Inversion Of Magnetic Data Research Articles

3-D inversion of gravity and magnetic data with depth resolution

Magnetization and density models with depth resolution are obtained by solving an inverse problem based on a 3-D set of potential field data. Such a data set is built from information on vertical and horizontal variations of the magnetic or gravity field. The a priori information consists of delimiting a source region and subdividing it in a set of blocks. In this case, the information related to a set of field data along the vertical direction is not generally redundant and is decisive in giving a depth resolution to the gravity and magnetic methods. Because of this depth resolution, which derives solely from the potential field data, an unconstrained and joint inversion of a multiobservation‐level data set is shown to provide surprising results for error‐free synthetic data. On the contrary, a single‐observation level data inversion produces an incorrect and too shallow model. Hence, a good depth resolution is likely to occur for the gravity and magnetic methods when based on the information along the vertical direction. This is also evidenced by an analysis of the kernel function versus the field altitude level and by a singular value analysis of the inversion operators for both the single and multilevel cases. Errors connected to numerical upward continuation do not affect the quality of the solution, provided that the data set extent is larger than that of the anomaly field. Application of the method to a 3-D magnetic data set relative to Vesuvius indicates that the method may significantly improve interpretation of potential fields.

Magnetic telechemistry and magmatic segmentation on the Southern East Pacific Rise

Results from axial dredges and a profile inversion of magnetic anomaly data along the axis of the East Pacific Rise (EPR) at 13–23°S provide an estimate of the average degree of fractionation for the extrusive layer at this ultrafast-spreading (∼145 mm/yr full rate) ridge. We find a high correlation ( R=0.81) between dredge mean FeO * (total iron as FeO) and natural remanence for 34 axial dredges with multiple samples having coincident geochemical and magnetic data. We attribute this good correlation to detailed sampling spanning the full range of cooling-related magnetization changes within a flow and to the young age (0–6 ka) of these axial samples, which effectively minimizes time-dependent magnetization changes due to geomagnetic intensity or alteration. A composite axial magnetic anomaly profile shows large amplitude (up to 400 nT) fluctuations with wavelengths of 50–200 km, which theoretical considerations suggest can reliably be related to the magnetization directly beneath the ship. For much of the southern EPR, seismic data provide independent limits on the axial thickness (259 ± 55 m) and the pattern of off-axis thickening of the extrusive magnetic source layer. These data also provide evidence for an axial magma lens that effectively eliminates anomaly contributions from deeper magnetic sources. Inversion of the axial magnetic anomaly data utilizing these geophysical constraints yields a magnetization solution which, through use of the regression relating FeO * and natural remanence, may be related to the average degree of differentiation of the extrusive source layer. The magnetic data reveal a pattern of magmatic segmentation that closely parallels the tectonic segmentation of the ridge, suggesting that magma supply may be an important control on the average degree of differentiation of the extrusive layer.

Thinning of the Goban Spur continental margin and formation of early oceanic crust: constraints from forward modelling and inversion of marine magnetic anomalies

The deep seismic reflection profile Western Approaches Margin (WAM) cuts across the Goban Spur continental margin, located southwest of Ireland- This non-volcanic margin is characterized by a few tilted blocks parallel to the margin. A volcanic sill has been emplaced on the westernmost tilted block. The shape of the eastern part of this sill is known from seismic data, but neither seismic nor gravity data allow a precise determination of the extent and shape of the volcanic body at depth. Forward modelling and inversion of magnetic data constrain the shape of this volcanic sill and the location of the ocean-continent transition. The volcanic body thickens towards the ocean, and seems to be in direct contact with the oceanic crust. In the contact zone, the volcanic body and the oceanic magnetic layer display approximately the same thickness. The oceanic magnetic layer is anomalously thick immediately west of the volcanic body, and gradually thins to reach more typical values 40 km further to the west. The volcanic sill would therefore represent the very first formation of oceanic crust, just before or at the continental break-up. The ocean-continent transition is limited to a zone 15 km wide. The continental magnetic layer seems to thin gradually oceanwards, as does the continental crust, but no simple relation is observed between their respective thinnings.

3-D inversion of magnetic data : Yaoguo Li & D. W. Oldenburg, Geophysics, 61(2), 1996, pp 394–408

3-D inversion of magnetic data : Yaoguo Li & D. W. Oldenburg, Geophysics, 61(2), 1996, pp 394–408

A model of precambrian geology of Kansas derived from gravity and magnetic data

The fabric of the Precambrian geology of Kansas is revealed through inversion of gravity and magnetic data to pseudo-lithology. There are five main steps in the inversion process: (1) reduction of potential-field data to a horizontal plane in the wavenumber domain; (2) separation of the residual anomaly of interest from the regional background, where an assumption is made that the regional anomaly could be represented by some order of polynomial; (3) subtraction of the signal due to the known topography on the Phanerozoic/Precambrian boundary from the residual anomaly (we assume what is left at this stage are the signals due to lateral variation in the Precambrian lithology); (4) inversion of the residual anomaly in the wavenumber domain to density and magnetization distribution in the top part of the Precambrian constrained by the known geologic information; (5) derivation of pseudo-lithology by characterization of density and magnetization. The boundary between the older Central Plains Province to the north and the Southern Granite-Rhyolite Province to the south is clearly delineated. The Midcontinent Rift System appears to widen in central Kansas and involve a considerable portion of southern Kansas. Lithologies in southwestern Kansas appear to change over fairly small areas and include mafic rocks which have not been encountered in drill holes. The texture of the potential field data from southwestern Kansas suggests a history of continental growth by broad extension.

Inversion of bathymetric and magnetic data from the Mid-Atlantic Ridge between 12� and 24� N: Evidence of spreading instabilities along a diverging plate boundary

Inversion of bathymetric and magnetic data from the Mid-Atlantic Ridge between 12� and 24� N: Evidence of spreading instabilities along a diverging plate boundary

Segmentation and morphotectonic variations of the Central Indian Ridge (21°10′S–22°25′S)

Bathymetric, magnetic, and petrographic data have been used to analyze the segmentation and the morphotectonic variations on the Central Indian Ridge (CIR) between 21°10′S and 22°25′S. Volcanoes, abyssal hills, and steep slopes, corresponding to fault scarps and to volcanic constructional slopes, have been obtained by image processing methods applied to Sea Beam data. In the survey area, segmentation of the CIR is similar to that of a slow spreading ridge. The plate boundary morphology is defined by a linear zone composed of an ensemble of median ridges and elongate depressions. Hourglass‐shaped valleys are bounded by second and third‐order discontinuities located at local along‐axis depth maxima (400–700 m depth variations) and marked by oblique extensional basins and en échelon jogs, respectively. Large‐throw faults are prevalent toward segment ends and suggest greater amagmatic extension in these places. Along the axial valley, the petrographic characteristics of the dredged basalts are correlated with the morphotectonic segmentation and suggest different magma reservoirs. The morphology and structure of the rift valley reflect the three‐dimensional structure of the axial lithosphere and the geometry of mantle upwelling beneath the spreading center. Abyssal hills are bounded by both inward and outward facing faults in ∼1.5 Ma crust, indicating that the formation of abyssal hills is not solely resulting from a combination of volcanic and tectonic processes within the central part of the ridge but that tectonic processes may also occur as far as 20–40 km from the axis by initiating or reactivating some faults at the outward facing slope of the abyssal hills. Reconstructions of the plate boundary geometry through time, using abyssal hills as isochrons, provide evidence to show that the nontransform discontinuity, located at 21°47′S, with an offset as small as 2–3 km, is associated with V‐shaped off‐axis traces in the form of alignments of disrupted abyssal hill lineations. These reconstructions suggest that a small ridge jump is responsible for the initiation of this discontinuity and that this latter migrates away from areas of higher melt delivery. Three‐dimensional inversion of magnetic data shows that this discontinuity has been initiated between 0.780 and 0.984 Ma and suggests postaccretionary crustal block rotations within the discordant zones.

3-D inversion of magnetic data

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.

GMINV: a computer program for gravity or magnetic data inversion : B. N. Rao, P. Ramakrishna & A. Markandeyulu, Computers & Geosciences, 21(2), 1995, pp 301–319

GMINV: a computer program for gravity or magnetic data inversion : B. N. Rao, P. Ramakrishna & A. Markandeyulu, Computers & Geosciences, 21(2), 1995, pp 301–319

GMINV: A computer program for gravity or magnetic data inversion

A computer program for inversion of potential field data using the damped approximate technique is presented. The underlying principles for the optimized damped approximate inversion scheme are discussed. The damping factors and threshold level are selected optimally so that maximum information contained in the data is retained. The facility for constraining or allowing the parameters to range freely is incorporated in GMINV. The analysis of the resolution matrix, eigenvalues, damping factors, V-matrix, and correlation matrix simultaneously facilitates the study of degree of uniqueness of the retrieved parameters and their interdependence. Synthetic gravity data generated across a basinal structure and two field examples are used to highlight the efficacy of the program.

Inversion of Two-Dimensional Magnetic Data Using Correlation Factors between High-Pass Filtered Anomalies

The magnetic anomaly expression produced by most geo ogic structures can be represented by a continuous function in depth and i dex parameter (magnetic inclination) with an amplitude coefficient (mag etic moment). Correlation factors between high-pass filtered anomalies 0 different or successive graticule spacings are used to determine the dept and the index parameter. The computed depths are determined automati ally from each correlation value for each index parameter value. The comp ted depths are plotted against the index parameter representing a contin ous correlation curve. The solution for the depth and the index parameter fthe buried structure is read at the common intersection of correlation cu ves. The method can be applied not only to true residual anomalies of short profile length but also to magnetic anomalies consisting of the combined ect of the residual component due to purely local structure and a regional omponent represented by a linear trend. Procedures are also formulated 0 estimate the amplitude coefficient. The method is independent of the filt ring process. The method is illustrated by a theoretical example and tested on a field example from Arizona.

Investigation of spreading center evolution by joint inversion of seafloor magnetic anomaly and tectonic fabric data

Spreading center segments that have experienced a complex tectonic history including rift propagation may have a complicated signature in bathymetric and magnetic anomaly data. To gain insight into the history of such regions, we have developed techniques in which both the magnetic anomaly patterns and seafloor fabric trends are predicted theoretically, and the combined predictions are compared numerically with the data to estimate best fitting parameters for the propagation history. Fitting functions are constructed to help determine which model best matches the digitized fabric and magnetic anomaly data. Such functions offer statistical criteria for choosing the best fit model. We use this approach to resolve the propagation history of the Cobb Offset along the Juan de Fuca ridge. In this example, the magnetic anomaly data prove more useful in defining the geometry of the propagation events, while the fabric, with its greater temporal resolution, is more useful for constraining the rate of propagation. It thus appears that joint inversion of magnetic and seafloor fabric data can be valuable in tectonic analyses.

Morphology and tectonics of the Mid‐Atlantic Ridge (25°–27°30′S) from Sea Beam and magnetic data

High‐resolution Sea Beam bathymetry and sea surface magnetic data have been collected between 25°S and 27°30′S on the Mid‐Atlantic Ridge. Analysis of the morphology and structure of the ridge axis and flanking terrain as well as the results of a three‐dimensional inversion of sea surface magnetic data are presented. This 227‐km‐long portion of the Mid‐Atlantic Ridge is offset 42 km by the right‐lateral Rio Grande Transform at 25°40′S and 9.5 km by the left‐lateral nontransform Moore Discontinuity at 26°30′S. A third nontransform discontinuity, the Midway Discontinuity, exists near 26°12′S and is defined by a small displacement of the axial magnetization distribution and the disruption in the along‐strike continuity of ridge‐parallel terrain elements. Although the detailed survey presented in this paper extends out to only 5‐ to 7‐m.y.‐old crust, a regional compilation of magnetic data from this area by Cande et al. (1988) indicates that the relative positions and dimensions of the spreading cells have characterized this part of the Mid‐Atlantic Ridge for at least the past 55 m.y. The offsets dimensions and geometries, however, have changed markedly because of prolonged differential asymmetric spreading between segments. Between and within the accretionary units that are spreading at uniform rates (35 mm/yr total opening rate), the morphology of the ridge axis varies dramatically, from a well‐defined rift valley (20–25 km wide, 1–1.5 km deep) to an axial swell that rises 1500 m above the adjacent valley floor. The axial magnetic structure is also highly variable along‐strike. The inversion solution shows a series of generally linear, short‐wavelength (<10 km) magnetization highs within the central Brunhes anomaly over each of the four segments in the survey area. These anomalies are interpreted to be the central anomaly magnetization high that is observed over the neovolcanic zones of many of the world's mid‐ocean spreading centers. The distinct axial magnetization highs can extend out to 2‐m.y.‐old crust at ridge‐discontinuity intersections, suggesting that in some instances they may also be the product temporal variations in the geochemistry of the extrusive rocks, e.g., highly fractionated and strongly magnetized basalts enriched in iron and titanium. The magnetic inversion shows that the central anomaly is locally attenuated at the minimum depth points of three of the four spreading segments in the survey area. Both inversion and forward modeling of magnetic data show that topography alone cannot produce the anomalously low values observed. In the case of an axial swell centered at 26°S, attenuation of the central anomaly is attributed to the effective thinning of the source layer by demagnetization effects of a crustal thermal anomaly and/or a zone of substantial alteration. Taken together, the bathymetric data and magnetic modeling document strong along‐axis gradients in crustal and upper mantle properties.

Lithospheric magnetic property contrasts within the South American plate derived from damped least-squares inversion of satellite magnetic data

A ridge regression (or damped least-squares) method has been used in a large-scale equivalent source inversion of South American MAGSAT data. The optimum damping parameter is selected based on percent increase in the sum of squared residual of the observed and the calculated anomaly and on the variance and the range of the solution for a series of damping parameters. Solutions obtained by the damping parameter selected in this manner are numerically stable and geologically meaningful. Consequently, these solutions are used in various applications such as transformation into effective magnetic susceptibility variation, altitude normalization, differential reduction-to-pole, and downward continuation of the data set. The spacing of equivalent sources and the source-observation distance are shown to introduce significant errors in the estimation of the physical property variation from equivalent source solutions for the large source spacing (> 1°) commonly in use. The correction for these geometric factors is essential in estimating the physical property variation from the equivalent source solutions. A continental and an oceanic profile have been analyzed from the South American maps derived from the above techniques. The continental profile transects a variety of geologic/tectonic features, including shields, aulacogens, basins and fold belts, near the north coast of South America. Along the profile, there is a good correlation between the radially polarized MAGSAT magnetic anomalies and other available geologic and geophysical information. In addition, the variation in effective susceptibility obtained from the damped equivalent source inversion is consistent with our present knowledge of continental lithospheric susceptibilities expected from the geologic/tectonic provinces along the profile. The oceanic profile extends from the trailing margin of South America through the Cretaceous normal polarity rocks of the South Atlantic Ocean. The variations in the magnetic properties along this profile can be broadly correlated with the depth anomaly variation, indicating a possible genetic relationship. Two conceptual models requiring undepleted mantle intrusions under the oceanic uplifts appear possible. In the first model, the high magnetization can be accounted for by a (weakly) magnetic upper mantle below the uplifts; in the second model, very highly magnetic rocks are required in the crust of these uplifted regions to account for the observed anomaly values.

Noniterative three‐dimensional inversion of magnetic data

The interpretation of magnetic or aeromagnetic data often requires the inverse problem’s solution of the structure of the magnetization interface. This nonlinear inverse problem of mapping the basement topography from potential field data was first discussed by Peters (1949).

Joint three-dimensional inversion of gravity and magnetic data from Jombo Hill alkaline complex, Kenya

Jombo alkaline complex is the largest of the alkaline complexes in Kenya. It has been the subject of several geological and geochemical studies. However, the surface geology puts few constraints on the subsurface shape of the intrusion which we here attempt to determine by simultaneous inversion of gravity and aeromagnetic data. The major feature of the gravity map is an elliptical high >800g.u. in amplitude centred near Jombo Hill. When the filtered magnetic map is reduced to the pole and pseudo-gravity transformed, a strikingly similar anomaly is revealed, suggesting a common source. Using an iterative least-squares technique, joint inversion of the gravity and unfiltered magnetic data for a three-dimensional model established that both data sets can be adequately modelled by a thick slab tapering upwards from c . 29 km depth and striking approximately E-W. Only the upper c . 18 km is magnetized which we interpret as an indication of the depth to the Curie isotherm. The body is predicted to be of ultramafic composition capped by the exposed syenites and ijolites.

JOINT INTERPRETATION OF GRAVITY AND MAGNETIC DATA OVER AXIAL SYMMETRIC BODIES WITH APPLICATION TO THE DARNLEY BAY ANOMALY, NWT CANADA*

ABSTRACTA method is presented for determining bounds of the properties of axial symmetric bodies from a finite number of gravity and magnetic observations based on Parker's theory of ideal bodies. Bounds on the density contrast and the intensity of magnetization are calculated as a function of depth to the top of the anomalous source, restricting the range of smallest possible solutions to fit the data.The model studied is approximated by an array of vertical annuli cylinders, each of uniform density and magnetization. Linear programming algorithms based on the ideal body theory were used to calculate the distribution of these parameters within the body.Simultaneous inversion of gravity and magnetic data is performed assuming a constant ratio between the density contrast and the intensity of magnetization and that a common body is responsible for both observed fields. The parameter k(|J|/δp) provides information about the rock type of the structure.Interpretation of gravity and aeromagnetic data from Darnley Bay, NWT, Canada, indicated the presence of a shallow ultrabasic intrusion.

Detailed study of the Brunhes/Matuyama reversal boundary on the east Pacific rise at 19°30′ S: Implications for crustal emplacement processes at an ultra fast spreading center

We have conducted the first detailed survey of the recording of a geomagnetic reversal at an ultra-fast spreading center. The survey straddles the Brunhes/Matuyama reversal boundary at 19°30′ S on the east flank of the East Pacific Rise (EPR), which spreads at the half rate of 82 mm yr-1. In the vicinity of the reversal boundary, we performed a three-dimensional inversion of the surface magnetic field and two-dimensional inversions of several near-bottom profiles including the effects of bathymetry. The surface inversion solution shows that the polarity transition is sharp and linear, and less than 3–4 km wide. These values constitute an upper bound because the interpretation of marine magnetic anomalies observed at the sea surface is limited to wavelengths greater than 3–4 km. The polarity transition width, which represents the distance over which 90% of the change in polarity occurs, is narrow (1.5–2.1 km) as measured on individual 2-D inversion profiles of near-bottom data. This suggests a crustal zone of accretion only 3.0–4.2 km wide. Our method offers little control on accretionary processes below layer 2B because the pillow and the dike layers in young oceanic crust are by far the most significant contributors to the generation of marine magnetic anomalies. The Deep-Tow instrument package was used to determine in situ the polarity of individual volcanoes and fault scarps in the same area. We were able to make 96 in situ polarity determinations which allowed us to locate the scafloor transition boundary which separates positively and negatively magnetized lava flows. The shift between the inversion transition boundary and the seafloor transition boundary can be used to obtain an estimate of the width of the neovolcanic zone of 4–10 km. This width is significantly larger than the present width of the neovolcanic zone at 19°30′ S as documented from near-bottom bathymetric and photographic data (Bicknell et al., 1987), and also larger than the width of the neovolcanic zone at 21° N on the EPR as inferred by the three-dimensional inversion of near-bottom magnetic data (Macdonald et al., 1983). The eruption of positively magnetized lava flows over negatively magnetized crust from the numerous volcanoes present in the survey area and episodic flooding of the flanks of the ridge axis by extensive outpourings of lava erupting from a particularly robust magma chamber may result in a widened neovolcanic zone. We studied the relationship between spreading rate and polarity transition widths obtained from 2-D inversions of the near-bottom magnetic field over various spreading centers. The mean transition width corrected for the time necessary for the reversal to occur decreases with increasing spreading rate but our data set is still too sparse to draw firm conclusions from these observations. Perhaps more interesting is the fact that the range of the measured transition widths also decreases with spreading rate. In the light of these results, we propose a new model for the spreading rate dependency of polarity transition widths. At slow spreading centers, the zone of dike injection is narrow but the locus of crustal accretion is prone to small lateral shifts depending on the availability of magmatic sources, and the resulting polarity transition widths can be narrow or wide. At intermediate spreading centers, the zone of crustal accretion is narrow and does not shift laterally, which leads to narrower transition widths on the average than at slow spreading centers. An intermediate, or even a slow spreading center, may behave like a fast or hot-spot dominated ridge for short periods of time when its magmatic budget is increased due to melting events in the upper mantle. At fast spreading centers, the zone of dike injection is narrow, but the large magmatic budget of fast spreading centers may result in occasional extensive flows less than a few tens of meters thick from the axis and off-axis volcanic cones. These thin flows will not significantly contribute to the polarity transition widths, which remain narrow, but they may greatly increase the width of the neovolcanic zone. Finally the gabbro layer in the lower section of oceanic crust may also contribute to the observed polarity transition widths but this contribution will only become significant in older oceanic crust (≈50–100 m.y.).

DP 1 and DP 2 current systems for the March 22, 1979 substorms

The March 22, 1979 substorm interval selected for analysis by the CDAW 6 has been investigated using a ground magnetic data inversion scheme which computes equivalent current patterns as well as real ionospheric and field aligned current distributions. These have been computed at 5‐minute increments during the two substorm intervals on this day. The computed results have been analyzed using a differential technique which permits us to isolate the current development which occurs during selected time intervals. We find that both DP 1 and DP 2 currents develop during the course of the substorm activity. The first substorm is characterized by the gradual enhancement of a DP 2 equivalent current system following the southward turning of the interplanetary magnetic field. The major magnetic disturbance associated with the expansion phase of the substorm is dominated by the development of a DP 1 current system. During the second interval which consists of several hours of magnetic disturbance, the DP 2 system grows to be much stronger and is the dominant contribution to much of the auroral magnetic activity. The peak of the activity during the second substorm interval appears to be composed of both strong DP 2 and DP 1 currents coexisting. Following the decay of the DP 1 system a strong DP 2 system continues to exist during the enhanced convection phase of the substorm.

Gravity and magnetic inversion with minimization of a specific functional

The nonuniqueness of gravity or magnetic data inversion is well known. In order to remove ambiguity, some authors have sought solutions minimizing a functional describing geometrical or physical properties. Last and Kubik (1983), in particular, developed a method explaining the observed anomaly by structures of minimum volume. In this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast. Each elementary contrast is allowed to vary individually. Thus a contrast distribution is computed. The search for this kind of solution leads in general to geologically more appropriate bodies, but exceptions do occur. In this paper, the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it. The resulting structures are both deeper and more compact, precisely as is required in specific cases. Theoretical and actual examples illustrate this flexible inversion technique.