Gravity Study using Multi-2.5D Modeling and 3D Presentation for Al Ma'aniyah Depression, Southwest of Iraq

Tectonic depression area within and/or beside widespread basin is regarded as an important location for sub-basin sedimentary sequence of Iraq which may represent an excellent accumulation of bounded sediments. Al-Ma'aniyah depression, southwest Iraq is one of such type of sub-basin. Free-air gravity data show a NS extend of this depression inside Saudi Arabia. This work focuses on studying and multi-2.5D model creation for the depression in the Iraqi territory part using Bouguer gravity data and mapping its basement relief. Firstly, the exact boundary of the depression was outlined utilizing the Free-Air gravity data. Then, a precise selection of regional field for the study area was determined by using the power spectrum method, which accordingly defines the residual anomalies that could represent structural enclosures. Many positive anomalies were assigned and enhanced using vertical and total horizontal derivatives, where they were interpreted as basement-related features. Subsequently, a 2.5D multi modeling and depth inversion for the Bouguer gravity data were accomplished by converting the gravity map to a stacked profiles depth map. A nineteen gravity profiles, which cover the study area, were modeled by assuming 2D intra-sedimentary bodies. These bodies were best presented by a 3D view that clarifies the nature of the subsurface modeled structures. The modeling shows an extra density at the northern part of the depression, in contrast, it suggests low density bodies at its southern part, the case that appears inconsistent with a previously performed magnetic interpretation. The inversion of gravity data shows that the basement depth at Al-Ma'aniyah depression ranges from 7.5 to10 km.

A note on the exact boundary controllability for an imperfect transmission problem

In this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of the Hilbert Uniqueness Method, introduced by J. L. Lions, we study the related boundary exact controllability problem. The key point is to derive an observability inequality by using the so called Lagrange multipliers method, and then to construct the exact control through the solution of an adjoint problem. Eventually, we prove a lower bound for the control time which depends on the geometry of the domain, on the coefficients matrix and on the proportionality between the jump of the solution and the conormal derivatives on the interface.

Exact boundary null controllability for a coupled system of plate equations with variable coefficients

<p style='text-indent:20px;'>This paper studies a coupled system of plate equations with variable coefficients, subject to the clamped boundary conditions. By the Riemannian geometry approach, the duality method, the multiplier technique and a compact perturbation method, we establish exact boundary null controllability of the system under verifiable assumptions.</p>