3D depth-to-basement and density contrast estimates using gravity and borehole data
We present a gravity inversion method for simultaneously estimating the 3D basement relief of a sedimentary basin and the parameters defining the parabolic decay of the density contrast with depth in a sedimentary pack assuming the prior knowledge about the basement depth at a few points. The sedimentary pack is approximated by a grid of 3D vertical prisms juxtaposed in both horizontal directions, x and y, of a right-handed coordinate system. The prisms' thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data. To produce stable depth-to-basement estimates we impose smoothness on the basement depths through minimization of the spatial derivatives of the parameters in the x and y directions. To estimate the parameters defining the parabolic decay of the density contrast with depth we mapped a functional containing prior information about the basement depths at a few points. We apply our method to synthetic data from a simulated complex 3D basement relief with two sedimentary sections having distinct parabolic laws describing the density contrast variation with depth. Our method retrieves the true parameters of the parabolic law of density contrast decay with depth and produces good estimates of the basement relief if the number and the distribution of boreholes are sufficient. We also applied our method to real gravity data from the onshore and part of the shallow offshore Almada Basin, on Brazil's northeastern coast. The estimated 3D Almada's basement shows geologic structures that cannot be easily inferred just from the inspection of the gravity anomaly. The estimated Almada relief presents steep borders evidencing the presence of gravity faults. Also, we note the existence of three terraces separating two local subbasins. These geologic features are consistent with Almada's geodynamic origin (the Mesozoic breakup of Gondwana and the opening of the South Atlantic Ocean) and they are important in understanding the basin evolution and in detecting structural oil traps.
3D constrained inversion of geophysical and geological information applying Spatial Mutually Constrained Inversion.
The need for increaseding accuracy and reduced ambiguities in the inversion results has resulted in focus on the development of more advanced inversion methods of geophysical data. Over the past few years more advanced inversion techniques have been developed to improve the results. Real 3D-inversion is time consuming and therefore often not the best solution in a cost-efficient perspective. This has motivated the development of 3D constrained inversions, where 1D-models are constrained in 3D, also known as a Spatial Constrained Inversion (SCI). Moreover, inversion of several different data types in one inversion has been developed, known as Mutually Constrained Inversion (MCI). In this paper a presentation of a Spatial Mutually Constrained Inversion method (SMCI) is given. This method allows 1D-inversion applied to different geophysical datasets and geological information constrained in 3D. Application of two or more types of geophysical methods in the inversion has proved to reduce the equivalence problem and to increase the resolution in the inversion results. The use of geological information from borehole data or digital geological models can be integrated in the inversion. In the SMCI, a 1D inversion code is used to model soundings that are constrained in three dimensions according to their relative position in space. This solution enhances the accuracy of the inversion and produces distinct layers thicknesses and resistivities. It is very efficient in the mapping of a layered geology but still also capable of mapping layer discontinuities that are, in many cases, related to fracturing and faulting or due to valley fills. Geological information may be included in the inversion directly or used only to form a starting model for the individual soundings in the inversion. In order to show the effectiveness of the method, examples are presented from both synthetic data and real data. The examples include DC-soundings as well as land-based and airborne TEM-soundings. The SMCI here combines the capability of the DC- resistivity method to map resistive areas with the capability of the EM method to map conductive zones in order to produce models that are more in agreement with the expected geological formations. Furthermore, the results from the SMCI inversion are compared with traditional inversion methods. The comparison is made from resistivity maps where the resolution of the method can be evaluated with known lithology, water levels, etc. The results from SMCI inversion demonstrate significant improvement over those derived from standard 2D constrained inversion. The SMCI is applicable in general geological mapping, groundwater surveys, mineral exploration or other surveys where geophysical information of different types can be combined or where geological information is available.
The Marine CSEM Response of a Resistive Sheet: Straightforward but not Trivial
Thin conductive sheets are often used to model base metal deposits for mineral exploration. In a similar manner, thin resistive sheets can be used as simple models for oil, gas, or gas hydrate reservoirs. One would expect that the calculation of the electromagnetic response of a resistive sheet using an integral equation method should follow trivially from the well-studied solution methods for a conductive sheet. The only physical difference between the two situations is the fact that the conductive solution relies on the continuity of the electric field tangential to the sheet surface whereas the resistive solution requires continuity of the normal current density. We started to develop a practical tool which would be useful in our marine controlled-source electromagnetic projects. Progress proved slow. We eventually realized that the approximations used in the conductive calculation resulted in solutions in the resistive case that failed to converge! It turns out that the resistive problem is far more subtle than one might expect, for both the full three-dimensional case and the simplified two-dimensional version. We outline the fundamental theory required to correctly calculate the marine CSEM response of 2D and 3D resistive sheets in a double halfspace; we further validate the software against results obtained independently through 3D finite difference modelling and through layered earth solutions. Results show that a thin resistive sheet behaves in a similar way as a "thick" plate with corresponding finite thickness and resistivity, suggesting that a sheet is a good representation of an idealized buried resistive zone.
A Deterministic Approach to Analyzing Audiomagnetotelluric Models and Borehole Data in a Hydrological Environment
We present a three-step deterministic approach to understand the relationship between borehole data and surface geophysics using audiomagnetotelluric (AMT) data. Traditionally, geoscientists have used borehole data as ground truth, but it is not clear how representative a point measurement is for laterally extensive or regional areas. Furthermore, it is unclear when and where it is valid to compare borehole and surface data. Geophysics is used to site wells, but the borehole data are often used to calibrate the geophysics, and it is the relationship between the two data sets that we quantitatively investigate here. As part of a hydrological study of the Basin and Range province, an arid, mountainous, sparsely populated region of the western United States, many AMT surveys were conducted. AMT soundings were typically collected along profiles at stations spaced roughly 200-400 m. The resulting two-dimensional resistivity models successfully imaged subsurface faults and structures down to roughly 500 m depth. These faults are a primary structural control on the hydrogeology of many valleys in this region. Borehole data, including both lithological and geophysical logs, were available from several water monitoring and testing wells close to our AMT stations. Wells were located between 10m and 1.6 km from our AMT profiles, and extended down to 600 m below the surface. Although borehole data, whether lithological or geophysical logs, have excellent vertical resolution they are essentially point source data, and there are many reasons that the borehole data may not faithfully represent the survey area. The borehole can be unfortunately sited so that it is located in an anomalous area, or problems with instrumentation can cause inaccuracies with the logs. In addition, there is a great deal of borehole data that has been poorly archived and may be difficult to decipher or use. Our approach to quantitatively compare the AMT and borehole data involves three steps: 1) One-dimensional forward modeling based on borehole data; 2) Inverse modeling of AMT data using various starting models; and 3) A resolution/sensitivity analysis based on comparison of forward and inverse models. Our results fall into three categories: 1) The AMT and borehole data are consistent and image similar subsurface electrical structure; 2) There is a discrepancy that can be explained; and 3) There is a strong discrepancy that cannot be readily explained, but one result is clearly preferred.
dielectric properties of salt clay mixtures
Dielectric properties of salt clay mixtures Sanaa Aqil and Douglas Schmitt Ground Penetrating Radar (GPR) is a technique that is frequently used in salt mines to locate hazardous zones such as clay and salt contaminated with clay. These zones can be identified on a GPR map. GPR reflection occurs because of the difference of the dielectric permittivity. We measured the complex dielectric permittivity of synthetic and natural salt clay mixture using coaxial line sensor in conjunction with a network analyser that operates between frequencies of 10MHz and 3GHz. These measurements and their application to the interpretation of GPR data will be discussed.
Rayleigh Waves Traveling Along the Impermeable Surface of an Unsaturated Poroelastic Half-space
This study presents an analytical model of Rayleigh waves propagating along the impermeable surface of an unsaturated poroelastic half-space. The developed equation reveals that there are three modes of Rayleigh waves, based on the poroelastic equations in a porous medium containing two immiscible viscous compressible fluids formulated by Lo et al.[Wave propagation through elastic porous media containing two immiscible fluids. Water Resour Res 2005;41:W02025]. These three Rayleigh waves induced by three modes, corresponding to three dilatational waves in a medium saturated by two fluids, can be expressed as the R1, R2, and R3 waves in the descending order of magnitude, respectively. As an excitation frequency is given, the dispersion equation of a cubic polynomial will be solved numerically to derive the three phase speeds and the attenuation coefficients of the R1, R2, and R3 waves in Columbia fine sandy loam penetrated by air and water fluids. The numerical results show that the phase speed of the R1 wave is frequency independent, approximately 93 % to 95 % of the shear wave speed, and nearly 28 % to 49 % of the first dilatational wave speed at the frequencies of 1 Hz, 10 Hz, and 100Hz related to relative water saturation ranges (0.01-0.99). Nevertheless, the R2 and R3 waves are dispersive. In the same frequency ranges, we also find the two ratios of the phase speeds of the R2 and R3 waves to the second and third dilatational wave speeds are both around 56 % to 90 %. In addition, the R1 wave attenuates least while the R3 wave has the highest attenuation coefficient along the impermeable surface. Lastly, all the three modes of Rayleigh wave satisfy the condition of decaying exponentially with the distance far away from the surface of a porous medium.