Euler Deconvolution Solutions Research Articles

Reliable Euler deconvolution solutions of gravity data throughout the β-VDR and THGED methods: Application to mineral exploration and geological structural mapping

Reliable Euler deconvolution solutions of gravity data throughout the β-VDR and THGED methods: Application to mineral exploration and geological structural mapping

Selection of Euler deconvolution solutions using the enhanced horizontal gradient and stable vertical differentiation

Abstract Euler deconvolution is widely used for interpreting magnetic anomalies as it estimates the edges and depths of magnetic sources. Since this method was proposed, there has been an intensive effort to mitigate its primary deficiencies, namely, the generation of many spurious solutions and the high noise sensitivity. To select the most significant solutions, we adopt the strategy of constraining the moving window to the source edges, whose locations are estimated using the enhanced horizontal gradient amplitude method. On the other hand, we reduce noise propagation by performing a stable calculation of the vertical derivatives. For this purpose, we use the β-VDR method, a finite-difference method that yields a robust approximation of the vertical derivatives of magnetic data. The accuracy of the proposed technique is demonstrated on synthetic magnetic anomalies, providing the depths more precisely and being insensitive to noise. Application of this technique is also demonstrated on aeromagnetic anomalies from the Olympic Peninsula (USA), where the obtained result is in good agreement with known information of the study region.

An Application of Softsign Function (SF) Filter to Low-Latitude Aeromagnetic Data of Tafawa-Balewa Area, Northern Nigeria for Geostructural Mapping and Tectonic Analysis

A recently proposed edge detection technique – Softsign Function (SF) filter was applied to a synthetic magnetic data to illustrate its application. It was then applied in combination with 3D Euler deconvolution and 2D magnetic modelling techniques to the low-latitude aeromagnetic data of Tafawa-Balewa Area, Northern Nigeria, aimed at subsurface geostructural mapping and tectonic analysis of the study area. This was corroborated with mapping and analysis of surface lineaments from Landsat-9 image of the study area. The SF filter depicted edges of magnetic sources from the synthetic magnetic and aeromagnetic data as distinct peaks. The 3D Euler deconvolution solutions and 2D magnetic model showed two dominant depth ranges ∼ 10 m to ∼ 400 m (D1) and ∼ 400 m to ∼ 1000 m (D2) of magnetic sources. The subsurface and surface lineaments from the aeromagnetic data and Landsat-9 image, respectively, fairly agreed in location, trends, even distribution, and density. The trends of mapped lineaments are majorly ENE – WSW direction, and the minor trends are WNW – ESE, NE – SW, NNW – SSE, NNE – SSW, and NW – SE directions. These linear structures, consistent with regional tectonics, are suspected to be strike-slip faults generated by the conjugate system of strike-slip NE – SW and NW – SE faults, including the Romanche and Chain fault systems, produced by the oceanic-continental transcurrent movements which affected the Nigerian basement complex. Explicitly, Softsign Function (SF) filter is a valuable edge detection technique in mapping geological structures from a real low-latitude aeromagnetic data reduced to the geomagnetic equator for tectonic analysis.

Carbonate-rock aquifers in arid environments (central Tunisia, Western Mediterranean province): gravity and time domain electromagnetic methods investigations

Gravity and time domain electromagnetic (TDEM) methods were used in this study to investigate the subsurface hydrogeology of the carbonate-rock aquifer in arid environments (central Tunisia, Western Mediterranean province). The El Houdh basin can be considered an appropriate case for evaluating the vulnerability of groundwater resources under present-day climate change. The identification of structural context and the discontinuities affecting the Eocene or Campanian to Maastrichtian carbonates is an important key to recognize water recharge and discharge pathways and to develop effective and long-term groundwater exploration strategies. First, we have produced an available residual gravity field using a specific Gaussian filter. Then, we generated derivative maps, Euler deconvolution solutions map and a 3D gravity model to delineate different anomalies and to estimate the depth-to-basement parameter and the subsurface density contrasts. Positive and negative anomalies mapping and 3D gravity modelling showed that the El Houdh basin is associated with an asymmetric ‘perched syncline’ with a segmentation into NE–SW sub-basins (local negative residual anomalies) separated by NW–SE lineaments. The TDEM survey was calibrated using boreholes to image the karst saturated and unsaturated zone and to deduce the epikarst and endokarst relationship. Finally, the proposed method provides a fast and valuable approach for better management of hydrogeological exploitation. Thematic collection: This article is part of the Climate change and resilience in Engineering Geology and Hydrogeology collection available at: https://www.lyellcollection.org/cc/climate-change-and-resilience-in-engineering-geology-and-hydrogeology

Investigating groundwater recharge potential of Notwane catchment in Botswana using geophysical and geospatial tools

Study regionThis study is conducted over the Notwane Catchment Area (NCA) in Southeastern Botswana using geospatial and geophysical tools. Study focusGeospatial and geophysical tools, which provide spatial information for both the surface and subsurface have been widely used in groundwater exploration because of their capability in detecting physical properties that are related to groundwater phenomena. In this research, relevant remotely sensed data including aeromagnetic data and satellite images were used to identify potential groundwater recharge zones within the NCA as a contribution towards improved water resources management amid the changing climate. The multi-disciplinary approach used could offer a more reliable way to identify potential recharge zones, particularly in semi-arid hard rock terrains. New hydrological insights for the regionAssessment of groundwater recharge potential looking at remotely sensed data revealed that built-up areas expanded significantly between 2009 and 2019 with implications for run-off and flooding. Through aeromagnetic data interpretation of Euler deconvolution solutions and apparent susceptibility computations, weathered zones and geologic lineaments, mainly dykes and faults, indicating areas with increased secondary porosity were identified. Consequently, the groundwater recharge optimization model was used to determine areas with higher recharge potential which lie on the central part of the NCA, northeastern margin and the southernmost part bounded by topographical relief of hills with thick vegetation. These areas are characterized by approximately 200 m depth of weathering and predominantly east-west structural features.

Geological preconstruction assessment of the proposed site for Layifa housing estate, Jigawa State, Nigeria from aeromagnetic data

Preliminary geological preconstruction assessment of a proposed housing estate site in Jigawa State, northern Nigeria has been done from analysis of aeromagnetic data for the purpose of optimised physical planning, particularly in the area of forestalling any potential risk that may be associated with the existence of linear geological structures or sub-surface conditions that may be inimical to engineering structures. The techniques adopted for the data enhancement include the total horizontal derivative, second vertical derivative and Euler deconvolution solutions. Spectral analysis was also performed on the data to determine depth to the magnetic basement rock, hence overburden thickness and basement topography. Data enhancement analyses delineated considerable number of semi-regional to regional-scaled lineaments, the existence of which presented the study area as a suspected shear zone. Basement topography was found to be highly rugged with evidence of rift-controlled subsidence detected in the eastern section. Having just a few lineaments traversing through it and being located where the basement topography is relatively less undulating, a trapezium-shaped area in the central southern region was identified as the most stable location within the study area, geologically. Two unmapped geologic bodies were delineated from the magnetic data as well. Drilling efforts confirmed an initially unmapped quartzite at the location where one of the two unmapped bodies were delineated and this validated the potency of magnetic data as an aid for geologic mapping. If established that lineaments F25, F26 and F28 traversing through this area are not seismically active, the trapezium-shaped area, said to be least affected by geological factors, could be used for building constructions. However, it is advised that high-rise buildings should not be concentrated in the area but cascaded buildings are recommended due to the fact that a portion of the area is located on a hill-slope and the topography of the basement rock underneath is also coincidentally sloppy. The study area was found to be a shear zone with highly undulating basement topography. Therefore, construction on the site must be approached with caution.

Structural Analysis of Selected Ring Complexes in Some Parts of the Nigerian Younger Granite Provinces

The study area falls within the basement complex of northcentral Nigeria and covers four adjacent quarter degree sheets of 126 (Ririwai), 127 (Kalatu), 147 (Lere) and 148 (Toro) in some parts of Kaduna, Bauchi and Plateau States, Nigeria. This paper is aimed at interpreting the Aeromagnetic data to delineate structures in some parts of the Nigerian younger granite province. This was achieved by determining depth to basement, and developing a 2D model of the shape, location and depth of structures in some parts of the younger granite province. The anomalies on the aeromagnetic map were defined by fitting a first order polynomial to the total fields, by the method of least squares to obtain the residual field data. First vertical derivative and analytic signal computed, defined distinct pattern of the magnetic signatures. Depths to the source of the geologic structures where obtained from Werner and Euler deconvolution solutions which gives an average depths range of 231.2 m to 1040 m, with very few solutions having depths less than 200 m, the most prominent structure particularly the Ririwai ring complex have a depth range of 337.5 m to 465.5 m. The depth to basement for Werner solution ranged from 60 m to 420 m and the depth to basement of the contact model is shallow with depth of (60 to 420m) as compared to the dike model (200 to 420 m).

Mineralisation potential assessment using analytical hierarchy process (AHP) modeling technique: A case study of Ilesha schist belt, southwestern Nigeria

A mineralisation potential assessment in part of Ilesha Schist belt of southwestern Nigeria was carried out using multi criteria decision analysis (MCDA) in the context of analytical hierarchy process (AHP). Three parameters sourced from aeromagnetic, electrical resistivity and geological data were identified to favour gold mineralisation in the study area. These parameters include lineament density (Ld), lithology (Lt), and electrically derived coefficient of anisotropy (An). The application of data enhancement techniques such as total horizontal derivative, 3-D Euler deconvolution and source edge detection were employed in the production of lineament map of the study area. Two hundred and sixty-five (265) vertical electrical sounding (VES) points were investigated using Schlumberger configuration. Coefficient of anisotropy derived from the Dar-Zarouk parameters was obtained from the synthesized VES data. The lithologic information was obtained from the existing geological map of the area. The orientations of lineaments displayed on the aeromagnetic results suggest predominantly NE-SW trending structures, which are characteristic of the Pan African orogenic events in the area. However, few of the E-W trending lineaments are imprints of secondary structural alteration. Furthermore, the Euler deconvolution solutions revealed that the area is characterised by geological contacts with estimated depth of 94–600 m. The coefficient of anisotropy results obtained from the geo-electric parameters vary from 1.00–2.87. AHP weighting and ranking technique was used to develop a reliable mineralisation potential model (MPM). In line with the recommended lower limit of 10 %, the consistency ratio of the developed model is 9.61 %. The produced MPM was classified into low, moderate and high mineralisation potential zones. Preliminary validation of the MPM using the existing pits in the area showed 79 % success rate. The validation of the model using the existing geochemical information from the previous studies indicated 85 % agreement with the conceptual model; thus, confirming the reliability of the produced MPM. The developed model is therefore believed to serve as a future reference in the resource management of the study area.

Joint Gravity and Seismic Reflection Methods to Characterize the Deep Aquifers in Arid Ain El Beidha Plain (Central Tunisia, North Africa)

Electric resistivity sounding and tomography, as well as electromagnetic sounding, are the classical methods frequently used for hydrogeological studies. In this work, we propose the development and implementation of an original integrated approach using the unconventional hydro–geophysical methods of gravity and seismic reflection for the fast, large–scale characterization of hydrogeological potential using the Ain El Beidha plain (central Tunisia) as an analogue. Extending the values of vintage petroleum seismic reflection profiles and gravity data, in conjunction with available geological and hydrogeological information, we performed an advanced analysis to characterize the geometry of deep tertiary (Oligocene and Eocene) aquifers in this arid area. Residual and tilt angle gravity maps revealed that most gravity anomalies have a short wavelength. The study area was mainly composed of three major areas: the Oued Ben Zitoun and Ain El Beidha basins, which are both related to negative gravity trends corresponding to low–density subsiding depocenters. These basins are separated by an important NE–SW trend called “El Gonna–J. El Mguataa–Kroumet Zemla” gravity high. Evaluation of the superposition of detected lineaments and Euler deconvolution solutions’ maps showed several NE–SW and N–S relay system faults. The 3D density inversion model using a lateral and vertical cutting plane suggested the presence of two different tectonic styles (thin VS thick). Results from the gravity analysis were in concordance with the seismic analysis. The deep Oligocene and Eocene seismic horizons were calibrated to the hydraulic wells and surrounding outcrops. Oligocene and Eocene geological reservoirs appear very fractured and compartmented. The faulting network also plays an important role in enhancing groundwater recharge process of the Oligocene and Eocene aquifers. Finally, generated isochron maps provided an excellent opportunity to develop future comprehensive exploration surveys over smaller and more favorable areas’ sub–basins.

Can Euler deconvolution outline three‐dimensional magnetic sources?

ABSTRACTSevere limitations of the standard Euler deconvolution to outline source shapes have been pointed out. However, Euler deconvolution has been widely employed on field data to outline interfaces, as faults and thrust zones. We investigate the limitations of the 3D Euler deconvolution–derived estimates of source dip and volume with the use of reduced‐to‐the‐pole synthetic and field anomalies. The synthetic anomalies are generated by two types of source bodies: (1) uniformly magnetized prisms, presenting either smooth or rough interfaces, and (2) bodies presenting smooth delimiting interfaces but strong internal variation of magnetization intensity. The dip of the first type of body might be estimated from the Euler deconvolution solution cluster if the ratio between the depth to the top and vertical extent is relatively high (>1/4). For the second type of body, besides dip, the source volume can be approximately delimited from the solution cluster envelope, regardless of the referred ratio. We apply Euler deconvolution to two field anomalies which are caused by a curved‐shape thrust zone and by a banded iron formation. These anomalies are chosen because they share characteristics with the two types of synthetic bodies. For the thrust zone, the obtained Euler deconvolution solutions show spatial distribution allowing to estimate a source dip that is consistent with the surface geology data, even if the above‐mentioned ratio is much less than 1/4. Thus, there are other factors, such as a heterogeneous magnetization, which might be controlling the vertical spreading of the Euler deconvolution solutions in the thrust zone. On the other hand, for the iron‐ore formation, the solution cluster spreads out occupying a volume, in accordance with the results obtained with the synthetic sources having internal variation of magnetization intensity. As conclusion, although Euler deconvolution–derived solutions cannot offer accurate estimates of source shapes, they might provide a sufficient degree of reliability in the initial estimates of the source dip and volume, which may be useful in a later phase of more accurate modelling.

Neogene-Quaternary structuring of the Kalaa Khesba Graben, northwestern Tunisia: A push-up inversion structure

Interpretation of lithostratigraphic, seismic and gravity data from Kalaa Khesba Graben shows (i) lateral and in-depth variation of the lithostratigraphic series, (ii) complex structuring of faulting. Reverse faults affected Paleocene to Quaternary horizons with a duplication of Eocene-Paleocene series occurred at subsurface evidenced within well W6. Isochron, isovelocity and isobath maps, combined with gravity data, show subsurface structures oriented predominantly NW-SE to NS and NE-SW to EW. Faults and horizons on the seismic lines, superimposed to gravity lineaments, reveal negative anomalies occurring at shallow depth. Such features may reflect the existence of low density Neogene-Quaternary series, strike-slips and thrust faults within Kalaa Khesba Graben. Depths deduced from Euler deconvolution solutions vary from 0.5 to 4 km. At subsurface, well log data located in the center of the graben, ensured the presence of Triassic bodies. A model of initiation of Kalaa Khesba Graben through a N160° σ1 transpression is proposed.

Aeromagnetic Investigation of Geologic Structures Associated with Gold Mineralization along Danja, Northwestern Nigeria

The study area falls within the basement complex of northwestern Nigeria and covers four adjacent quarter degree sheets of Funtua, Malumfashi, Masks and Zaria. Gold occurrence in the area was not reported until the recent discovery by artisanal miners. Previous works have shown that primary gold mineralization within the Nigerian basement complex is controlled by geologic structures where they act as conduits for fluids flow and as loci for mineralization. This paper is aimed at characterizing the major structural controls of gold mineralization in the study area. This was achieved by determining depth to basement, producing a magnetization map showing magnetic susceptibility range across the entire study area, and a model of the shape, location and depth of structures in the study area. The anomalies on the aeromagnetic map were defined by fitting a first order polynomial to the total fields, by the method of least squares to obtain the residual field data. First vertical derivative and analytic signal computed, defined distinct pattern of the magnetic signatures. Depths to the surface of the geologic structures (which appears as lineaments on aeromagnetic maps) were obtained from Euler deconvolution solutions which gives an average depths range of 200.2 m to 2229.1 m, with very few solutions having depths less than 300 m. The most prominent lineament and all major subtle lineaments have a depth range of 200 m to 600 m which shows that the structures are deep seated. The magnetic susceptibility values obtained from the magnetization map ranges from 0.000666 to 0.000996 SI. The lineament expected to be the major conduit for possible fluid flow that emplaced the Gold mineralization in the area is suspected to be the continuation of Kalangai fault which trends NE-SW along Malumfashi in the study area.

Aeromagnetic mapping of basement structures and mineralisation characterisation of Ilesa Schist Belt, Southwestern Nigeria

This paper analysed aeromagnetic data over the southern Ilesa schist belt of Nigeria with a view to assessing the sub surface structural settings that might favour mineralisation in the study area. Enhancement of the total magnetic intensity map was carried out to improve the anomaly characteristic of source bodies through upward continuation and reduction to the equator (RTE) of the magnetic field intensity. Estimation of depth to the deep, intermediate and near surface structures was based on the Spectral analysis and Euler deconvolution of the aeromagnetic data. Extracted magnetic anomalies from the RTE map range in amplitude from −115 to 134 nT, with the high magnetic intensities occurring over amphibolite, schist, porphyritic granite, gneiss and undifferentiated Migmatite, while low magnetic intensities were observed over quartzite and the undifferentiated schist. The Euler deconvolution solutions revealed that the area is mainly affected by sill/dyke and horizontal cylinder/pipe geologic model with estimated depth to the magnetic source ranging from 73 m–345 m. The depth estimated from the spectral analysis was in the range of 100 m–300 m for the intermediate and shallow sources; this compares reasonably well with the results from the Euler deconvolution. The orientations of lineaments extracted from the total horizontal derivative, source edge detection and Euler deconvolution suggest predominantly NE-SW trending structures, characteristic of primary geologic events in the area, while few E-W trending lineaments are imprints of secondary structural alteration in magnetic fabrics in this direction. Thus, the delineated structures are believed to be the hosts to the mineralised targets as observed from small scale mining activities in the area.

Morphology, tectonic significance, and relationship to the Wenchuan earthquake of the Xiaoyudong Fault in Western China based on gravity and magnetic data

The appearance of the surface rupture of the NW-striking Xiaoyudong Fault during the Wenchuan earthquake has attracted attentions of scholars and subsequently aroused debates about it. The size and tectonic significance of this fault is the key of the debates. Based on maps of gravity and magnetic in the scale of 1:500,000, the wavelet multi-scale method and the power spectrum method were used to obtain the wavelet fault analysis maps at different scales with average field source depths. Furthermore, the Euler deconvolution solutions of magnetic were determined and a simple model of the crust was built through the joint inversion of gravity and aeromagnetic data to analyze the penetration depth of the Xiaoyudong Fault. Combining these data with aftershock relocation data of Wenchuan earthquake provides better understanding of the Xiaoyudong Fault. We found that the Xiaoyudong Fault strikes NW cutting through the Pengguan and Xuelongbao complexes, and extending to the Yibasan area of Dazhou in Sichuan Province. The total length of the Xiaoyudong Fault is estimated to be 100km, and its depth of penetration is less than 20km, indicative of the Xiaoyudong Fault as a part of the decollement structural system. The parallel Miyaluo Fault is on the west of the Xiaoyudong Fault, cuts to a depth of less than 20km, and is also a part of the same decollement structural system. The Xiaoyudong and Miyaluo faults are both part of the NW-striking tectonic system in the Songpan–Ganzi Fold Belt. The Xiaoyudong Fault was active during the Mesozoic and was reactivated during the earthquake with the Longmenshan Fault Belt under the present tectonic stress regime. However, only the southern most part of the Xiaoyudong Fault ruptured at the ground surface in the Wenchuan earthquake.

Integration of Ground Magnetics and Energy Dispersive X-Ray Fluorescence Spectroscopy in Ilmenite Prospection in Magaoni, Kenya

The geology of Magaoni area is associated with the presence of heavy minerals [1]. Magaoni’s neighbours Maumba and Nguluku where ilmenite was discovered by Tiomin Resource Inc. in 1996, using drilling and chemical analysis [2]. Ilmenite mineral is known to be magnetically weak, but provides observable magnetic response [3]. In this study, ground magnetic survey method was carried out to map magnetic anomalies of established stations, associated with ilmenite bearing formations. The magnetic contour map plotted showed weak and shallow magnetic signatures spread throughout the study area. 2D Euler deconvolution solutions revealed presence of magnetised formations from near surface to a maximum depth of about 450 m at some points. The weak magnetic formations of near surface indicated presence of ilmenite. Energy dispersive X-ray spectroscopy was done on soil samples collected randomly from the study area to determine the percentage of iron and titanium oxides. The results showed elevated values of titanium dioxide, ranging from 1.5% to 13% which is way above the global average of about 0.7% [4]. The percentage of iron oxide was low, ranging from 1.5% to 4%, this being the reason for weak magnetisation of the study area.

Orogenic bending around a rigid Proterozoic magmatic rift beneath the Central Appalachian Mountains

The transition zone between the modern northern and southern Appalachian Mountains is located in Pennsylvania, where the structural orientation of the fold-and-thrust belt changes from north–south to east–west, and the orogeny narrows significantly. Vintage studies of wide-angle reflection and temporary broadband seismic data suggest that the crust beneath the ∼8 km of foreland basin sequences was thickened and heavily intruded around the margins of and beneath a failed Neoproterozoic rift. We use receiver function analysis of broadband seismic data recorded by additional and permanent stations, along with forward and inverse modeling of Bouguer gravity data to constrain the geometry and depth extent of mafic intrusion and underplating in the rift, as well as the role of this Proterozoic heterogeneity on the location and geometry of the curvature of the Appalachian orogen. The receiver function analyses suggest that the crust is ∼47–49 km thick beneath the ancient rift, about 5–7 km thicker than the surrounding area. Inverse models of gravity data indicate that the ∼300 km-long zone of thickened, high density crust is bounded on both the NW and SE sides by steep contacts; its shorter NE and SW margins are also steep contacts interpreted as crustal-scale faults. Forward modeling of the gravity data, constrained by the receiver function crustal thickness estimates, sparse seismic reflection data and Euler deconvolution solutions, implies that the Proterozoic rift has been heavily intruded as well as thickened by a 7–10 km mafic underplate. Its margins appear to have been sheared along NE-striking fault zones that parallel Appalachian thrust sheet transport directions. These combined results suggest that the mid- and lower-crust of the Proterozoic rift was enriched with pyroxene, which strengthened the crust locally and localized compressional strain along its margins during the North American–African collision. Compressional strain in the pre-Appalachian crystalline crust to the southwest and northeast of the Proterozoic rift may have been more distributed, leading to the formation of oblique-slip faults orthogonal to the axes of folds, and leading to the curvature in the Pennsylvania salient. Additionally, the thrust sheets are stacked most thickly in front of the rift, suggesting that the rift served as a backstop during collision.

Cluster analysis of Euler deconvolution solutions: New filtering techniques and geologic strike determination

Euler deconvolution often presents the problem of filtering coherent solutions from uncorrelated ones. We have applied clustering and kernel density distribution techniques to a Euler-generated data set. First a kernel density distribution algorithm filters uncorrelated Euler solutions from those consistently located near an anomalous magnetic-gravimetric source. Then a fuzzy [Formula: see text]-means clustering algorithm is applied to the filtered data set. The computation of cluster centers reduces the size of the data set considerably, yet maintains its statistical consistency. Finally, the computation of eigenvectors and eigenvalues on the cluster centers yields an estimate of the geologic strike of the anomalous sources responsible for the observed geophysical anomalies. Therefore, we can obtain an improved strike and depth estimation of the magnetic sources. Although the algorithm can filter and cluster any Euler data set, we recommend obtaining the best solutions possible before any clustering. Hence, we have used a hybrid 3D extended Euler and 3D Werner deconvolution algorithm. We have developed synthetic and real examples from the Bathurst Mining Camp (New Brunswick, Canada). The output of this algorithm can be used as an input to any 3D geologic-modeling package.

The Application Of Fractional Calculus To Potential Field Data

Gradients of magnetic and gravity data are used routinely to enhance the edges of anomalies, or as input to interpretation techniques such as analytic signal analysis or Euler deconvolution. The most commonly used gradients are of first and second order, higher orders being used less frequently due to noise problems. This paper discusses the benefits of a generalized approach using fractional gradients, demonstrating their usefulness as an aid to interpretation, both on theoretical models and on aeromagnetic data from the Free State province, South Africa. Fractional horizontal gradients are suggested as a means of avoiding the instability problems present when magnetic data from low latitudes is reduced to the pole. They also allow the use of an improved sunshading algorithm that is less affected by noise than the standard method. Fractional vertical gradients may be used to generate both enhanced analytic signal data and enhanced Euler deconvolution solutions.

The application of fractional calculus to potential field data

Gradients of magnetic and gravity data are used routinely to enhance the edges of anomalies, or as input to interpretation techniques such as analytic signal analysis or Euler deconvolution. The most commonly used gradients are of first and second order, higher orders being used less frequently due to noise problems. This paper discusses the benefits of a generalized approach using fractional gradients, demonstrating their usefulness as an aid to interpretation, both on theoretical models and on aeromagnetic data from the Free State province, South Africa. Fractional horizontal gradients are suggested as a means of avoiding the instability problems present when magnetic data from low latitudes is reduced to the pole. They also allow the use of an improved sunshading algorithm that is less affected by noise than the standard method. Fractional vertical gradients may be used to generate both enhanced analytic signal data and enhanced Euler deconvolution solutions.

Tertiary extension in the central British Columbia Intermontane Belt: magnetic and paleomagnetic evidence from the Endako region

New magnetic and paleomagnetic data for central British Columbia support and quantify the hypothesis that the area underwent significant Tertiary-age transtensional deformation. Paleomagnetically determined tilts in Eocene rocks indicate that four fault-bounded pits, which constitute the Endako molybdenum mine, were displaced on a series of normal (probably listric) faults that have separations of less than a kilometre. The interpretation also suggests there can be little vertical offset on the Denak West Fault, which separates the Denak East and Denak West pits. Regional paleomagnetic data indicate a predominance of easterly directed tilts to the east of the Casey Fault, but to the west a large variation in the orientation and magnitude of tilts is observed. Results at one site proximal to the Casey Fault indicate a component of dip-slip displacement on this dominantly dextral strike-slip fault. Mapped northeast- and northwest-trending faults commonly correspond to linear zones of steep magnetic gradient and near-surface magnetic sources. Several additional northwest- and northeast-trending lineaments are imaged in the magnetic data where no faults are mapped (particularly over massive and lithologically homogeneous phases of the Endako batholith). Euler deconvolution solutions confirm most such lineaments are also associated with shallow magnetic sources. In profile, they have either a fault or dyke character and are interpreted to be unmapped faults, some locally intruded by mafic dykes, which cut the region into a series of fault-bounded blocks.