Geophysical research: The Earth’s non-linear properties

Geophysical research

Hatam H. Guliyev and Rashid J. Javanshir discuss a fascinating aspect of geophysical research that concerns the Earth’s non-linear properties

Successful integration between the mechanics of deformable solid bodies and Earth Sciences resulted in a new theory of non-classical tectonophysics. By moving from the idea of linearity of elastic waves and deformations of solid media to the concept of nonlinearity, an approach is proposed for an adequate determination of the tectonophysical parameters of the geodynamically evolving Earth.


The turn of the 20th century was marked by the formation of the scientific view that Earth represents a huge composite ball consisting of crust, mantle, liquid and solid core. Over the next hundred years, theoretical ideas about the Earth’s structure have progressed. Integration of mechanics with the Earth Sciences contributed immensely to the development of those ideas. Initially, geologists were focussing on the simple collection of the rock samples and subsequent experimental studies. Gradually, different theories of the Earth have been presented to the scientific community. Amongst the developments was the creation of the Preliminary Reference Earth Model (PREM), which was presented in 1976 by outstanding scientists Don Anderson and Adam Dziewonsky and was received as a triumphant breakthrough. In parallel, “Tectonophysics” emerged as a new scientific discipline. Its main task was to synthesise linear physical, mechanical and elastic properties of geological media from a huge primary data stream. Since then PREM has been actively used in scientific research. The concept has been adopted across a broad range of Earth sciences and remains unchanged. It is interesting that in 2015 Adam Dziewonsky noted that PREM was called “preliminary” as the authors believed it would be improved in a few years. However, for various reasons, revisions did not happen.

Non-classically linearized approach (NLP)

For decades, geological, geophysical, seismological and experimental data has been processed based on the theories of elastic waves and elastic deformations, which form the basis of what we call “classical” tectonophysics. These theories are rather simplified and approximate and unfortunately have one rather fatal flaw largely due to the use of the term “elasticity.” The problem is that “elasticity” is broadly associated with linearity, which subsequently led to the theories of tectonophysics also being viewed as linear.

It was indeed believed that data represents linear elastic physical and mechanical properties. This is what PREM is also based on. Our research shows that processed data does not represent parameters of the linear elastic properties of the media, which demonstrates that PREM is essentially incomplete. Moreover, it shows insolvency of its data from a geomechanical perspective.

50 years have passed since the beginning of the creation of the non-classically linearized approach of mechanics of a deformable solid body. We have dedicated our research to the development of this method to a more complex interdisciplinary problem such as Earth Sciences. We are considering aspects directly related to natural objects of the Earth and phenomena occurring in them. As a result, this approach turned into a highly efficient working tool called nonlinear linearized approach (NLA) of nonlinear elastodynamics. Several important fundamental results have been obtained in the field of mining mechanics, internal structural formations and dynamics of the Earth, seismology, modern geodynamics, seismic surveys and tectonophysics. Most of them are used in the processing and interpretation of geological-geophysical and seismological data and have an innovative character. The results of the standard approach differ from the actual values of elastic parameters of the medium to 30% for some rocks of the Earth’s first 10 km. It would be significantly higher for deep portions of the Earth.

Critical conclusions have been reached through processing and interpretation of nonlinear theories of elastic waves and deformation of solids. We are presenting theoretical foundations of nonlinear tectonophysics and can eliminate the above-mentioned flaws and inaccuracies. This represents an historic result in geophysics.

We have developed a non-classically linearized approach (NLP) within the framework of classical tectonophysics in order to avoid unnecessary mathematical complications and ambiguous readings of nonlinear theories. Tasks here are not simplified but studied strictly in three-dimensional settings, which are a major advantage over the commonly used one- and two-dimensional approximations. This is not just a method for solving nonlinear problems. Along with this important mission, it significantly expands the understanding of the processes under study. This extension is included in the methodology.

The need for better international cooperation

This approach and the proposed method of nonlinear geo-mechanical analysis open new horizons and directions for future research, which will last for decades or longer. It is necessary to bring this innovation to the attention of the broader scientific community and initiate a collaborative effort across various scientific disciplines and institutions aiming to improve the reliability of knowledge in the understanding of Earth and its evolution.

First, it is necessary to analyse a complex set of data for the entire Earth and its structural elements for continents, oceans, as well as vertically, from the crust to the core. Secondly, it is important to stop the use of classical tectonophysics. Third, considering the features of nonlinear deformation, improve the methodology and practice of collecting geological, geophysical and seismological data.

Nonlinear tectonophysics allows determining the true parameters of Earth and its structural elements taking into account the ongoing geodynamic changes over 4.5 billion years, under the influence of large-scale cosmogenic, exogenous and endogenous forces of natural and technogenic nature, which is unattainable within the framework of classical tectonophysics.

Throughout the last 35-40 years, we have published our results in hundreds of books and papers. Yet despite this success, wider communities of Earth sciences have not properly discussed these theories. We believe that such an issue has been driven by a lack of collaboration between researchers from different cultural backgrounds, especially the former Soviet Union and the West. We now hope, however, that such cooperation will be improved. We are now planning to use NLP in recently agreed joint collaborative research programme between Azerbaijan National Academy of Sciences and Oxford University. Sides are conducting a multi-disciplinary study that draws together earthquake geology, paleoseismology, earthquake seismology, and seismic reflection imaging of the sub-surface. We expect exciting years ahead.


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Corresponding Member, Department of Geodynamics and Rock Mechanics
Institute of Geology and Geophysics, Azerbaijan National Academy of Sciences
Phone: +44 77698 10156
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Contributor Profile

Head of Department, Department of Geodynamics and Rock Mechanics
Institute of Geology and Geophysics, Azerbaijan National Academy of Sciences
Phone: +99450 369 4749
Website: Visit Website


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