Highly efficient density inversion of gravity data using nonlinear density polynomial fitting

The density inversion of gravity data is commonly achieved by discretizing the subsurface into prismatic cells and calculating the density of each cell. During this process, a weighting function is introduced to the iterative computation to reduce the skin effect during the inversion. Thus, the computation process requires a significant number of matrix operations, which results in low computational efficiency. We have adopted a density inversion method with nonlinear polynomial fitting (NPF) that uses a polynomial to represent the density variation of prismatic cells in a certain space. The computation of each cell is substituted by the computation of the nonlinear polynomial coefficients. Consequently, the efficiency of the inversion is significantly improved because the number of nonlinear polynomial coefficients is less than the number of cells used. Moreover, because representing the density change of all of the cells poses a significant challenge when the cell number is large, we adopt the use of a polynomial to represent the density change of a subregion with fewer cells and multiple nonlinear polynomials to represent the density changes of all prism cells. Using theoretical model tests, we determine that the NPF method more efficiently recovers the density distribution of gravity data compared with conventional density inversion methods. In addition, the density variation of a subregion with 8 × 8 × 8 prismatic cells can be accurately and efficiently obtained using our cubic NPF method, which can also be used for noisy data. Finally, the NPF method was applied to real gravity data in an iron mining area in Shandong Province, China. Convergent results of a 3D perspective view and the distribution of the iron ore bodies were acquired using this method, demonstrating the real-life applicability of this method.

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Interpretation and inversion of microgravity anomalies belong to important tasks of near-surface geophysics, mostly in cavities detection in engineering, environmental and archaeological applications. One of the mostly used concepts of inversion in applied gravimetry is based on the approximation of the model space by means of 2D or 3D elementary sources with the aim to estimate their densities by means of the solution of a corresponding linear equation system. There were published several approaches trying to obtain correct and realistic results, which describe real parameters of the sources. In the proposed contribution we analyse the properties of two additional functionals, which describe additional properties of the searched solution – namely so-called L2-smoothing and minimum support focusing stabilizers. For the inversion itself, we have used the regularized conjugate gradient method. We have studied properties of these two stabilizers in the case of one synthetic model and one real-world dataset (microgravity data from St. Nicholas church in Trnava). Results have shown that proposed algorithm with the minimum support stabilizer can generate satisfactory model results, from which we can describe real geometry, dimensions and physical properties of interpreted cavities.

Numerical Investigation of Natural Convection and Entropy Generation of Water near Density Inversion in a Cavity Having Circular and Elliptical Body

In this chapter, a water-filled square cavity with left hot wall and right cold wall was numerically investigated. The hot and cold wall temperatures are 10°C and 0°C respectively to examine the density inversion of natural convection water, i.e. water at 4°C. In the middle of the square, there are circular and elliptical bodies to study fluid–structure interaction in terms of the thermohydraulic behavior and entropy generation. 2D numerical simulation was performed using finite volume method in Ansys fluent software with the assumption of laminar flow. The simulation results are compared with benchmark data to determine reliability. The results indicate that the body insertions increase the convection heat transfer coefficients at the best heat transfer positions due to impingement heat transfer. An increase in heat transfer rate of 1.06 times is observed in the case of circular body compared to none. There are three primary eddies in the cavity with bodies, whereas the cavity without body has two primary eddies. Maximum entropy generation was found in the upper right corner of cavity mainly due to high horizontal temperature gradient. Bodies of circle and vertical ellipse have almost the same thermohydraulic and entropy generation characteristics due to the same horizontal dimension which mainly effects on the downward natural convection current. The entropy generation of cavity with circular body is 1.23 times higher than that of the cavity without body. At positions y/L = 1 on the hot wall and y/L = 0.74 on the cold wall, the convection heat transfer coefficient is close to zero due to stagnant fluid.

Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit

The prevention of hydrodynamic instabilities can lead to important insights for understanding the instabilities’ underlying dynamics. The Rayleigh-Taylor instability that arises when a dense fluid sinks into and displaces a lighter one is particularly difficult to arrest. By preparing a density inversion between two miscible fluids inside the thin gap separating two flat plates, we create a clean initial stationary interface. Under these conditions, we find that the instability is suppressed below a critical plate spacing. With increasing spacing, the system transitions from the limit of stability where mass diffusion dominates over buoyant forces, through a regime where the gap sets the wavelength of the instability, to the unconfined regime governed by the competition between buoyancy and momentum diffusion. Our study, including experiment, simulation, and linear stability analysis, characterizes all three regimes of confinement and opens new routes for controlling mixing processes.

The Efficient 3D Gravity Focusing Density Inversion Based on Preconditioned JFNK Method under Undulating Terrain: A Case Study from Huayangchuan, Shaanxi Province, China

Since polymetallic ores show higher anomalies in gravity exploration methods, we usually obtain the position and range of ore bodies by density inversion of gravity data. The three-dimensional (3D) gravity focusing density inversion is a common interpretation method in mineral exploration, which can directly and quantitatively obtain the density distribution of subsurface targets. However, in actual cases, it is computation inefficient. We proposed the preconditioned Jacobian-free Newton-Krylov (JFNK) method to accomplish the focusing inversion. The JFNK method is an efficient algorithm in solving large sparse systems of nonlinear equations, and we further accelerate the inversion process by the preconditioned technique. In the actual area, the gravity anomalies are distributed on the naturally undulating surface. Nowadays, the gravity inversion under undulating terrain was mainly achieved by discretizing the ground into unstructured meshes, but it is complicated and time-consuming. To improve the practicality, we presented an equivalent-dimensional method that incorporates unstructured meshes with structured meshes in gravity inversion, and the horizontal size is determined by the gradient of observed gravity and terrain data. The small size meshes are adopted at the position where the terrain or gravity gradient is large. We used synthetic data with undulating-terrain to test our new method. The results indicated that the recovered model obtained by this method was similar to the inversion method of unstructured meshes, and the new method computes faster. We also applied the method to field data in Huayangchuan, Shaanxi Province. The survey area has complicated terrain conditions and contains multiple polymetallic ores. Based on the high-density characteristics of polymetallic ore bodies in the area, we calculate the field data into 3D density models of the subsurface by the preconditioned JFNK method and infer six polymetallic ores.

Microfaulting by early diagenesis of micritic continental carbonates - dilatant and compactive shear localization (Montpellier area, France)

<p>Microfaults formed in continental carbonates reveal poorly known mechanisms of shear localization induced by early diagenesis during compaction. These faults are characterized by sinuous shape, bed-controlled, pervasive distribution, no calcite precipitation, and mainly disaggregation processes. Two main sets were described: (1) The first set is composed by normal-sense, high-angle microfaults affecting the top of carbonate beds showing undulating pedogenic bed surface. They show porosity increase and are sometimes organized in polygonal patterns. Their occurrence seems related to overconsolidation of pedogenic surface and density inversion – phreatic loading – fluid expulsion processes in the surficial carbonate bed. (2) The second set is composed by low-angle compactive microfaults with large slickenlines and incipient shear-offset. Their organization within two conjugate systems (normal-sense set and strike-slip set) almost contemporaneous is consistent with a NS extension following the slope induced by the basin subsidence to the south. Their occurrence seems related to vertical loading below few meters depth and occurred by shear-enhanced compaction and incipient pressure-solution process. The presence of such structures gives news information concerning dilatant or compactive shear processes and rheological properties of micritic carbonates during early diagenesis.</p><p> </p>