International Journal Geology and Mining Vol. 4(1), pp , March, ISSN: XXXX-XXXX
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1 International Journal Geology and Mining Vol. 4(1), pp , March, ISSN: XXXX-XXXX IJGM Research Article A Study of Anomalous Value of Free-Air Vertical Gradient for Density Determination Used in a Mine at Barberton City of Ohio, United States BAUMGRATZ, Leonardo Lucas Fundação Agência das Bacias Hidrográficas dos Rios Piracicaba, Capivari e Jundiaí expansaoescalar@gmail.com; Tel: Underground Gravity Vertical Gradient is an important practice for prospecting underground densities, although in most cases it does not match the densities obtained directly in the laboratory from rock samples representative of the location. The densities of the laboratory samples were systematically lower when compared to the densities calculated by gravimetric determination suggesting some kind of systematic error. Several researchers propose different sources to explain these systematic errors including an anomalous value of the free-air vertical gradient. The anomalous value was admitted for the free-air vertical gradient in this paper to reinterpret the densities determination research made in a mine at Barberton, Ohio, in 1950, by gravimetric measurements and by laboratory rock samples. The results of both approaches reached similar densities agreeing with the free-air vertical gradient proposed. Keywords: Gravimetry, Underground gravity, Free-air vertical gradient, Anomalous vertical gradient. INTRODUCTION Gravimetric prospecting methods depend fundamentally on the density of the adjacent underground, which can be achieved by two different processes. It can be measured directly in the laboratory using a set of samples representing the region of interest, or it can be calculated by the variation of gravity on a vertical profile, which is the method for determining density by the Underground Gravity Vertical Gradient (UGVG). A lot of practical works done in deep mines show that in most cases the densities obtained by the two processes are discordant, as mentioned by Hammer (1950) whose research investigated carefully the underground densities in a mine 2, feet deep by means of gravimetric methods. To check the results, measurements of the density of several rock samples representing the profile in the laboratory were made. Each sample was selected carefully to be as representative as possible of the 5-foot interval depth. The densities of the samples presented a large discordance with the gravimeter results. He reported that the laboratory samples have a clear and systematic tendency to have low-density values when compared to densities determined by gravimetry, and the conclusion was that "...the main suspect of causing this systematic error could be an anomalous value of the free-air vertical gradient caused by local or regional anomalies of gravity in the mine vicinity. Later, he studied local and regional maps of Bouguer anomalies trying to explain this anomaly but did not find any evidence that could justify it. It is interesting to note that Hammer (1950) suggested as the main cause of the error an anomalous value of the free-air vertical gradient. His work was so precise and highlighted an issue so important that several authors such as Rogers (1952) and Fajklewicz et al. (1982) cited him. Problems with the free-air vertical gradient are very old. They were detected in the nineteenth century according to the list of researchers cited by Thyssen-Bornemisza and Stachler (1956), shown in Table 1.
2 Baumgratz LL. 152 Table 1: Experimental values of the free-air vertical gradient and its deviation from the standard value of mgal, according to Thyssen-Bornemisza and Stachler (1956). Authors Year Height (ft) Free-air vertical gradient observed Deviation from normal (mgal/m) value Jolly M.Thiesen Scheel and Diesselhorst Richarz and Kriegar-Menzel By studying this list of authors, it is possible to see that the mean gradient value is mgal/m. According to the concepts proposed by Baumgratz (2003), the free-air vertical gradient could be mgal. MATERIALS AND METHODS Gravimetric determination of underground densities is based on the correct interpretation of the gravimetric variations. It is the methodology normally used in UGVG studies. In this context, the free-air vertical gradient is of fundamental importance. Hammer (1950) investigated the underground densities in a mine by laboratory measurements of a set of samples representing the region and by UGVG method. The laboratory samples mean density was g/cm and standard deviation of This author admitted for F the standard value of mgal. Using this new value of F= is the main change to reinterpret Hammer (1950) in the calculations of the underground density by gravimetric determination. The method for calculating the underground density applied in this paper is the same that was used by Hammer (1950) in his work. The only modification made here was in relation to the free-air vertical gradient that became mgal. RESULTS Determination of the Mean Density by Regression Analysis The data gathered by Hammer (1950), which are respectively depth (H) and gravity observed ( g 0) are in Column 1 and 2 of Table 2. The regression function is the Eq. (1): g H Equation (1) The angular coefficient dg 0/dH expresses gravity variation per unit of depth. The correlation coefficient is 0.999, so is valid the relation: g / H g0 / H Equation (2) It is known that in an underground vertical profile the difference in gravity between two stations makes it possible to calculate the density through the well-known expressions (Hammer, 1950): g F 4 G H Equation (3) Eq. (3) may be solved directly for the density giving: F ( g ) 4 G 4 G. H Equation (4) The density σ can be calculated by Eq. 4 where F is the free-air vertical gradient, G is the gravitational constant, and Δg/ΔH is the angular coefficient dg 0/dH obtained by regression analysis. The term ΔT represents the variation of the Terrain Correction over the elevation interval ΔH, and this term is ordinarily so small that no appreciate error is introduced by using an assumed value of the density for it (Hammer, 1950). This author admitted for F the standard value of , and then Eq. (4) resulted in: ( g ) / H Equation (5) For H given in foot, which explains the value The solution showed a high density of 2.75 g/cm 3, diverging from the mean density of the laboratory samples that was g/cm 3 (Hammer, 1950). When adjusting F = the solution for Eq. (4) is: ( g ) / H Equation (6) In this case, the regression analysis shows a profile's mean density of g/cm³ compatible with laboratory samples (2.562 g/cm³) obtained by Hammer (1950). If density was calculated by Eq. 4 adopting F= (this value was obtained from Table 1), the result would be g/cm³; it is very close to the laboratory samples density. Determination of Density for Each Depth Based on the Bouguer Anomaly These equations above apply to determine the profile's mean density. These cannot be used to highlight the small variations in density that occur naturally underground because to do this it would be necessary to consider Bouguer anomalies. The normal gravity ( gn) is a theoretical value calculated by regression analyses and its correct interpretation depends on field studies. According to Hammer (1950), there are no external gravity anomalies interfering in the system under study; it can be assumed that the difference between the observed and normal gravity is caused by local variations of densities. Table 2
3 Int. J. Geol. Min. 153 (from Column 1 to 11) shows the calculations of the depth densities through the anomalous free-air vertical gradient proposed here. Columns 1, 2 and 5 are the data gathered by Hammer (1950), which are respectively depth, gravity observed and Terrestrial Correction. The normal gravity results are in Column 3. It is noteworthy that these should be the gravity values that the profile would have if its density was constant, it was calculated by Eq. (1). This is a purely theoretical concept and the theory must be confirmed by practice. The results found for gravity observed should be equal to normal gravity, but they are different as shown in Column 4. Terrestrial Correction (TC) (topographical and internal corrections of the mine) was obtained from the tables made by Hammer (1939). The difference between observed and normal gravity summed to TC can be interpreted and studied as a Bouguer Anomaly; their values are in Column 6. The variations presented by the Bouguer anomaly and identified as B make it possible to calculate how much the density varies between two stations. Table 2: Reinterpretation of the Hammer (1950) based on new gravity vertical gradient*. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) H g0 Normal ΔgN TC Bouger Anomaly ΔB ΔH (ΔB/ΔH) x 10 4 ΔϬ Ϭ** (2) - (3) (4) + (5) (7)/(8) Feet mgal mgal mgal mgal mgal feet g/cm³ g/cm³ Surface , *For assumed F= mgal. **For assumed "normal" density g/cm³ Column 7 shows the Bouguer variations and Column 8 the depth variation. These data give the variation of density by Eq. (7) and shown in Column ( B / H ) Equation (7) The density of each station (Column 11) is the mean density of summed to density variation, Eq. (8) Equation (8) DISCUSSION The densities obtained by Hammer (1950) in the laboratory and by gravimetric determination show a significant difference, and most of the density results of gravity determination exceeded the standard deviation of mean laboratory samples, only at 1596 and 2202 feet depth they did not exceed. According to this author, the densities, calculated by the UGVG method, in some depth intervals exceeded the density of all individual laboratory samples in the respective interval. He discussed the sources of errors in his work; errors in the gravity readings; errors in elevation interval; errors in reductions and, lastly, in anomalous vertical gradient. He concluded the main suspect of causing this systematic error would be an anomalous value of the free-air vertical gradient caused by local or regional gravity anomalies in the vicinity of the mine. Table 3 and Figure 1 make it possible to compare the three results of densities, which are the laboratory samples in Column 2, calculated by Hammer (1950) in Column 3 and calculated to free-air anomalous value proposed in Column 4. The density difference between laboratory samples and free-air proposed has never exceeded the standard deviation in all depths. This can be easily seen in Figure 1, its curves practically intertwined and it shows more clearly how these two densities are next to each other. The curve of free-air proposed keeps the same curvature of the free-air standard because the same method was used for the booth. A lot of practical works done in deep mines show that in most cases the densities obtained by the two processes are discordant. So; further studies should be done to investigate this anomalous value of freeair in a vicinity of the mine (i.e Barberton, Ohio, U.S.A.) to
4 Baumgratz LL. 154 Table 3 Underground densities (g/cm3) in a vertical profile calculated by different methods. (1) (2) (3) (4) Density obtained through UGVG Depth Density of laboratory samples Calculated by Hammer (1950) Calculated through Free-air proposed F= F= Mean 2.562* * It is the mean of all laboratory samples in Hammer (1950), and its standard deviation is understand if this anomalous value is only in this place, or whether it is generalized value as proposed by Baumgratz (2003). It needs to consider that value of free-air= mgal is not a mere supposition, it has a mathematical and conceptual basis developed in respect to the principles of mechanics, and it has already been applied to the works of Bullen (1953) and Götze et al. (1988) satisfactorily explaining the anomalies they pointed out according to Baumgratz (2003, 2013). If the anomalous value of free-air will be correct in this specific case, the densities determination of a finite interval of underground rocks in a place with the gravimeter is so accuracy like as laboratory measurements of rock samples. Anomalous value of the free-air vertical gradient can be the main cause of systematic error found by Hammer (1950). CONCLUSION In this specific case, the anomalous value of free-air vertical gradient of mgal justifies the density results found by Hammer (1950) at Barberton, Ohio, United States. REFERENCES Baumgratz LL (2003). Os Padrões em um Universo Surrealista: Uma introdução à teoria da expansão. Piracicaba, Br: Editora Degaspari Ltda, 162 p. Baumgratz LL (2013) Scalar Expansion the universe in inflation. Available in: _The_Universe_in_Inflation Accessed: October 7, Bullen KE (1953). An Introduction to the Theory of Seismology. Cambridge at the University Press, Cambridge, 499 p.
5 Int. J. Geol. Min. 155 Fajklewicz Z, Glinski A & Sliz J (1982). Some applications of the underground tower gravity vertical gradient. Geophysics 47: Götze HJ, Lahmeyer B, Schmidt S. Strunk S (1988). Aplicaciones de gravimetria en geología: curso de postgrado. Universidad Nacional de Salta, Argentina, pp Hammer S (1939). Terrain corrections for gravimeter stations. Geophysics, 4: Hammer S (1950) Density determinations by underground gravity measurements. Geophysics, 15: Rogers GR (1952). Subsurface gravity measurements. Geophysics, 17: Thyssen-Bornemisza S, Stackler WF (1956). Observation of the vertical gradient of gravity in the field. Geophysics, 21: Accepted 23 February 2018 Citation: Baumgratz LL (2018). A Study of Anomalous Value of Free-Air Vertical Gradient for Density Determination Used in a Mine at Barberton City of Ohio, United States. International Journal Geology and Mining 4(1): Copyright: Baumgratz LL. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
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