1. Introduction. 2. Geomagnetic Field. Volume 6 Issue 12, December Licensed Under Creative Commons Attribution CC BY

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1 Abstract:The maximum depth rules have benn derived for total magnetic field anomalies at low latitude using ho model. Three different rules were derived for both N-S and E-W profiles over the centre point of magnetic sphere. Fo rules are: Inflexion Point Rule (IPR); Half-Width Rule (HWR); and Amplitude-Slope Rule (ASR) and for N-S trave ASR and Amplitude-Distance Rule (ADR). The reliability of these rules was tested using a set of synthetic total magne over 0 linear spherical magnetic source bodies of 0 m depth range. The rules give very close values to the true source bodies with maximum variation of ± m. On E-W profile, the correlation coefficients between computed and th 0.96 and 0.97 respectively for IPR, HWR and ASR. Also, on N-S profile, the correlation coeffecient between comput are 0.96, 0.97 and 0.96 respectively for IPR, ADR and ASR. The maximum depth rules are adjudged reliable on the ba Keywords: maximum depth, inflexion point, half-width, amplitude, slope, sphere, magnetic anomaly. Introduction Depth determination to magnetic source bodies is a major parameter in the interpretation of magnetic anomalies both in the mineral industry and petroleum industry. In the mineral industry depths to magnetic source bodies determine the depth of exploratory boreholes and in the petroleum industry depths to magnetic source bodies are used to approximate the depth to basement surface, which gives a measure of the volume of sediments available in a given basin. This is made possible because most basement rocks have more magnetite and are more magnetic than nearly all sedimentary rocks, therefore for practical purposes, the magnetic effect recorded by an airborne magnetometer can be considered the same as it would be if the sediments were not present (Nettleton, 976). Many methods of depth to magnetic source bodies have been developed by various workers. Peter (949) published a rather complete system of quantitative magnetic interpretation which involved downward continuation to the basement surface and also introduced the concept of the measurements of maximum slope and half slope distances as depth criteria. Bean (966) gave a graphical method of depth estimation based on inflection and half-slope method. Hartman et al (97) described a Werner Deconvolution method, that uses a vertical- gradient profile which may be measured or calculated and a calculated horizontal gradient profile in addition to the recorded total-magnetic intensity curve. Spector and Grant (970) described a two-dimensional spectral analysis of a given map or region. Another very useful and efficient method of depth determination is modeling. This involves the calculation of magnetic field of a given model at the points of observation (usually by computer) and comparing it with the measured data. The depth and the dimensional parameters of the body are adjusted until satisfactory agreement is achieved between the calculated and the measured values. However, the ambiguity in the interpretat anomalies has made it impossible to det depth to magnetic source bodies. This ha of magnetic anomalies to be very s geologic information and experience interpreter will help to narrow down problems but for a survey where geo limited such as magnetic reconnaissance area for petroleum potential, interpretation influenced. But a possible approach to magnetic anomalies is to approximate the the causative bodies of these anomalies model. This is because for most anomalies equivalently be developed on which the d the body can be developed.. Geomagnetic Field The earth behaves like a weak magnetic b field can be approximated to that of a magnetic dipole at the center of the ear.5º to the axis of rotation (Kearey and origin of the geomagnetic field is not w attributed to convection currents of c circulating in the outer, fluid, part of the et al, 990). The direction of the ambient taken to be the direction a freely suspende any point on the surface of the earth will depends on the location with respect to which is measured by the location of the magnetic latitude. The direction of the a field is at an angle to both the vertical a The earth therefore possesses a magnetic be resolved into certain vector com component, B hor, and vertical componen component also has components along t

2 are given in Fig. and Fig.. The δ horizontal field for N-S traverse is zero an for δb hor and δb abs are approximately δb x curves.also, the typical -D anomaly contour maps for B x, of a sphere is shown Figure: Geomagnetic Elements (After Kearey and Brooks, 988). Magnetic Anomalies of A Sphere A sphere as a geologic body is rare in the real situations, however, the study of its magnetic anomalies is useful in that it incorporates many features of the anomalies of bodies of complex but roughly isometric shape (Parasnis, 994). For a homogeneous spherical body, the components of anomaly due to only induced magnetization are given by Rosler (984) as: Figure: Magnetic anomaly along a N-S of radius m, magnetization A/m and c low latitude δb x (x, y,0),δb x (x,y,0) and δb x (x,y,0) are respectively the north-, east- and vertical components of the magnetic field measured at a position x, y on the surface, produced by a spherical, magnetized body with radiusa and components magnetization M, M, and M buried at a depthd. µ o is the magnetic permeability of free space and is equal to 4π 0-7. M, M, and M are McosI m cosd m, McosI m sind m and 4. Maximum Depth Rules at L the East Componentof Magna The homogeneous sphere is usually used determination of the maximum depth bodies. At low latitude where inclinati zero and assuming that declination of the zero, Equ. () will reduce to:

3 If x and x represent respectively the pos the right maximum amplitudes in Fig., t 4.. Inflexion Point Rule Figure : Magnetic anomaly along an E-W profile overa sphere of radius m, magnetization A/m and centre depth 0 m at low latitude Bx (nt) 'c:\mon\sphere6.dat' u :: S-N (m) 0 W-E (m) Figure 4: -D magnetic anomaly over a sphere of radius m, magnetization A\m, and centre depth 0 m at low latitude. The depth function d to the center of a sphere has relationship with many parameters of the anomaly of the sphere. These relationships can be used to derive some formulae for the calculation of depth depending on the direction of profile. Some of the parameters are: ) Maximum amplitude width ) Inflexion point and ) Amplitude and maximum slope Inflexion point rule gives the relationship from the point of maximum slope to poi and the center depth of a magnetic sphe differentiated At inflexion point B x 0. Hence Dividing equation () by 4d 4, Andmaking y = x4 d4 equation (4) become Therefore, Applying this to the model in Fig., equ by the first and the last inflexion poin equation (7) is satisfied by the second an points. 4.. Amplitudes-Slope Rule Amplitudes-Slope rule relates depth to th maximum and minimum magnetic field slope. From equation (7), when x = 0, δb given as: 4. Maximum Depth Rules on a N-S Traverse For a S-N traverse, at y = 0 equation (6) reduces to:

4 4.. Amplitude-Slope Rule or 4. Maximum depth rules on an E-W traverse for the δb x components On an E-W traverse, whenxis zero, equation (6) becomes 0Ma ( y d ) B x (0, y,0) (4) 5 / ( y d ) 4.. Half width rule The half width is the horizontal distance between the principal maximum or minimum of an anomaly (assumed to be over the center of source) and the point where the value of the anomaly is exactly one half the maximum amplitude.at y = 0, equation (6) becomes 0Ma B x (0, y,0) (5) d If b is assumed to be equal to the minimum, then 0Ma b (6) Therefore, at half width ( Hence Thus y ) b ( y d 0Ma (7) / d ) 0Ma 0Ma (8) / 6d ( y d ) d.y (9) This rule relates depth to the minimum maximum slope. At B x 0, y = maximum i.e. 0M B x.49 Dividing at minimum by B x at ma Thus Bx B B min max B d.6 B min m 5. Testing of Maximum Depth R All the derived formulae (Equ.,7,, determination of depth to the centcre causing magnetic anomalies were tested magnetic data. The sets of data were generated over spherical bodiesalong E-W and N-S respective first derivatives (Fig. 5 and Fig out in order to create a real field situa interference and the magnetic effect observation gives a sum of the con themagnetic bodies in the vicinity of the p of the spheres are shown in Table. For east-west profile, three maximum dep The rules are: Inflexion Point Rule (IPR (HWR); and Amplitude-Slope Rule (AS were testedon N-S profile. The rules Amplitude-Distance Rule (ADR).

5 Figure 5: Total magnetic field anomaly over the center points of 0 linear spheres along east-west profil Magnetic field (above) and first derivative of magnetic field (below)

6 Figure 6: Total magnetic field anomaly over the center points of 0 linear spheres along north-south profi Magnetic field (above) and first derivative of magnetic field (below)

7 6. Results and Discussion The results of the depth rules for east-west and north-south directions are shown in Table and Table respectively.on E-W profile, results were obtained for only 8 spheres and 0 spheres on N-S profile. In real field situation, some magnetic anomalies are superimposed on higher magnetic field, though, dependent on the distance between the magnetic bodies and the direction of profile. This is the case in the E-W profile, where only 8 anomalies were clearly shown and the other two spheres and 5 are not conspicuous (Fig. 5) but clearly shown in N-S profile (Fig. 6). The results show that the depth rules give very close values to the true depth of the magnetic source bodies with maximum variation of ± m. Table : Results of maximum depth rules on E-W profile Sphere Obtained Depth (m) True Depth IPR HWR ASR (m) Nill Nill Nill Nill Nill Nill Table : Results of maximum depth rules on N-S profile Sphere Obtained Depth (m) True Depth IPR ADR ASR (m) From the results of the depth rules on E-W profile, the absolute mean values variation between the computed depth and the real depth of the magnetic source bodies are 0.5 for depth valuie with minimal error. 7. Conclusion Three maximum depth rules of magnetic W profile (IPR,HWR and ASR) and N-S and ASR) have been developed for lo using homogeneous spherical magnetic so On testing, their results gave similar and c the real depths. Therefore these rules ca calculate the maximun depth to magnetic latitudinal regions. For a valid result, the must fall within same range and the a middle value can then be taken as the dep Therules can be applied in producing sed in reconnaisance survey for oil exploirati estimating cost of drilling to magnetic exploitation. References [] Bean, R.J., (966): A rapid graph aeromagnetic anomaly of the two body. Geophysics, vol. no. 5, p. 9 [] Hartman, R.R., Teskey, D.J., and Fr A system for rapid digitalaeromag Geophysics, 6, p [] Kearey, P. and Brooks M., (988) geophysical exploration. GardenCit Herts. p. 96. [4] Nettleton, L.L. (976): Gravity an exploration. McGraw-Hill, New Yor [5] Parasnis, D.S. (994): Principles of Chapman and Hill ltd., London. p. 4 [6] Peters, L.J., (949): The direct ap interpretation and its practicalappli 4, p [7] Rosler, R., (984): Theoretisch angewandten. Gravimetric and Ma Geophysik Band. Springer-Verl andakademie- Verlag Berlin. P -66 [8] Spector, A. and Grant, F.S., (970): interpreting aeromagnetic data. Geo, p [9] Telford, W.M, Geldart, L.P. and S Applied Cambridge. p Geophysics.CambridgeU