] 3. Description of object motion behavior resulted from the action of forces on the object and energy release in it.
[12] Thus, the objective of the geodynamic zonation is a search for different stable combinations of parameters describing a geodynamic object and analysis of their distribution in space.
[13] The first works concerning the qualitative approach to solution of geodynamical problems
using several parameters are those by
Reisner and Reisner [1987, 1990].
They made the analysis of endogenous regimes for most of Europe, Caucasus, and the Carpathians.
Calculations using the cluster analysis algorithm as a version of popular multi-dimensional
statistic classification of objects. This method is of practical importance because a man cannot
make a reliable visual correlation of parameters if their number is above four. Such parameters as
thickness and average seismic velocity of the Earth's crust, elevation, depth to the consolidated
basement were discussed in the works mentioned. Heat flow is taken as a parameter describing
energy release. Isostatic gravity anomalies and velocity of recent vertical movements were used
to describe the resultant motion of geomedia. A complete set of parameters was presented for the
land and grouped into average values
2030
cell of arc minutes defining
stable combinations, i.e. clusters of geodynamic parameters. The latter allowed to find a new type
of endogenous regime.
[14] The paper by Ioganson and Boltyshev [2000] presented the cluster analysis for the eastern Eurasia. This study differs from the previous works by showing changes in cluster classification as the number of clusters increases and in revealing of stable (homogenous) areas. This does not result in differentiation of a separate region into subclasses of smaller area. Qualitatively, they used linear and dispersed heterogeneity of territories. The former assumes division of territory into contrasting classes much smaller in area (size) than homogeneous areas. At the same time, it made possible to retain a stable mosaic pattern as the classification number increases. Dispersed heterogeneity was meant as "comminution'' of territory into small and comparable with size of a zone cell with different combination of main parameters chaotically covering territory. Prior to the processing stage the study area was homogeneous (linearly heterogeneous) on steps having small classification number.
[15] This paper discusses the Atlantic ocean structure in terms of linear heterogeneity. However, situation will be considered to be optimal when the number of classes allowing to divide the study territory (see Section 5) does not result in critical comminution of the recognized stable zones into much smaller zones whose size is comparable with that of a cell. The authors believe that dispersed (scattered) heterogeneity mentioned in the paper by Ioganson and Boltyshev [2000] is directly associated with the scatter of parameters used for their analysis. Its qualitative measure is the scatter of parameters values within a zone of one or another cluster.
[17] Parameters to be selected must describe three groups of properties mentioned in Section 2.1. Parameters describing structural features of the lithosphere (group 1) are very easy to select (see Section 3).
[18] Parameters defining energy release (group 2) can be easily selected except for problems related to irregular heat flow measurements.
[19] Most difficult is to describe the resultant motion (group 3). Vertical movements inferred from repeated geodetic measurements from GPS data can be used for the land. There is no such measurements for the sea floor and a regular observation network (measurement grid) can hardly be obtained in future. Therefore, to include data of 3-type group into calculations one should use the so-called "surrogate'' parameters reflecting indirectly values no measured or partially measured in the ocean or they present a combination of many effects including those to be processed. In this case, such an approach is the only way to show the necessary information in absence of detailed data.
[20] All the parameters used in this paper are values inferred from instrumental measurements reflecting only the present state of all three groups of parameters. Paleogeodynamic reconstructions of the Atlantic ocean are always based on incomplete information with many assumptions for values remaining unknown. In paleogeodynamics not measurements but interpretations of geological-geophysical data that should reflect paleostate of the lithosphere become important. The ambiguity of interpretation will always make the result debatable.
[21] The paper discusses only the recent state of the lithosphere. Besides, the authors do not use the age of the oceanic lithosphere inferred from magnetometric data as a parameter for calculation [Mueller et al., 1993] because the authors of a data source do not define general linear anomaly position in most complex and important parts of the Atlantic (transition from northern to southern segment), important for geodynamic. The latter follows from the data [Cande et al., 1993] used for the construction of the known age map. Nevertheless, the map in fact completely covers the Atlantic. It means that all the estimates for which we use it in most important areas will reflect the pecularities of interpolation algorithms and not value a parameter. Therefore, the information on the age of the lithosphere can at best be used as a coordinate parameter to present the analysis results along with latitude and longitude.
[22] In this study one arc degree is proposed as the best size for a cell within which the parameters used show similar detail level. In other words, the latter of all the parameters is not worse than this value. The dimensions of the cell are comparable with an average thickness of the lithosphere. The more detailed parameters are to be fit to a chosen threshold by frequency filtration or by moving average. The real size of an area created by a chosen cell decreases at high latitudes which creates less statistical importance of parameters. Nonetheless, as this concerns all the parameters at once the authors do not use estimates in the projection space having equal size. However, the average value of parameters within cell is evaluated well enough.
[24] The discriminant analysis is aimed at classification of objects by selection of its parameters and comparing their values with "learning'' standards. Requiring the presence of known a priori stable type, this method is not applicable because prior to the analysis we can not be sure in the result.
[25] The factor analysis assumes that the available object data set consists of combination of two or more processes actions, each of them contributing to values of all parameters. In other words, there are independent geodynamic phenomena that form superposition of measurement values (we subdivide them by means of factor analysis). At present, it is fairly difficult to construct a model for operation of two or more global processes whose contribution to all the parameters will be of statistical importance, however, this can be done in future.
[26] The cluster analysis assumes recognition of stable combinations of parameters not discernible by visual analysis of maps and seems to be the most adequate at this stage of the study as has been shown earlier for other regions (see Section 2.1.). The factor analysis might be used in case of geodynamic model construction exhibiting one (or more) mechanisms affecting surface tectogenesis.
Citation: 2008), Geodynamic zonation of the Atlantic Ocean lithosphere: Application of cluster analysis procedure and zoning inferred from geophysical data, Russ. J. Earth Sci., 10, ES4001, doi:10.2205/2007ES000218.
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