Walter Brown's Hydroplate Model

Copyright 2003 G.R. Morton. This may be freely distributed so long as no charge is made and no alterations to the text are made.

Walter Brown has advanced the idea that Noah's flood was caused by the escape of water from underground chambers. This is a very old idea having been first advanced to my knowledge prior to 1840 (Murray, 1840, p. 215-217). Prior to the flood, the earth had waterfilled subterranean chambers about 10 miles or 16 km below the surface.(Brown, 2002, ref 1). The flood was caused when the crust split open, the water spewed out and flooded the earth and the rebound of the crust (like a rubberband) caused the continents to rapidly drift across the earth's surface (thus accounting for continental drift).  The drawing below illustrates his basic setup

1. Brown's model requires that no mountains be on the preflood  earth, forcing the Bible to be wrong.
Brown's earth model is constructed as follows: a solid center, a water layer, then above that a layer of granite or basalt which 'floats' on the water.  This is as shown below:

                        ------   a mountain ps=2.1 g/cc height=h
                       I      I
                       I      I
------------------------      -----------------------------
Earth's crust (granite 2.65 g/cc, or basalt 3.3 g/cc thickness=T

water  density 1.0 g/cc  Thickness=tw
Earth center       a solid  density > 3.3

There are several things to notice about this situation.  First the crust must be absolutely impermeable to the water.  There must be no earthquakes before the flood since the first crack in this sphere would allow the water to escape.   This means that there must be no meteorites before the flood.  And heaven help mankind if he ever were to have drilled into the crust for curiosity sake.  This means the flood would have happened regardless of whether or not man sinned. There are certain theological problems with that idea.
        There must  absolutely not have been any elevation differences. The effects of a load on the top of the crust can be seen from using an elastic sheet solution to the load.  The 4th order differential equation is 
D ----  +  (pm-pw)zg  = P(x)
where P(x) is the load as a function of horizontal distance, z is the  displacement of the load, g is the acceleration of gravity, pm is the density of the crust, pw is the density of water, D= ET3 /(12(1-sig2 ) where E is Young's modulus, 1011  dynes/cm2, sig is Poison's ratio, .25, and T is the thickness of the crustal layer into which the load sinks. For a two dimensional load with a 1/2 width, A,  the flexure of the crust is 
z max= h(ps-pw)(1-e-LA   cos(LA))/(pm-ps)
where L=4th root((pm-pw) g)/(4D)) 
With a crust thickness of 5 km (5x105  cm) sig=.25, E=1011   we have
D=1.1 x 1028   
L=4.37 x 10-7

Now for a mountain 10 km (1 x 106 cm) in radius and 5 km (5 x 105 cm) in height (h), the  minimum thickness of the crust must be  5 x 105  (2.1-1) (1-e-LA  cos(LA))/(2.65-2.1)=1.1 x 106 cm =4.1 km
The bending of the crust by 4.1 km will occur by fracture.  This would  immediately release the water.  Thus, there are no mountains.  Even a hill 1 km high would require that the crust bend by 830 meters. 
        Therefore the crust must be perfectly smooth. Thus, you must  violate the Biblical record where it says that all the high mountains were covered.  In your conception of the flood there could be no mountains or hills.

2. Early collapse of the subterranean water (regardless of whether or not man would sin. This collapse could come from a collision of the outer crust with the mantle with the intervening water flowing out of the way. In such a model, one must have pillars to retain the physical connection with the core.  If you do not do this, you will have the certainty that the crust will eventually crash into the core.  Friction between the crust and the water and the water and the core will cause the outer crust to begin to move in a fashion different to that of the earth's interior.  This would cause turbulence and would lead to  a crash. The outer crust is free to move in relation to the core in response to tidal forces.
3. Everybody will cook.
    Suppose you placed the water under 10 km of crust, the pressure of the water would be 10 x 105  * 980 * 2.65 = 2.58 x 109  dynes= 2562 atmospheres of pressure.
    The temperature gradient is 1 deg C for every 30 m so there is a 166 deg. C  increase in temperature as we go deeper. 330 + 30 deg C (the surface temperature) =360 deg. C. (see below for justification of the temperature. For a layer of cave water 2 km thick all around the earth would contain 1 x 1024  cubic centimeters of water. At 360 deg C, the high temperature water would contain 3.3 x 1026    calories. (1 calorie per degree rise (330 degree rise)). The minute the pressure is released the water will turn to steam and you will cook the earth.  Dividing the calories by the surface area of the earth shows that heat /cm2   = 3.3 x 1026  Calories/5.09 x 1018  square centimeters = 6.4 x 107  Cal/cm2.
This energy represents 1 year's worth of sunshine on a square centimeter at the equator. (The sun gives each square centimeter 2 calories per square centimeter per second) I don't think Noah could survive this. This enough energy to raise water to 64 million degrees C (assuming a specific heat of 1 cal/degree. Even if you use the 121 deg C value that Brown wants to use, this represents over 4 month's of solar radiation per square centimeter. No one could survive this event. It is a poor mechanism for a flood.
        On final item.  I have seen the IPOD seismic line, from the continent out into the Atlantic mid oceanic ridge, every  inch of it, and there is ABSOLUTELY NO EVIDENCE OF ANY RESIDUAL BURIED WATER OR DEEPLY BURIED CAVE TO HOLD THE WATER.  There are no indications of collapse structures of the size your model would require anywhere on  any seismic data I have ever examined in the past 25 years.
I would also point out that there is a type of seismic wave, called a shear wave which doesn't travel through water.  In Brown's scenario, there would be no way to absolutely eliminate all the subterranean water.  As the crust collapsed, rubble would block the escape route for some of the water.  Given that shear waves don't travel through liquids, those of us in the seismology business should be able to find places where shear waves don't travel to the receivers.  If the water is shallow, it would only block a few seismology stations. 
But, we don't find any places in the shallow earth which won't transmit shear waves.  That is very strong evidence that there is no residual water remaining under the crust.
for Young's Modulus and Poison's Ratio see Milton Dobrin _Introduction to  Geophysical Prospecting_ (New York: McGraw-Hill Book Co., 1952), p. 178
For the Elastic Equation see Philip Keary and Frederick J. Vine,_Global Tectonics_ (Boston: Blackwell Scientific Publications, 1990), p. 35
Tide is from Charles B. Officer _Introduction to Theoretical Geophysics_ New York: Springer-Verlag, 1974 p. 340
Temperature Gradient is from O. M. Phillips, _The Heart of the Earth_ San Francisco: Freeman & Cooper, 1968, p. 138
Brown, Walter, 2002 reference 1. The Hydroplate Theory: An Overview     94. He writes: Assumption 1: Subterranean Water. About half the water now in the oceans was once in interconnected chambers about 10 miles below the earth’s surface. Excluding the solid structure of the interconnected chambers, the subterranean water, containing a large amount of dissolved salt, would have approximated a thin, spherical shell, about 3/4 of a mile in thickness.28 Above the subterranean water was a granite crust; beneath the water was a layer of basaltic rock. (See Figure 51.)
Brown, Walter, 2002 reference 2 The Hydroplate Theory: An Overview     96.

Murray, John, 1840, Truth of Revelation,(London: William Smith).

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