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The location of gold veins, due to a slanting magma dike intrusion in a cold rock, considering earth surface effects is determined. The 400 °C and 500 °C isotherm evolution resulting from this magma intrusion are studied considering a 2-D model. In this analysis, it is shown that the isotherm envelopes are the most important surfaces. Analytic solutions have been found as a function of the angle a between the dike and the vertical planes. The present results are more general than previous ones in the contest of vertical dikes. Magma convection has been considered in a simplified way. The agreement found that the results in the work the actual vein sites at the gold mine, called Colombia, in the auriferous area of El Callao, located 180 Km south of Ciudad Guayana in Bolivar state, Venezuela, are much better than in previous works.

Intrusion related gold systems is a term that reflects a tendency common to all magmatic hydrothermal environ- ments to form gold ores in spatial associations with intrusive centres. The global distribution and the large number of these types of gold deposits have produced an increasing interest in the investigation and exploration of intrusion related gold systems. Excellent references of our previous statements can be found in the work of Lang and Baker (2001) [

As it was pointed out in a previous paper [

As in previous work [

a higher melting point temperature

In the present treatment the magma intrusion is considered to fill up the half-space on the left of the axis

The heat flux q is due to temperature gradient, that is

where k is the thermal conductivity coefficient and T the temperature.

The heat diverging from the system is compensated by the heat changes in the country rocks, that is,

where c is the specific heat,

From this two equations, the time dependent heat conduction equation is obtained

where

Now it is useful to use the dimensionless variable

where the dimensionless temperature

here

For the matematical treatment, it is convenient to define dimensionless and similarity variables

As in previous paper, x is measured along the horizontal right line at the earth surface, and perpendicular to the intersection line between dike and earth surface. The vertical line corresponds to the coordinate y. Now it is convenient to introduce a new coordinate-axis

The surface separating magma and country rock at any time is not a plane, and this surface will be determined at any time t with our equations. The usual orthogonal coordinates x and y are now related with the new coordinates

The new dimensionless coordinates

Using these new similarity variables, the heat diffusion equation [

where

In this way the diffusion Equation (10) is transformed in the equation

Now, we can follow the same procedure as in previous paper [

where

and

equation for

The solutions of these equations are the error functions

and

Any linear combination of both functions is a solution. The boundary conditions will determine the right combination. Let us analyse first when x tend to infinite

The analysis for the earth, now it is a little different than in our previous paper [

Then the surface with

will be horizontal. As in previous papers [

where now

We know also that the parameters

where L is the latent heat of the magma.

One very important isotherm is the contact surface between the magma and the country rock defined by the dimensionless equation

where the points of the isotherms are denoted by

where

and

These equations are shown in

In

where it has been used that

Another important characteristic in

In

The determination of the gold vein location, is performed looking to the envelopes of the 400˚C and 500˚C isotherm families. The procedure to obtain the envelope is performing the partial derivatives with respect the parameter t of Equation (20) obtaining

where

Considering now a particular isotherm for the temperature

From this system of equations with two unknowns

Equation (36) can also be written down in a more convenient way as

where

In the case of

and^{2}, 10^{3}, 10^{4} and 10^{5} days, and similarly for

We want now to compare our results with those of the gold mine Colombia selected in previous paper [

In

It is clear now, that our results are good since the actual galleries are almost inside the angle formed by the 400˚C and the 500˚C isotherms envelopes. The differences between our results and the actual site of the galleries, seems to be due to the magma convection which has not been taken in account until now. However in the introduction, we discuss that a simple way to include this effect in the calculations, it is to consider that the heat coming out due to convection is equivalent to heat source overheating the magma. If this analisys is

performed and a 20% overheating is considered, that is, the new

This is shown in

Horizontal distances to the vertical reference plane (m) | ||||
---|---|---|---|---|

Depth (m) | Galleries | Envelope isotherm for 400˚C | Envelope isotherm for 500˚C | Dike |

134 | 150 | 134 | 101 | 36 |

184 | 200 | 184 | 139 | 49 |

230 | 250 | 230 | 173 | 62 |

280 | 300 | 280 | 211 | 75 |

330 | 385 | 330 | 249 | 88 |

380 | 425 | 380 | 286 | 102 |

The gold vein location around magma intrusive dikes have been analyzed considering a 2-D isotherm problem, that is, including the earth surface effects. The present analysis differs from the most common previous studies in that the boundary conditions is now 2-D instead of 1-D. Previous treatments considering 2-D boundary conditions were performed considering that the magma dike was vertical. A more general analysis has been realized in the present work, where the boundary conditions have been applied to a general dike, inclined an angle a with respect to vertical plane. In this work, it is shown that the isotherm envelopes are the most important surface to find out the location of the gold veins. Analytic solutions have been obtained for this general case, using error functions. Accurate calculations have also been performed in the case of El Callao gold mines, and the present results agree much better with the actual situation of galleries in these mines, than any previous ones. Two main lines of analysis have been performed. In the first one, the convention effects were not considered, and in this case the calculations predicting the gold galleries location agree only a litle better with the actual sites than previous ones. However, when the heat convection effect was included in a simple way, a total agreement was found.

This work was partially supported by FONACIT, Programa de Estimulo a la Investigación, PEI, Grant Project N˚3125, Venezuela; Universidad de Antofagasta, Programa Mecesup, Grant Project ANT128, and Decanatura de Ciencias Básicas, Chile.

P. Martin,F. Maass,J. Puerta,L. Cortes, (2016) Gold Veins Location in Deposits Originated by a Slanting Magma Intrusion Dike. International Journal of Geosciences,07,548-557. doi: 10.4236/ijg.2016.74042