Long-term optical variability of PKS 2155-304

Aims: The optical variability of the blazar PKS 2155-304 is investigated to characterise the red noise behaviour at largely different time scales from 20 days to O(>10 yrs). Methods: The long-term optical light curve of PKS 2155-304 is assembled from archival data as well as from so-far unpublished observations mostly carried out with the ROTSE-III and the ASAS robotic telescopes. A forward folding technique is used to determine the best-fit parameters for a model of a power law with a break in the power spectral density function (PSD). The best-fit parameters are estimated using a maximum-likelihood method with simulated light curves in conjunction with the Lomb Scargle Periodogram (LSP) and the first-order Structure Function (SF). In addition, a new approach based upon the so-called Multiple Fragments Variance Function (MFVF) is introduced and compared to the other methods. Simulated light curves have been used to confirm the reliability of these methods as well as to estimate the uncertainties of the best-fit parameters. Results: The light curve is consistent with the assumed broken power-law PSD. All three methods agree within the estimated uncertainties with the MFVF providing the most accurate results. The red-noise behaviour of the PSD in frequency f follows a power law with f^-{\beta}, {\beta}=1.8 +0.1/-0.2 and a break towards f^0 at frequencies lower than f_min=(2.7 +2.2/-1.6 yrs)^-1.Comment: 10 pages, 8 figures, the ROTSE-light curve can be downloaded from http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/531/A12

A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging

International audienceModelling methods are nowadays at the heart of any geophysical interpretation approach. These are heavily relied upon by imaging techniques in elastodynamics and electromagnetism, where they are crucial for the extraction of subsurface characteristics from ever larger and denser datasets. While high-frequency or one-way approximations are very powerful and efficient, they reach their limits when complex geological settings and solutions of full equations are required at finite frequencies. A review of three important formulations is carried out here: the spectral method, which is very efficient and accurate but generally restricted to simple earth structures and often layered earth structures; the pseudo-spectral, finite-difference and finite-volume methods based on strong formulation of the partial differential equations, which are easy to implement and currently represent a good compromise between accuracy, efficiency and flexibility and the continuous or discontinuous Galerkin finite-element methods that are based on the weak formulation, which lead to more accurate earth representations and therefore to more accurate solutions, although with higher computational costs and more complex use. The choice between these different approaches is still difficult and depends on the applications. Guidelines are given here through discussion of the requirements for imaging/inversion