We describe the implementation of a versatile method for interpreting gravity and magnetic data in terms of 3D structures. The algorithm combines a number of features that have proven useful in other algorithms. To accommodate structures of arbitrary geometry, we define the subsurface using a large number of prisms, with the depths to the tops and bottoms as unknowns to be determined by optimization. Included in the optimization process are the three components of the magnetization vector and the density contrast, which is assumed to be a continuous function with depth. We use polynomial variations of the density contrast to simulate the natural increase of rock density with depth in deep sedimentary basins. The algorithm minimizes the quadratic norm of residuals combined with a regularization term. This term controls the roughness of the upper and lower topographies defined by the prisms. This results in simple shapes by penalizing the norms of the first and second horizontal derivatives of the prism depths and bottoms. Finally, with the use of quadratic programming, it is a simple matter to include a priori information about the model in the form of equality or inequality constraints. The method is first tested using a hypothetical model, and then it is used to estimate the geometry of the Ensenada basin by means of joint inversion of land and offshore gravity and land, offshore, and airborne magnetic data. The inversion helps constrain the structure of the basin and helps extend the interpretation of known surface faults to the offshore.
We consider that all types of electromagnetic measurements represent weighted averages of the subsurface electrical conductivity distribution, and that to each type of measurement there corresponds a different weighting function. We use this concept for the quantitative interpretation of dc resistivity, magnetometric resistivity, and low‐frequency electric and magnetic measurements at low induction numbers. In all three cases the corresponding inverse problems are nonlinear because the weighting functions depend on the unknown conductivity distribution. We use linear approximations that adapt to the data and do not require reference resistivity values. The problem is formulated numerically as a solution of a system of linear equations. The unknown conductivity values are obtained by minimizing an objective function that includes the quadratic norm of the residuals as well as the spatial derivatives of the unknowns. We also apply constraints through the use of quadratic programming. The final product is the flattest model that is compatible with the data under the assumption of the given weighting functions. This approximate inversion or imaging technique produces reasonably good results for low and moderate conductivity contrasts. We present the results of inverting jointly and individually different data sets using synthetic and field data.
Our electrical method for exploring beneath the sea consists of a long, vertical, bipolar ac source, extending downward from the sea surface to the bottom of the sea and a remote, encapsulated, microprocessor‐controlled magnetometer located on the sea floor. The amplitude and phase of the magnetic field are measured over a range of suitable frequencies and transmitter‐magnetometer separations. At the low‐frequency static limit, apparent resistivity curves, similar to standard Schlumberger resistivity sounding curves, are constructed as an aid in the direct interpretation of isotropic crustal resistivity. An intermediate relatively resistive or relatively conductive zone is detectable when the transmitter‐receiver separation exceeds the order of twice the depth to the zone. The physical property resolved by the method in an anisotropic crust, which has different horizontal and vertical resistivities, is the geometric mean of the two independent resistivities. The thickness of a layer is indeterminate. A layer with a coefficient of anisotropy f responds like an isotropic layer f times thicker. At higher frequencies, when induction in the sea water is significant, the apparent resistivity curves remain valid provided locally induced current flow does not dominate the galvanic flow in the crustal material beneath the sea. The presence of some locally induced current, at the electromagnetic resistive limit, is advantageous. It enables the coefficient of anisotropy f of an anisotropic zone to be determined jointly with the mean resistivity. An approximate direct scheme involves the calculation of the apparent anisotropy, a formula which, like the apparent resistivity formula, is a function only of field observations, in particular the phase difference between the measured magnetic field and the transmitted current. The depth of penetration and the resolution of mean resistivity and anisotropy are presented in terms of Fréchet kernels and resolving kernels. The kernels are analytic for the special case of a uniform crust. The shape of the Fréchet kernels for resistivity and anisotropy are different. At low frequency, this reflects the different behaviours of the galvanic in‐phase current flow and quadrature locally induced current flow. The sensitivity function for anisotropy vanishes identically at zero frequency. The inclusion of the complication of anisotropy for the interpretation of data collected over sedimentary basins is mainly for numerical convenience. The sediments themselves are unlikely to be anisotropic on a small scale. The anisotropic behavior is due to macro‐anisotropy, the grouping together of thin isotropic layers of different isotropic resistivities. Such a grouping is introduced into both forward and inverse computer algorithms when the resolving kernels about a given depth are wider than the thickness of a typical layer.
Extraction of gold from quartz–carbonate shear zones has left a barren deposit of tailings at Central Manitoba mine, which remains unchanged after 70 years. In this study, the shape of the basin, the groundwater and surface water flow regime, and the electrical conductivity of the tailings have been delineated using a combination of geotechnical, geophysical, and geochemical techniques. Groundwater and surface water flow from the north–south-fractured bedrock outwards to the east and west. A component of upward groundwater movement in the deposit is due to evaporation in hot, dry summers, limited recharge from precipitation, and the tailings basin being a local groundwater discharge zone. Electromagnetic surveys indicate that the thickness of the tailings and underlying peat bog material increases from ∼1 m at the south of the tailings to ∼5 m at the north. The surveys provided an effective way of mapping the spatial distribution of acidic pore fluids and associated increased salinity. Zones of acidification, occurring mainly on the south side of the tailings, support the hypothesis that acidification is due to differential settling during the initial discharge of carbonate and sulfide minerals.
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