BIRD, BCAM's Institutional Repository Data
http://bird.bcamath.org:80
The BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.2019-03-23T17:28:56ZFast inversion of logging-while-drilling resistivity measurements acquired in multiple wells
http://hdl.handle.net/20.500.11824/953
Fast inversion of logging-while-drilling resistivity measurements acquired in multiple wells
Bakr S. A.; Pardo D.; Torres-Verdín C.
This paper introduces a new method for the fast inversion of borehole resistivity measurements acquired in multiple wells using logging-while-drilling (LWD) instruments. There are two key novel contributions. First, we approximate general three-dimensional (3D) transversely isotropic (TI) formations with a sequence of several \stitched" one-dimensional (1D) planarly layered TI sections. This allows us to approximate the solution of rather complex 3D formations using only 1.5D simulations. Second, the developed method supports the simultaneous inversion of measurements acquired in different neighboring wells and/or with different logging instruments.
Numerical experiments performed with realistic 3D synthetic formations confirm the flexibility of the method and the reliability of inversion products. The method yields relative errors below 5% on the model space, and it enables the interpretation of resistivity measurements acquired in multiple wells (e.g., an exploratory, an offset, and a geosteering well) and with any combination of co-axial and/or tri-axial commercial logging measurements acquired with known antennae configurations. Numerical results also indicate that thinly-bedded resistive formations are very sensitive to the presence of noise on the measurements and/or to possible errors on bed boundary locations, while conductive layers are only weakly sensitive to those effects.
2016-10-01T00:00:00ZFinite element approximation of electromagnetic fields using nonfitting meshes for Geophysics
http://hdl.handle.net/20.500.11824/952
Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics
Chaumont-Frelet T.; Nicaise S.; Pardo D.
We analyze the use of nonfitting meshes for simulating the propagation of electromagnetic waves inside the earth with applications to borehole logging. We avoid the use of parameter homogenization and employ standard edge finite element basis functions. For our geophysical applications, we consider a 3D Maxwell’s system with piecewise constant conductivity and globally constant permittivity and permeability. The model is analyzed and discretized using both the Eand H-formulations. Our main contribution is to develop a sharp error estimate for both the electric and magnetic fields. In the presence of singularities, our estimate shows that the magnetic field approximation is converging faster than the electric field approximation. As a result, we conclude that error estimates available in the literature are sharp with respect to the electric field error but provide pessimistic convergence rates for the magnetic field in our geophysical applications. Another surprising consequence of our analysis is that nonfitting meshes deliver the same convergence rate as fitting meshes to approximate the magnetic field. Our theoretical results are numerically illustrated via 2D experiments. For the analyzed cases, the accuracy loss due to the use of nonfitting meshes islimited, even for high conductivity contrasts.
2018-07-01T00:00:00ZTime-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
http://hdl.handle.net/20.500.11824/951
Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
Muñoz-Matute J.; Alberdi E.; Pardo D.; Calo V.M.
Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the context of frequency-domain wave-propagation problems has been developed. In this paper, we extend this error representation to the case of time-domain
problems. We express the entire problem in weak form in order to derive the adjoint formulation and apply goal-oriented adaptivity. One dimensional (1D) numerical results show that upper bounds for the new error representation are sharper than the classical ones. Therefore, this new error representation can be used to design more efficient goal-oriented adaptive methodologies.
2017-12-01T00:00:00ZBloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators
http://hdl.handle.net/20.500.11824/950
Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators
Li K.; Martikainen H.; Vuorinen E.
Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality
for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ is a bi-parameter singular integral
satisfying the assumptions of the bi-parameter representation theorem, then
$$
\| [b_k,\cdots[b_2, [b_1, T]]\cdots]\|_{L^p(\mu) \to L^p(\lambda)} \lesssim_{[\mu]_{A_p}, [\lambda]_{A_p}} \prod_{i=1}^k\|b_i\|_{{\rm{bmo}}(\nu^{\theta_i})} ,
$$
where $p \in (1,\infty)$, $\theta_i \in [0,1]$, $\sum_{i=1}^k\theta_i=1$, $\mu, \lambda \in A_p$, $\nu := \mu^{1/p}\lambda^{-1/p}$. Here
$A_p$ stands for the bi-parameter weights in $\mathbb R^n \times \mathbb R^m$ and ${\rm{bmo}}(\nu)$ is a suitable weighted little BMO space.
We also simplify the proof of the known first order case.
2019-03-14T00:00:00Z