Citation, Dr. James G. Berryman, M.A. Biot Medal, 2005

 

Dr. Berryman acquired his B.A. in Mathematics and B.S. in Physics from the University of Kansas, Lawrence, and an M.S. and a Ph.D. in Physics from the University of Wisconsin, Madison. He is currently a Physicist at the Earth Sciences Division of the Lawrence Livermore National Laboratory, where he has worked for more than 20 years. He is also a Consulting Professor of the Geophysics and Mathematics Department at Stanford University. He served as associate editor for the Journal of Mathematical Physics, and Inverse Problems in Engineering. He also owns four patents, two of them, “Using electrical impedance tomography to map subsurface hydraulic conductivity” and “Discrimination of porosity and fluid saturation using seismic velocity analysis”, are related to poromechanics.

 

Dr. Berryman has published more than 150 referred journal articles in areas of acoustics and mechanics of inhomogeneous and porous media, flow and transport in porous media, inverse problems in acoustics, seismology, and electromagnetics. A number of these papers are highly cited and have led to the development of several important subfields of poromechanics. A few samples are given below:

 

 

            These and other highly cited papers clearly demonstrate his deep influence to the poromechanics and related fields.

 

More specifically, Dr. Berryman’s contributions can be stated as follows:

 

o       His 1980 paper “Confirmation of Biot’s theory” was the first to show that T. J. Plona’s ultrasonic experimental data demonstrating the existence of a second compressional wave was actually consistent with Biot’s theory of wave propagation in poroelastic media. The same paper also showed how the slow wave speed was related to Biot’s structure factor (later called tortuosity). It was also the first paper to give a simple estimate of tortuosity in terms of effective mass concept.

o       He showed that a slow extensional mode is expected in a fluid saturated cylinder having an open surface: “Dispersion of extensional waves in fluid-saturated porous cylinders at ultrasonic frequencies,” J. Acoust. Soc. Am., 74: 1805-1812, 1993.

o       He gave the first analytical results concerning wave scattering from a spherical inclusion of a poroelastic material embedded in another homogeneous poroelastic medium: “Scattering by a spherical inhomogeneity in a fluid-saturated porous medium,” J. Math. Phys., 26: 1408-1419, 1985. This work became the basis for the development of effective medium theories in the context of poroelasticity: “Effective medium approximation for elastic-constants of porous solids with microscopic heterogeneity,” J. Appl. Phys., 59(4): 1136-1140, 1986; and “Single-scattering approximations for coefficients in Biot equations of poroelasticity,” J. Acoust. Soc. Am., 91(2): 551-571, 1992.

 

In the following, we quote from the supporting letters to demonstrate the influence of Dr. Berryman’s work in the field of poromechanics:

 

“For 23 years after the publication in 1956 by Biot of his prediction of a fast and a slow compressional wave (as well as a shear wave) in porous media, no one had ever observed the propagatory slow wave, thus putting into doubt the validity of the theory.  It was, then, significant that Plona reported his observation in fused glass bead samples of such a candidate slow wave in 1979. Within a year, Jim published an article in which he guesstimated the numerical values of the input parameters and thereby computed the expected speeds of propagation of the fast, slow, and shear waves in Plona’s samples.  Inasmuch as the computed values and the measured values were substantially the same, this article of Jim’s provided significant theoretical confirmation that, indeed, the long sought propagatory Biot slow wave had finally been observed. 

 

… His publications on acoustics of partially saturated systems, layered porous media, heterogeneous porous media, and double porosity systems have contributed to a much deeper understanding of the properties of complex systems, such as those occurring naturally in the subsurface of the earth.

 

So to say, the Biot theory cuts in half the problem of understanding the acoustic properties of porous media.  The other half is to understand the physics of the input parameters themselves, based on the underlying microstructure of the porous medium. Here, Jim has advanced the understanding of the tortuosity, which governs the speed of the slow wave, the permeability, which governs attenuation, and the elastic moduli of the dry frame, which set the overall scale of the velocities of sound.  These different parameters of the Biot theory depend upon different features of the microstructure and Jim has been a leader in identifying what depends upon what.

 

… two papers of his on the subject of random composites. … they are the two most important papers ever written on the subject of effective medium theories of elastic constants in composites.  … The Berryman theory allows one to see simply the effect of changing the shape of the inclusions.  It also clarifies that there is a big difference in the theory depending upon whether the host material is a solid or a fluid. Thus, with a relatively simple theory, Jim has brought unity to a variety of different results, most of which had been derived in different and very complicated theories.”

 

“… Jim has found sources for his work in the same general area that motivated Biot: geomechanics and rock physics. I have followed his work since the late 1970's, when he began publishing important papers—such as the Appl. Phys. Lett. article confirming Biot's theory in 1980. … This paper followed a series that Jim had published on properties of composite media, including the effect of scattering from inclusions. His work at that time, 1979-1985, focused on the foundations of describing disordered materials, particularly rocks and the earth. His wide interests—including layered solids (transverse isotropic models of the earth were novel in those days!)—from quasistatics to dynamical models that incorporated multiple scattering effects, made a strong impression on me at the time. One could study fundamental problems with interesting science and mathematics that had practical implications!

 

… He has worked on some of the hardest but most important problems: flow of single and multiphase fluids in porous solids, basic descriptions of poroelasticity with partial saturation, effective medium theories with single and multiple inclusions. His work in the past decade has been nothing less than phenomenal. His careful studies of the basis of the Gassmann relations, in linear and nonlinear, saturated and partially saturated, situations, have set the standard for poroelastic theories.”

 

“Jim has made seminal contributions to poroelasticity and in the application of Biot's equations. Notably, among many of these contributions, he extended effective medium theory approximations to poroelastic media, he derived formulae for the effective poroelastic constants of layered media, and he extended Gassmann's equations to composite porous media with two constituents. With over 150 refereed publications, many of them in the area of poromechanics there can be few scientists in his league.

 

… His research and his active collaboration with a wide spectrum of scientists, including engineers, geophysicists, physicists, and mathematicians places him squarely at the interface between disciplines. Particularly impressive is the breadth of his interests.  These include, but are not limited to, problems in tomography and other inverse problems, the Biot equations for elastic wave propagation in porous media, packings of hard spheres and disks, effective medium approximations for the elastic moduli of composites, digital image analysis, correlation functions characterizing the microgeometry of composites, problems concerning fluid flow through porous media, and the viscoelastic properties of composite materials.

 

In many of these areas Jim's work was pioneering.  For example, the use of digital image analysis to measure three point correlation functions was a much needed tool he developed. He also introduced an elegant analytic transformation (now called the Y-transformation) which simplified many of the important formulae of composites, such as those of the Hashin-Shtrikman and Beran bounds and the effective medium approximation. His work is oriented towards applications and frequently he uses experimental data in the analysis of his work.”

 

“… Jim has published approximately 150 journal articles in the applied math, computational physics, materials science, mechanical engineering, acoustics, and geophysics literature. … His writings on the mechanical behavior of composite materials have furthered and synthesized knowledge of the subject. He has eloquently shown the unity of different methodologies such as effective medium, differential effective medium, poroelasticity, scattering theory, and rigorous bounds. He is totally conversant with all of the methods, theories, experimental data, and analytical techniques of the mechanics of porous media so that he can connect them together with great insight. … he has contributed significantly to the development of solving nonlinear inverse problems in seismology and electromagnetics, particularly for applications to underground imaging of fluids in porous and fractured rock.

 

Jim is widely cited as well as prolific. For example, he is a coauthor on a 1999 paper on a nonlinear inversion method for 3D electromagnetic imaging that has had over 600 downloads of the electronic version of the paper from the journal’s website. His classic 1980 papers in Applied Physics Letters on confirmation of Biot’s theory and in the Journal of the Acoustical Society of America on an effective medium theory and his 1985-1986 papers in the Journal of Applied Physics on spatial correlation functions have all been cited over 100 times, according to the Scientific Citation Index. His 1995 book chapter on mixture theories for rock properties in an American Geophysical Union reference book is also a frequently-cited classic. In addition to publishing research papers, Jim is the author of several patents related to data analysis for underground imaging with electromagnetic and seismic methods.

 

… Jim’s contributions to poroelasticity and geophysical research go beyond authoring technical publications. He has a strong commitment to building the next generation of researchers and maintaining connections between this national laboratory and the external research community. He has brought many post docs and students to LLNL and has maintained numerous university collaborations, and has mentored many scientists and engineers. His list of publications demonstrates his strong commitment to mentoring young coauthors who, in turn, become leaders in their research areas as they benefit from his outstanding mentoring.”

 

“Dr. J.G. Berryman made absolutely outstanding contributions in applications of the poromechanics to a series of very important geophysical problems. This includes his works on double porosity media, on differential effective media, on attenuation of seismic waves, on anisotropy of seismic waves, on the nature of the Gassmann equations (static limit of the poroelasticity), on upscaling of permeability, on effective stress for different poroelastic parameters, on partially saturated rocks and on many many other important subjects of Geophysics of porous saturated structures. …His results on acoustics of porous fluid saturated materials are of crucial importance for modern developments of geophysical exploration of hydrocarbon reservoirs. They are, indeed, also of fundamental significance for earthquake seismology and theory of seismic wave propagation in real rocks.”

 

 “…to give specificity to Dr. Berryman’s contributions, I will use Dr. Berryman’s 1992 J. Acoust. Soc. Am. paper in which he obtains effective elastic constants of a material containing spherical inclusions of one Biot material imbedded in another. This paper contains the elements of the classic “Berryman” style, which is to 1) establish the problem, 2) obtain the required results in approximately three different ways, 3) demonstrate the results are consistent and reduce correctly for limiting cases, and 4) compare the results numerically for representative rocks. This last step closes the loop on the first step. In the case of the 1992 paper and many of Berryman’s papers, the motivation is to discover ways to approximate the phenomenological Biot coefficients in terms of the constituent properties of a rock and its included fluids. The problem is a general one in the mechanics of composites. In his classic 1992 paper Berryman established three methods for attacking the problem: the average T-matrix approximation (ATA), the coherent potential approximation (CPA), and the differential effective medium (DEM). After obtaining the desired expressions for effective bulk and shear modulus, Berryman shows that all three reduce to the exact formula of Hill when there is no contrast between inclusion and the matrix.” 

 

 “He has made outstanding and original contributions to the general areas of: (1) effective medium theories for the elastic moduli of porous media, including the extension of Eshelby theory to porous materials; (2) physics of wave propagation in saturated and unsaturated porous materials, including analysis of waves down porous rods; (3) creation of double porosity models for the acoustic of porous materials; (4) the statistics and mechanics of unconsolidated granular materials; (5) estimating rock properties from image analysis; and (6) clarification of the notion of effective stress as well as effective-stress models for all porous material properties. His multitude of groundbreaking papers on these and other topics have contributed directly (and enormously) to my own understanding and viewpoints on the subject area of porous media mechanics.”

 

2005