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The Forum > General Discussion > Geophysics and Earthquakes- Mathmatics and things that make you go Hmmm

Geophysics and Earthquakes- Mathmatics and things that make you go Hmmm

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Introduction:
No natural force is more destructive than earthquakes. The energy released by a magnitude 6.0 earthquake lasting 45 seconds, is several thousand times greater than a nuclear bomb. Furthermore, according to the USGS (united states geological survey), earthquake forecasting remains little more than an elusive goal.

Sadly, many earthquakes strike locations where the population and government institutions have little or no capability to deal with the aftermath. Places like southern Iran and rural China.

If you ask a geologist what causes an earthquake, he/she will tell you it's caused by slippage or abrupt movement between two plates of rock at a location called a fault zone.

They will go on to explain there is a slow but constant differential motion between the plates, and over time this results in deformation and the buildup of stress between the plates. When this stress exceeds the frictional resistance of the fault zone, slippage occurs causing an earthquake.

There are several problems with the standard model of earthquakes. First, not all earthquakes are associated with fault zones. Second, and even more troubling, the origin points for many earthquakes are greater than 100km below the surface of the earth.

At this depth, the rock is either plastic or fully liquefied and therefore no longer able to support the frictional slippage mechanism postulated by geologists as the primary cause of earthquakes.

Another poorly explained phenomena is the tendency of earthquakes to cluster over a brief period of time, lasting from hours to days and sometimes even weeks. The mechanical slippage paradigm would seem to predict just the opposite should take place, since the initial earthquake lowered the deformation stresses in the plates, making further slippage less likely.

While the standard model of earthquakes is appealing in it's simplicity, it is also clearly insufficient to explain many of the observed phenomena.
Posted by All-, Friday, 24 July 2009 1:33:21 PM
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Ok , hang in there now;
Advanced physics: It was much more difficult to break it down ; so here we go ;

Chemical phase change:
When two or more substances are involved in a chemical reaction, the resulting compound will occupy a different volume than that of the original substances.

In other words, the total volume will shrink or expand as a result of chemical reaction. Furthermore, pressure and/or temperature can cause the internal molecular arrangement of a compound to undergo an abrupt shift or phase change, thereby causing a change in volume of the compound. In many cases, the reaction or rearrangement is very swift, requiring mere fractions of a second to complete.

1.1.3
Piezoelectric & electrostriction effects:
Under the influence of mechanical stress, dielectric materials exhibit a phenomena known as the piezoelectric effect. Simply stated, an electric field or potential is generated within the material due to physical deformation created by the applied mechanical stress.

While generally considered to be an exclusive property of crystalline dielectrics, the phenomena is also observed in both amorphous solids and liquids. Any material that exhibits piezoelectric activity, will also exhibit electrostriction phenomena. This is the inverse of the piezoelectric effect, whereby the material changes shape and/or volume under the influence of an externally applied electric field.

1.1.4
Acoustic wave guides:
Most people associate acoustic (or sonic) waves with air, however these waves also travel through liquids and solids.

Different materials conduct acoustic waves at different propagation velocities. In general, propagation velocities in liquids are greater than in gases, and propagation velocities in solids are greater than in liquids, however each unique material has a specific propagation velocity, that is also dependent on environmental variables such as temperature and pressure.

Whenever an acoustic wave undergoes an abrupt change in propagation velocity, the wave is reflected to a greater or lesser extent, depending on the degree of propagation velocity shift.

A large change in propagation velocity will result in nearly total reflection, while a small change in propagation velocity will result in a partial reflection of the acoustic wave.
Posted by All-, Saturday, 25 July 2009 11:46:49 AM
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Continued:

Changes in acoustic wave propagation velocity are caused by transitions between differing materials, or because of a change in the environmental conditions within a single material.

A related phenomena known as a surface acoustic wave, results from the entrapment of the wave energy by an extreme shift in propagation velocity between differing materials.

In effect the boundary between very dissimilar materials acts as a wave guide, thereby channeling the acoustic wave energy along the surface of the boundary. Both cathedral whisper galleries, and pressure zone microphones (also known as boundary microphones) make use of the effect.

The fault zone between two plates (1.1.1) is also an excellent acoustic wave guide.

1.1.5
Acoustic energy transformation:
The energy contained in an acoustic wave is the product of both displacement (length of movement) and pressure (force per unit area). This relationship is shown in Equation 1.

[Eq. 1] E/a= l F/a= lP

Where:
E = Energy (in Joules).
a = Area (meters squared).
l = Length of displacement (in meters).
F = Force (in Newtons).
P = Pressure in Pascals (Newtons per meter squared).

Eq. 1 Implies that a high pressure small displacement acoustic wave contains the same energy as a low pressure large displacement wave.

Consider an acoustic wave with a 1 millimeter displacement, generated over a 1 meter square area, 5 kilometers below the surface of earth. The pressure at this depth will be over 100 million Pascals, and therefore this small (1 millimeter) displacement represents an enormous quantity of energy.

Next consider what happens as this acoustic wave travels upward to the surface of the planet. At the surface, atmospheric pressure is approximately 100,000 Pascals.

Conservation requires the energy contained in the wave to be constant. Therefore as the pressure drops, the displacement must increase. If the wave remained focused, and the pressure at a depth of 5 kilometers was exactly 100 million Pascals, the displacement at the planet surface would be 1 kilometer!

The acoustic wave energy would have to be spread over a surface area of 1 square kilometer to retain a 1 millimeter displacement
Posted by All-, Saturday, 25 July 2009 3:21:28 PM
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As this example clearly demonstrates, small displacements within the earth will create very large movements at the surface of the planet.

1.2.1
The alternant model:
Suppose a one cubic kilometer volume of mineral such as perovskite undergoes an abrupt chemical phase change, caused by a small alteration in pressure and/or temperature, thereby creating a change in volume of just 0.0001%.

A volumetric change of 0.0001% in one cubic kilometer represents a change of 1,000 cubic meters, or approximately 0.17 millimeters of displacement on all sides of the cubic kilometer volume. Furthermore, suppose this reaction takes place at a depth of just 10 kilometers.
The pressure at any depth can be calculated by:

[Eq. 2] P= g M/V d

Where:
P = Pressure (in Pascals).
g = Acceleration of gravity (in meters per second squared).
M = Mass (in kilograms).
V = Volume of mass (in cubic meters).
d = Depth (in meters).

Using granite, the mass is 2691 kilograms per cubic meter, and earth standard gravity at 9.8 meters per second2, gives a value of 2.637 x 107 Pascals. A displacement of 0.17 millimeters at this pressure, over a surface area of just 1 square meter represents an energy (1.1.5 Eq. 1) of 4.48 x 103 Joules per meter2, and when multiplied by the surface area of our 1 cubic kilometer of perovskite mineral (6 million meters2) equals a staggering 2.69 x 1010 Joules, or over two hundred billion Joules of energy! Spread this energy over one hundred square kilometers of planetary surface, and you still have 2,690 Joules of energy per square meter. More than enough energy to transform a home into a smoking pile rubbl
Posted by All-, Saturday, 25 July 2009 3:35:24 PM
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The real worry is that NZ just moved 30 cm closer to Australia in the last quake.Does that that mean that they get a discount on air fares as they come to collect the Aussie dole? Not only are the Kiwis cutting our vowels short,ie fush and chups, they are trying our patience.

Do we really need this cultural invasion to be aided and abetted by the the destructive forces of mother nature? We need an early warning system to stem the flow of this Kiwi invasion.Perhaps the baa of a sheep,or the acrid stench of a sulphurus spring.

The Indians really annoy us beyond any the constraints of fair play with their tele-marking banter.Just imagine a Kiwi selling you something you don't want or need? The rage would be insatiable,especially if they beat us at rugby!
Posted by Arjay, Saturday, 25 July 2009 6:13:59 PM
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LOL Arjay!
Posted by CJ Morgan, Saturday, 25 July 2009 6:24:07 PM
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