Leonardo was a geophysicist

The science of geophysics studies the physics of our planet, considering the atmosphere, the hydrosphere, and the core, mantle, and crust of the earth. It is highly interdisciplinary since it involves geology, astronomy, meteorology, physics, engineering, and scientific computing. Today, it is impossible for a single researcher to deal with all these fields.

Before the scientific method was introduced, Leonardo da Vinci (1452– 1519), one of the brightest minds of all time, excelled in every aspect of art, humanity, and science. Leonardo foresaw a number of geophysical phenomena. The list below is incomplete but illustrative of his discoveries.

Wave propagation, interference, and Huygens’ principle (1678):

Everything in the cosmos is propagated by means of waves...
Manuscript H, 67r, Institut de France, Paris.

I say: if you throw two small stones at the same time on a sheet of motionless water at some distance from each other, you will observe that around the two percussions numerous separate circles are formed; these will meet as they increase in size and then penetrate and intersect one another, all the while maintaining as their respective centres the spots struck by the stones.
Manuscript A, 61r, Institut de France, Paris.

The Doppler effect (1842):

If a stone is flung into motionless water, its circles will be equidistant from their centre. But if the stream is moving, these circles will be elongated, egg-shaped, and will travel with their centre away from the spot where they were created.
Manuscript I, 87, Institut de France, Paris.

Newton’s prism experiment (1666): If you place a glass full of water on the windowsill so that the sun’s rays will strike it from the other side, you will see the aforesaid colours formed in the impression made by the sun’s rays...
Codex Leicester, 19149r, Royal Library, Windsor.

Explanation of the blue sky, before Tyndall’s 1869 experiments and Rayleigh’s theory of 1871:

I say that the blue which is seen in the atmosphere is not given its own colour, but is caused by the heated moisture having evaporated into the most minute and imperceptible particles.
Codex Leicester, 4r Royal Library, Windsor.

The principle of the telescope, first constructed in the Netherlands in the early 17th century:

It is possible to find means by which the eye shall not see remote objects as much diminished as in natural perspective...
Manuscript E, 15v, Institut de France, Paris.

The further you place the eyeglass from the eye, the larger the objects appear in them.
Manuscript A, 12v, Institut de France, Paris.

Construct glasses to see the Moon magnified.
Codex Atlanticus, 190r, a, Ambrosiana Library, Milan.

A statement anticipating Newton’s third law of motion (1666):

As much pressure is exerted by the object against the air as by the air against the body.
Codex Atlanticus, 381, Ambrosiana Library, Milan.

The principle of least action, before Fermat in 1657 and Hamilton in 1834:

Every action in nature takes place in the shortest possible way.
Quaderni, IV, 16r.

The evolution of the earth and living creatures, preceding George Cuvier (1804) and Charles Lyell (1863), and plate tectonics, anticipating Wegener (1915):

That in the drifts, among one and another, there are still to be found the traces of the worms which crawled upon them when they were not yet dry. And all marine clays still contain shells, and the shells are petrified together with the clay.

...Strata were covered over again from time to time, with mud of various thickness, or carried down to the sea by the rivers and floods of more or less extent; and thus these layers of mud became raised to such a height, that they came up from the bottom to the air. At the present time these bottoms are so high that they form hills or high mountains, and the rivers, which wear away the sides of these mountains, uncover the strata of these shells,...
Codex Leicester, Royal Library, Windsor.

Q&A:

José, apart from working as a research geophysicist all through, you also worked as a nuclear physicist early on in your career. What made you switch over to geophysics?

Argentina was (and is) a developing country and the 80’s were hard times of political and economical turmoil. Nuclear physics was a too-basic research subject to find a stable job in that type of situation. This and the possibility to work in the industry were the reasons why I changed to exploration geophysics. In the 80’s there was a research team at YPF (the former Argentine national oil company) so I decided to join that team and perform a mix of basic-practical research on oil prospecting. I actually started with seismic processing and interpretation and these practical aspects guided my future research activities.

The main focus of your research work in all your publications, as I have noticed it, is the wave propagation in media, and you tackle problems of attenuation, anisotropy, upscaling and others. Do you agree and could you comment on it.

These subjects are related to oil prospecting, environmental (near-surface) geophysics and seismology, so the purpose of my research work is to improve and refine existing techniques and methodologies to describe the constitutive equations and wave propagation features of real media, i.e., rocks and geological systems. Note that I mean constitutive equation and not stress-strain relations, since part of my work is also concerned with electromagnetic geophysical methods, such as the surface radar and low-frequency techniques. There is a chapter in my book “Wave Fields in Real Media” devoted to the acoustic-electromagnetic analogy, which exploits the mathematical analogies between both fields to avoid re-inventing the wheel and providing a shortcut for those researchers who wish to study both subjects. Moreover, I have publications dealing with other aspects of practical research, such as borehole geophysics stability during drilling, advanced seismic processing, geophysical diffusion fields and design of numerical algorithms. Recently, my methods have been applied to gas-hydrate and CO2-monitoring related projects.

José, I notice that your research work entails applications of geophysical techniques to even ‘partially frozen orange juice’, which is uncommon. Could you comment on that?

This is because of the general aspect of our research work. Take into account that wave mechanics is one of the most important subjects in physics (and geophysics). Think of Maxwell’s equations or the theory of quantum mechanics and their impact on society. Subjects that “were born” as basic research with no clear application at those times. The Schroedinger equation can be understood and solved with the theories and numerical algorithms we use in geophysical prospecting. The most famous scientists in history, such as Hooke, Fresnel, Maxwell, Lord Kelvin, Dirac, were dealing all the time with wave theory, in the acoustic and electromagnetic senses. Actually, the general approach with which my book is written facilitates its sale in several fields of research, not only geophysics. In fact, I was asked days ago to write the third edition. Regarding the orange juice, Biot’s theory of poroelasticity was a candidate to describe the ultrasonic properties of partially frozen orange juice. I have noticed by reading the papers about food technology that those authors were using empirical equations (polynomials) to related juice saturation and P-wave velocity. Biot’s theory was successful in this case and predicted the experimental attenuation curves very well.

Another observation is that you consider viscoelastic media in many of the problems you tackle, which is closer to reality rather than the assumptions of elastic media made in much of the seismic data analysis we carry out today. I believe the simplicity of the analysis is what is responsible for the latter. What do you think needs to be done to be able to carry out our geophysical analysis viscoelastically, rather than continue with simplistic assumptions?

Anelasticity became more important during the last 10 to 20 years when we have realized that we can obtain information from the seismic quality factor. One of the dominant loss mechanisms in porous media (hydrocarbon rocks in our research) is the so-called mesoscopic attenuation mechanism by which energy is lost by conversion from the fast P wave to the slow diffusive wave (the second Biot P wave). When Biot developed the theory of wave propagation in porous media in the 50’s he discovered the slow P wave and predicted a loss mechanism with a peak at the kHz range. During more than 40 years Biot theory was not considered until J. E. White discovered the mesoscopic mechanism, different from the Biot one. The point is to apply Biot theory to heterogeneous media and a relaxation peak appears at the seismic band for realistic situations (patchy saturation, thin and partially saturated layers, fractures filled with fluid, etc.). Other researchers improved the theory, namely, Dutta, Johnson, Gurevich, Batzle, Pride, etc. The point is that the expression of the Q factor can be related to saturation, fluid type, porosity and permeability. We are presently working on this subject, analytically and computationally. Basically, you take the seismic data, perform velocity and attenuation tomography and apply the rock-physics theory to obtain those important properties. Previously, in the 70’s, attenuation was related to the presence of fluids phenomenologically, i.e., high attenuation meant high porosity and partial (gas) saturation. This was one of the direct indicators. Moreover, full-wave inversion requires a viscoelastic description, otherwise the amplitudes and phases of the signal are not correctly modeled. You may have a simple modeling, acoustic (no S waves) or elastic (no loss) but are you sure that it reflects reality?. Comparisons between elastic and viscoelastic show that this is not the case. Another issue is anisotropy.

An interesting paper you published in ‘Geophysics’ a few years ago discussed the AVO modeled response in a source rock layer, by considering orthorhombic anisotropy in this zone, while I notice much of the geophysical modeled response work being done considers either the VTI media assumptions, or the HTI media assumptions. Is there a way to collaborate with the industry and speed up the implementation of such analysis, considering unconventional resource exploitation is a hot commodity these days?

That was a paper published in 2001, “AVO effects of a hydrocarbon source-rock layer”, and described the AVO properties of a TI sourcerock layer with vertical fractures (an orthorhombic medium) including dissipation. That was a paper ahead of the times, since few people were working on this subject in the 90’s. I guess that the point is that the forward problem is easier to deal with than the inverse problem and you have to tackle first the inversion problem for simple cases such as isotropy and transverse isotropy. At present, we have a proposal to characterize the seismic response of unconventional resources and estimate, for instance, kerogen content through traveltime and Q tomography, and in addition, map the microfracture cloud due to hydraulic fracturing. The European Union is not funding this type of research so we are trying to offer it to the industry.

Most of your work on wave theory and numerical modeling is drenched heavily in mathematics, which I understand is the tool to carry it out. This is also something that steers many people away from embracing such analysis. Do you think there is a strong need to explain difficult concepts in simple ways, rather than always talk the ‘mathematical’ way, so that more people are drawn to these kinds of analysis?

Mathematics is certainly essential in geophysics. Richard Feynman said: “to those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.” But he also stated that “The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. Pure mathematics is just an abstraction from the real world, … but this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.”

Geophysicists come from many disciplines; mathematicians are one important component, but there is a limit to the mathematical language in applied research. As you said, difficult concepts can be explained in simple ways, think of Feynman’s book. There are certain books in our field that I could not use, because of the heavy mathematical jargon.

One of the problems that you have considered in your work is fine-layering in the subsurface and the attenuation anisotropy associated with it. From a practical standpoint, do you think we are at all bringing such effects into our analysis? Our knowledge on determination of Q from seismic data while possible theoretically, if riddled with uncertainty, and that is possibly one of the reasons, Q-compensation is not done as a routine in our industry. Could you give us your take on this?

I wrote a paper on Q anisotropy in 1992, that was one of the first or the first in the geophysical literature. It is based on Backus averaging and viscoelasticity. The model is semi-phenomenological, that is, predictive to a certain degree. Now, we have reached the point that we have a model for Q anisotropy based on poroelasticity which includes fine porous layers and even fractures. This model is fully based on physical grounds and basically it incorporate the mesoscopic loss mechanism which I mentioned before. So, we know very well the theory of Q anisotropy. The problem is the quality of the seismic data, because it is not the same to invert for velocity than quality factor for which the presence of noise and uncertainties of measurements may yield unreliable results. Doing Q compensation is fine since one can generate more refined images of the subsurface but it is also important is the use Q to obtain petrophysical information as I said before. The first is already in practice and some service companies are offering the technique, while the second aspect is a challenge yet.