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Phil Holbrook Ph.D.
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Scientist Force Balanced Petrophysics

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Textbooks

Books

These two books are a significant advance in physical science that now includes the mechanics
inside of our earth.

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Order Your Copy Today!

Deterministic Earth
Mechanical Science

$60.00
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Pore Pressure through Earth Mechanical Systems
$70.00
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Educational discounts can be obtained from education
friendly Phil by
e-mail.

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You can get any number of copies at the retail price from Amazon.com

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the unique ISBN's found below.

Deterministic Earth
Mechanical Science
ISBN: 0-9708083-3X

Pore Pressure through Earth Mechanical Systems
ISBN: 0-9708083-2-1

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News of the scientific and practical consequences of
Deterministic Earth Mechanical Science

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"Deterministic Earth Mechanical Science" is a milestone in the history of science. Earth Mechanical Science is a deterministic field theory that is entirely composed of physical laws. They are mathematically inter-related by a few earth material properties coefficients. The earth's surface is the outer boundary condition. The first two essays explain the consequences of this scientific advancement.

Energy Minimization, Gravity, Electrostatics, and Earth Mechanics.
by Phil Holbrook Ph.D.

The laws of mechanics, chemistry and deterministic earth mechanics have much in common. They describe the relationships of particles with finite mass at minimum energy. These are a subset of universal laws which apparently operate simultaneously on and within planet earth.

The lower atomic numbered elements tend to form into minimum energy molecules. Almost all of the earth is composed of natural solid and liquid molecules. Energy is continuous within and across the solid-liquid phase boundaries.

[Mass-energy] is apparently conserved within the earth and universe. Energy minimization on and in the earth primarily involves the weaker forces of gravity and electrostatics its actions. These depend upon two inverse square force-at-a-distance laws of the same physical-mathematical form. Newton’s Gravitational law and Coulomb’s electrostatic law are;

Earth Gravitational Attractive Force = G (Mass 1 * Mass 2 ) / distance <2>

Electron Cloud Electrostatic Repulsive Force = k ( Charge1 * Charge2 )/ distance <2>

Gravitational forces extend to the edge of the visible universe. Molecular electrostatic forces are 1038 times stronger than gravity. But electrostatic forces don’t reach beyond the next nearest electron cloud. Without the repulsive force of neighboring electron clouds the earth would be the size of a walnut with the density of a black hole.

Both of the above laws are physically symmetrical about their distance <2> terms. The acceleration due to gravity is a physically symmetrical time <2> term.

There is a direct connecting bridge across the fantastic numbers of the universe and earth. Mass and energy are related by mathematically equivalent [stress/strain] tie lines in the earth. Simple equations represent the static elastic and plastic [stress/strain] limits of molecular matter. The bulk modulus and compressibility of natural minerals and fluids may be found in the Handbook of Physics and Chemistry. The elastic constants and their energy conserved PV/T variances are measurable bulk material properties.

The equation matrix below expresses [mass-energy] conservation at minimum energy conditions. Each line of this matrix is a physical or conservation law that applies in Normal Fault Regime tectonic settings in the earth.

Unified Matrix

Energy terms and equations are background color coded tan. Mass terms and equations are background color coded light blue. Bold blue are composite mineral physical constants, and red is a composite bulk fluid property.   RETURN TO TOP

Crust General Governing Physics

This is how Gravity (Sv) and Electron Cloud repulsive forces (Save) interact in the earth's sedimentary crust. Both forces use the same solid-fluid partitioning coefficient (1.0 – f) in the earth . The first three lines of the explanatory matrices are the same, applying to all tectonic regimes.

The solid fraction of a rock bears the effective stress load. Gravity Sv is an integral component of the total load. If effective stress energy is minimized, Sv could be the maximum, intermediate, or minimum principal stress. Physical minimization in the earth crustal case requires that the ratio of the effective stresses be of integer proportions that are symmetrical about the positive integer <2>. Newton's and Coulomb's laws are also physically symmetrical about the positive integer <2>.

Gravitational and electrostatic forces cross the [energy-mass] (=) diagonal of this matrix. This equation matrix formulation is a closed mathematical form as are Newton’s Force = mass acceleration and Einstein’s limit energy = mass c<2>. There are more parameters in the earth’s matrix representation, because the earth’s interior is different from the vacuum of space. All three expressions are physically and mathematically symmetrical. Each line equates and balances mass with energy.

The three different tectonic regime minima
The fourth equation in the matrix is the minimum energy effective stress ratio in Normal Fault Regime Basins. There are two companion equation matrices for strike-slip, and thrust fault tectonic regimes. Only the Normal Fault Regime will be discussed here. Fault regimes are discussed at length in Chapter 13 of “Deterministic Earth Mechanical Science”.
Each tectonic regime specific matrix has the same first three lines mentioned in Crust General Governing Physics. These three matrices are the simplest and most general force balance in the earth.  
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Energy in Subsurface Mechanics
The remaining four equations of each matrix are rearrangements of terms that yield the energies pore fluid pressure and fracture propagation pressure. Fracture propagation pressure describes the action of fluid pressure release valves that are perpendicular to the minimum principal stress. All the mechanical terms in each [energy-mass] matrix interact deterministically to explain the fundamentals of earth mechanics.
There are circumstances such as [
stress/strain] hysteresis and two phase fluids that occasionally come into play. These are second order effects which can be resolved using the appropriate second order physics. Energy is locally conserved and minimized through accepted physics on these levels as well.   RETURN TO TOP

The similarity of atoms, planets and stars
The Earth and other planets in the Solar System have spherical shapes. The Earth, Sun and Jupiter have an intermediate convective layer. The stronger nuclear binding forces are not directly involved in earth mechanics. Nuclear fusion generates the Sun’s light and heat. Fortunately for us we are near the Sun. Also fortunate is that the heat from the earth’s molten core comes principally from nuclear fission not fusion. The earth's natural radioactivity generates heat but doesn’t propagate nuclear chain reactions.

The mantle is mechanically de-coupled from the liquid metal core. Hence we have had frequent magnetic polar reversals. Core to mantle mechanical stick-slip probably accounts for the magnetic polarity reversals.

The mantle is coupled to the overlying sedimentary basins over broad areas as evidenced by the prevalence of minimum energy stress ratios that are observed. The shapes of all of the objects below are basically spherical with physically explainable deviations.   RETURN TO TOP

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The transfer of mechanical forces (including acoustic waves) within the earth is through molecular electron clouds. There is two phase mechanics in the earth’s sediments and sedimentary crust. That is portrayed on the right of the collage above. The surface of a SiAlic clay mineral perpendicular to the c-axis is a layer of positively charged oxygen anions. Positive charge falls off as distance <2> from the oxygen anionic surface. Water dipoles are aligned for a short distance by this charged plate. Net neutrally charged mineral surfaces neither attract nor repel water dipoles.

The plastic drag forces from the convective mantle move the continental and oceanic plates around as illustrated by the earth cutaway model in the collage. Newton’s, Hooke’s and Coulomb’s laws apply simultaneously in the earth. Their images are superimposed over the earth’s continental plates. The earth’s crust is semi-brittle on a geologic time scale. Continental crust is SiAlic and floats high on the turbulent mantle. Basaltic crust is denser. It underlies the earth’s oceans that are color coded blue.

Single element nuclear centered electron clouds tend to be spherical. Niels Bohr and DeBroglie explained the paths of individual electrons in any single atom. Both won Nobel prizes. Continuous standing particle-waves are the minimum energy electron configurations in an atom. The bright line or dark line spectra of each element are symmetrical characteristics of each atom. The electrons choose minimum energy paths as do the spherical planets in the solar system and universe.

The light from each star reveals the chemistry of its intermediate convective layer. The red shift of the bright line spectrum from a star reveals how fast that star or galaxy is receding from earth. It appears as if the visible universe began with a singularity that we call the Big Bang. The composition of matter evolved over time to form the 92 natural elements that we know of today on earth. Elemental bright and dark line spectra on earth provide scientists with elaborate natural compositional and timing devices.   RETURN TO TOP

In the short period since Isaac Newton, humans have assembled a huge body of mathematically deterministic inter-relationships. Newton’s scientific and philosophical explanations have been extended by fifteen to twenty generations of subsequent scientists. The mathematical forms of Newton’s and ensuing laws have been verified by many scientists through empirical observations. Scientists following Galileo have looked into Nature to determine the truth of a scientific argument.

I am happy and proud to make my contribution to this body of knowledge. That contribution is that the earth obeys the same physical and chemical laws as the rest of the universe. “Deterministic Earth Mechanical Science” and “Pore Pressure through Earth Mechanical Systems” are the two books that were written to demonstrate and explain earth mechanics.

The books contain abundant data and sufficient technical explanations. This explanation has the fewest possible equations. It also uses the fewest possible linking coefficients. All of the linking coefficients are measurable material properties. It simultaneously explains a host of subsurface mechanical questions.

I give hundreds of earth scientists’ credit for assembling a descriptive body of knowledge about planet earth. I am most grateful to my doctoral advisor E.G. Williams who taught me much of science and philosophy. These two terms had the same meaning in Newton’s lifetime. They still coincide at the highest levels of science.

Significant scientific progress will likely be made by those who let Nature be their guide. The Foundation of the Physical Sciences is being written to be popular reading for scientifically curious people of all ages.   RETURN TO TOP

Books

Earth Physical Limits; Minimum Energy pathways shown on selected

Two dimensional Mechanical Planes.

by Phil Holbrook Ph.D.

Minimum Energy is the selection criterion for physical and chemical laws. For instance the shortest distance between two points is a straight line i.e. a minimum energy pathway . The equivalent pathways inside the earth are hidden, but they meet the same minimum energy criteria.

Energy minimization within the earth reduces the multi-dimensional problem to that which can be described on two dimensional planes. These are analogous to the nodes of an n dimensional standing wave. Minimum energy increases away from these nodes, but the average is smooth and continuous. [Mass-energy] is generally conserved. Energy minimization on the most important two dimensional planes inside the earth will be discussed.

The pathway in space is through a vacuum. The pathway in the earth is through the earth’s matter. The fundamental unit of energy communication in the earth is the molecule. Liquid phase molecules at earthly temperatures will be color coded bold red. Solid phase molecules will be color coded bold blue.

Natural minerals are the predominant minimum energy phases of solid matter in the earth. Fluids have no shear strength. Everything below sea level or the water table is a two phase (mineral-fluid) mechanical system. The two phases are in intimate contact with each other through their contiguous molecular electron clouds.

The earth is approximately spherical with all molecules being attracted toward its center of mass. This is also the earth’s geometric center. Vertical is the direction toward the earth’s center. The two orthogonal horizontal axes are oriented by the near surface [energy-mass] field. The dominant factor affecting horizontal effective stress orientation is the local tectonic regime.

Continental plates shear past one another or are thrust toward one another. These relationships are discussed in Chapter 11 of Deterministic Earth Mechanical Science.

The [stress/strain] response of solid molecular electron clouds is symmetrical. The fluids provide a neutral scalar supporting role in proportion to their composite fluid bulk modulus. The scalar fluid and solid bulk moduli are equally represented in proportion to their abundance throughout the earth. We need to first group the molecules according to phase. The earth’s mechanical energy can be represented by different two dimensional planes.

One of the mechanical planes will contain both the maximum and minimum principal stresses. Both the fluid and solid molecules have scalar mass and energy terms. These scalars are contributing factors to the [stress/strain] slope. That mechanical energy slope will be greatest on that two dimensional plane.

The difference of any measured effective stress from the deterministic energy minimum is a measure of the effective stress energy that is accumulated in the molecular electron clouds. If there is no difference, there is no tendency toward movement within any mechanical system.

The first and most fundamental in situ [stress/strain] relationships of the most abundant natural minerals are shown below. This two dimensional plane shows mineral specific compactional equilibria.   RETURN TO TOP

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This two dimensional plane is a mechanical view of the plastic [stress/strain] relationships inside the earth. The scalar effective stress energy is on the ordinate or “y” axis. Solid mass (solidity) is the scalar on the abscissa or “x” axis. [Mass-energy] is conserved on this plane. Any combination of mathematical operations that comprise a [stress/strain] relationship will be a straight line on this two dimensional plane.

Over 90% of the earth’s SiAlic crustal matter is contained in the five mineral types shown. Quartz, SiAlic claystones, calcite, anhydrite and halite are in a decreasing order of compaction resistance. The crossover between Quartz and SiAlic claystones is due to an additional compaction resistance between individual clay particles. This is a particle size phenomenon that is peculiar to clay minerals. The plastic compactional [stress/strain] response of water wet clay minerals is green on this plane.

The [stress/strain] relationships of the non-clay minerals are sub-parallel. They are offset in rough proportion to their scratch or indentation hardness. The offsets reflect differences in the mineral’s internal scalar average electrostatic bond strengths. Quartz is the hardest and halite is the softest of the abundant natural minerals. The mineral Quartz has about ten times the compaction resistance of Calcite.

A great deal of empirical data was assembled and analyzed to arrive at these straight lines. Extreme edge effects have been removed. The fit was better than five percent (5%) over the entire range of porosities that are represented in natural sediments and sedimentary rocks. The porosity data ranges from several feet below an undisturbed mud line to total solidity.

All of the major non clay minerals occur as supporting grains or intergranular cements. The effects of post compaction chemical cementation were removed by fitting to the highest porosities at any given effective stress.

The empirical straight lines have additionally been tested against observed pore pressures in over 300 wells worldwide. The straight line curves shown are natural [stress/strain] loading limb pathways on this two dimensional plane. Effective stress (energy) and solid (mass) conserved strain are balanced scalars on this plane. Hence the figure title is “First Fundamental in situ [stress/strain] relationship”.

The straight lines shown represent plastic loading limb data. Effective stress unloading involves a different [stress/strain] pathway. Elasticity is a limit for effective stress unloading and reloading. Hooke’s law as expanded by Cauchy is a relationship between bulk modulus and shear modulus summarized on the next two dimensional plane. This plane describes the natural elastic coefficients for sedimentary rocks with randomly oriented natural flaws.   RETURN TO TOP

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Both bulk and shear moduli include a density i.e. (mass term) as a devisor. These elastic moduli have mathematically related energy terms. The positive offset of all the straight lines is the bulk modulus of the pore fluid. It is NaCl brine in this case.

This represents a macroscopically static mechanical system. Any combination of fluids and gasses in the pore space of a granular solid would have a composite fluid bulk modulus property. This would be lower limit of an elastic [stress/strain] lever.

The upper limit of the lever would be the weighted average of the solid elastic moduli. The entire ranges of porosities from zero to 100% lie on a straight line lever with these mineral and fluid end points. Any preferred orientation of flaws would affect these relationships.

There is a smooth scale change along the straight line on this two dimensional plane. This owes to the transition from a matrix supported granular solid to a suspended solid slurry. The [stress/strain] of slurries are explained by the Woods equation which is a degenerate form of Hooke’s law. The assemblage of these equations on this two dimensional plane is attributed to Michel Kreif. Many authors have measured the elastic moduli of clay minerals. The results indicate a high level of uniformity.

This two dimensional plane is physically symmetrical i.e.<2>. Vp2 is proportional to Vp2 for body waves on this two dimensional plane. These acoustic waves can be remotely generated and recorded either from the surface or from the inside of a borehole in the earth.

The plastic and elastic limiting [stress/strain] relationships are shown together on the following two dimensional plane. Effective stress (energy) is on the ordinate and solid mass conserved strain is on the abscissa. This follows the thread of governing physics through the earth.   RETURN TO TOP

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Realistic units are shown on this plane. The [mass-energy] and [stress/strain] values are equivalent if you insert the color coded mineral coefficients. The slope of the plastic compactional relationship alpha(a) is that of the average mineralogy present. The intercept sigmamax is that of the average mineralogy as well.

If compaction does not reach its sigmamax limit, there will be an intermediate peak loading limb point. Any subsequent unloading or reloading will be between the two straight line limits that are shown. There may be time dependant hysteresis loops about the straight line. At sigmamax and beyond, the solid material behaves as a plastic and yields to all stresses equally with no change in porosity. The change in volume beyond sigmamax stress is entirely in the spacing of molecular electron clouds.

Failure of materials on a two dimensional plane was introduced by the German engineer Otto Mohr in 1874. Energy minimization inside the earth allows for three dimensions to be shown on this Mohr two dimensional plane without loss of information.    RETURN TO TOP

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Mohr cleverly portrayed stress as circles with the average stress (scalar) at the center. In Normal Fault Regimes the maximum principal stress is gravity. The blue circle shows the maximum and minimum vectorial stress on the circle’s circumference. The scalar average stress is the center point.

Shear stress (t) is on the ordinate. Average confining stress, as well as the maximum and minimum vectorial stresses are on the abscissa. The color code purple is assigned to gravity. A tangent to a Mohr circle is a rock or sediment's failure condition. It is the coefficient of internal friction for a porous granular solid. Sedimentary grains resist both compaction and shear with all that they have i.e. their contiguous molecular electron clouds.

Each of the three Mohr circles shown is physically symmetrical, i.e. <2> . Their circumferences are even number multiples of their mean stress. Gravity is the maximum principal stress in Normal Fault regimes. Gravity is the intermediate principal stress in Strike-slip Fault regimes. Gravity is the minimum principal stress in Thrust Fault regimes. This closed and minimized mathematical system has actually reduced the earth’s multi dimensional mechanical systems onto a two dimensional plane.

The coefficient of internal friction (t) is a different measure of average mineral's electrostatic bond strength. This describes the behavior of composite macroscopic bodies based upon the average mineral electrostatic bond strengths.

The energy transfer between continental plates or fault blocks is through the same contiguous electron clouds. There are transition zones in the earth between normal, strike-slip, and thrust fault tectonic regimes. These zones could be up to several hundred miles wide, but the crust is not that deep. The earth’s surface area is huge by comparison.

The more general case is that the molecules of the earth will move toward one of the three deterministic minima. The answers to minimum energy questions outside local transition zones are to be found on the appropriate two dimensional plane.

The preceding discussion was broad but not comprehensive. These two dimensional planes illustrate the interactions of the governing laws of physics in the earth’s sedimentary crust. If history repeats as Niels Bohr predicted, there are many more answers to be found under this same physically deterministic bridge!
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On “The Foundation of the Physical Sciences”
by Phil and Marie Holbrook

Forward
Physical laws are continuous mathematical functions that describe the relationships between discrete entities. These can be as-large-as galaxies to sub-atomic particles in size. There are forces between all sizes of particles that govern their spacing, speed and motions. These apply at different distance scales. The governing laws describe mathematically how the forces interact.

Isaac Newton gave the laws for macro-particles in 1687. Niels Bohr explained Quantum Mechanics in 1925. Richard Feynman understood Newtonian mechanics, Quantum Electrodynamics and was working on sub-atomic particles at the time of his death.

Isaac Newton, Niels Bohr and Richard Feynman had deep understandings of physical law. It is revealed to us in their science and through their writings. “The Character of Physical Law ” is a milestone summary of our accumulated knowledge of physics given by Richard Feynman in 1965.

Newtonian mechanics is the core of the deterministic sciences. Newton’s laws are an interdependent set of postulates that apply to macroscopically distinct objects. [Mass-energy] conservation embraces physics, inorganic chemistry and earth mechanics. The laws of these sciences are symmetrical. They all describe natural minimum energy seeking systems. The most stable forms of motion and matter are minimum energy configurations.

A common pattern with respect to physical laws is evident. That pattern includes a simplest method for expressing physical and inorganic chemical laws given the tools of mathematics. One could learn this common pattern concurrently with the scientific facts as they are being taught.

The Foundation of the Physical Sciences” is an exposition of the physical facts related to a common straightforward pattern. This book uses our most important physical laws as examples to demonstrate the foundational pattern. They are arranged in a logical order where one law leads to the next. Newtonian mechanics is followed by Quantum mechanics which explains how we know what we do about the “Big Bang”.

The book follows a logical progression that leads to the most current physical answers. This accumulation of deterministic equations has occurred over three centuries. Einstein’s theory of relativity is the physical limit of Newtonian mechanics.

The motions of our Solar System was causally explained by Isaac Newton. The details of planetary and satellite orbits have first order gravitational explanations. The rings of Saturn are a smaller scale example of our disc shaped Solar System. Gravitational pulls over billions of years have shaped both Saturn's rings and the Solar system.

The Periodic Table is a masterpiece of atomic matter organization. The properties and reactivity of each atom can be predicted from its position on the table. Chemical equations balance perfectly about an equal (=) sign. The number of elements on each side of a chemical reaction equation are exactly equal (=) discrete integers. This is mathematically perfect electrical charge <symmetry>.

Only 14 elements compose over 96% of the earth’s SiAlic crust. Five simple molecules make up the bulk of this total. These molecules are late stage matter that has evolved in stars since the “Big Bang”. We can know all of this by combining our knowledge of the quantum spectra of starlight with chemical and spectral analyses measured now on planet earth.

The hierarchal order of physical laws is approximately the order in which we perceive them from birth. Infants can recognize symmetry and sequential order. The governing physics can be consciously taught in parallel with our natural order of perception. Every person can become consciously aware of the foundation of the physical sciences in elementary school. The foundational pattern unifies many observation and may be as important as the physical and chemical laws themselves.

This book will highlight our most famous physical and chemical laws. The intellectual and personal lives of the discovering scientists are interesting in themselves. Original scientists have an unusual common characteristic. They are passionate in their search for the truth. We hope that all readers will enjoy looking into the heart of Natural Science and the original scientists that looked into it.    RETURN TO TOP

 

About the Books Cover

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All that we see is the interaction of light with the matter of the Universe. The Earth is the third planet from the Sun in the Milky Way Galaxy. At night the sky is black and by day it is blue with occasional white clouds. The Sun radiates photons of light as do the rest of the Stars in the Universe. The peak frequency of the Sun is yellow but it radiates all colors. The planets and moons reflect the Sun’s light.

Blue skies originate from Nitrogen atoms which are about 80% of the Earth’s atmosphere. Nitrogen absorbs photons of blue light and re-radiates them in all directions. Atmospheric water coalesces into colorless spheres and crystals in the atmosphere forming white clouds.

These water particles are colorless and refract light of all colors. Rainbows result from the direct incidence of sunlight by colorless spherical water droplets.

We can only see short distances through clouds, rain or snow because solid particles scatter whatever light is present. Interestingly, grass is green because it absorbs all other colors. Bricks are red for the same reason.

The movement of all celestial objects is governed by Newton’s Law of Gravity. Stresses and fluid pressures within the earth involve electrostatic interactions with gravity. The electron clouds of the molecules that compose the earth repel each other. Coulomb’s Law of electrostatics has the same physically symmetrical <2> formulation as the Law of Gravity. Physical symmetry, [mass-energy] conservation, and mathematical equality (=) are the foundations of the physical sciences that are shown in the center of the books cover.

We actually see photons which are particle-waves that have no mass. They can travel up to the speed of light which is the limit of the universe that is visible from planet earth. There is strong indirect evidence of dark matter and dark energy within the visible universe.

Spheres are the highest symmetrical forms in the Universe. We see macro-spheres in the dark night sky. Stars, planets, moons, and atoms have a basic spherical symmetry that is modified slightly their internal forces. Convection causes bubbling Sun spots, the drift of continents on earth, and the swirling Giant Red Spot of Jupiter.

The rings of Saturn and Uranus have planar symmetry about these planets due to local variations in the force of gravity over billions of years. The planar disc shape of our Solar System results from many pulls of gravity from the larger solar system objects over time.

Physics explains what we perceive and see. The radial tie lines in the Venn diagram represent direct physical-mathematical connections. There are abundant reason for understanding "Foundation of the Physical Sciences". The foundation is mechanically simple and yet profound.

The physical sciences are mathematical combinations of A) continuous mathematical functions; B) real number constants; and C) integers. Mathematical operations are symmetrical about the (=) sign. The physical meanings of the A B C’s and mathematical (=) symmetry can be fully taught in elementary school. This book presents the foundation of the physical sciences that also apply at the highest levels of education.

For more information on how Deterministic Earth Mechanical Science springs directly from the Foundation of the Physical Sciences. You click the hyperlinks or browse this website starting immediately below. Most of the website material is focused on geomechanical science. The poster immediately below shows how seemingly complex the superposition of a few accepted physical laws can be.

It is not complex for a mindless electron. It simply chooses the minimum energy path between the other electrons that also orbit the same positively charged nucleus of an atom. The earth is built of these simple components.   RETURN TO TOP

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Geomechanics in the Gulf of Mexico conference in conjunction with OTC May 2, 2001 (NOTE; this is a large 3092 KB file that loads slowly over phone lines. It is copyrighted and contains a pictorial summary of the relationships between the Extended Elastic, and Grain-Matrix Compactional Mechanical systems. If you have a slow system, scroll down in this window. It will eventually upload after you get below the thumbnail explanation.

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This poster reproduction summarizes the relationships between the earth's end-member geomechanical systems. The primary loading limb compaction of sediments is portrayed from left to right across the top. Graphic documentation of the grain-matrix compactional mechanical system go from top to bottom on the left. Graphic documentation of the Extended Elastic Equations of Hooke's law go from top to bottom on the right. The in situ fracture pressure limit to pore pressure is in the lower left.

The force balanced equations that explain both grain-matrix compaction and low frequency acoustic waves are in the center. You can click on [mass-energy] conservation laws in the earth for an explanation.    RETURN TO TOP