Nonlinear regularization techniques for seismic tomography

The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $\ell_2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (edges of anomalies) should be resolved with a minimum of distortion, we prefer $\ell_1$ damping of Daubechies-4 wavelet coefficients. It has the additional advantage of yielding a noiseless reconstruction, contrary to simple $\ell_2$ minimization (`Tikhonov regularization') which should be avoided. In some of our examples, the $\ell_0$ method produced notable artifacts. In addition we show how nonlinear $\ell_1$ methods for finding sparse models can be competitive in speed with the widely used $\ell_2$ methods, certainly under noisy conditions, so that there is no need to shun $\ell_1$ penalizations.Comment: 23 pages, 7 figures. Typographical error corrected in accelerated algorithms (14) and (20

The dependence of the anomalous J/psi suppression on the number of participant nucleons

The observation of an anomalous J/psi suppression in Pb-Pb collisions by the NA50 Collaboration can be considered as the most striking indication for the deconfinement of quarks and gluons at SPS energies. In this Letter, we determine the J/psi suppression pattern as a function of the forward hadronic energy E-ZDC measured in a Zero Degree Calorimeter (ZDC). The direct connection between EZDC and the geometry of the collision allows us to calculate, within a Glauber approach, the precise relation between the number of participant nucleons N-part and E-ZDC. Then, we check if the experimental data can be better explained by a sudden or a smooth onset of the anomalous J/psi suppression as a function of the number of participants. (C) 2001 Elsevier Science B.V. All rights reserved.info:eu-repo/semantics/publishedVersio

Centrality Behaviour of J/ψ\psi Production in Na50

The J/$\psi$ production in 158 A GeV Pb-Pb interactions is studied, in the dimuon decay channel, as a function of centrality, as measured with the electromagnetic or with the very forward calorimeters. After a first sharp variation at mid centrality, both patterns continue to fall down and exhibit a curvature change at high centrality values. This trend excludes any conventional hadronic model and is in agreement with a deconfined quark-gluon phase scenario. We report also preliminary results on the measured charged multiplicity, as given by a dedicated detector.Comment: 5 pages, 7 figures (in eps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

Whole mantle shear structure beneath the East Pacific Rise

We model broadband seismograms containing triplicated S, S2, and S3 along with ScS to produce a pure path one‐dimensional model extending from the crust to the core‐mantle boundary beneath the East Pacific Rise. We simultaneously model all body wave shapes and amplitudes, thereby eliminating depth‐velocity ambiguities. The data consist of western North American broadband recordings of East Pacific Rise (EPR) affiliate transform events that form a continuous record section out to 82° and sample nearly the entire East Pacific Rise. The best fitting synthetics contain attenuation and small changes in lithospheric thickness needed to correct for variation in bounce point ages. The 660‐km discontinuity is particularly well resolved and requires a steep gradient (4%), extending down to 745 km. We find no discernible variation in apparent depths of the 405‐ and 660‐km discontinuities over ridge‐orthogonal distances on the order of 1000 km (or 20 Ma lithosphere). Body waveform comparisons indicate that we can resolve discontinuity depths to less than ±10 km, providing an upper limit to transition zone topography. These depth estimates, in conjunction with the fan shot nature of the ray paths, lower the detection limit from S2 precursor analysis of the lateral length scale over which short‐wavelength topographic variation could occur and indicate the sub‐EPR Transition Zone and upper mantle are remarkably homogeneous. The lower mantle beneath the East Pacific Rise is well modeled by PREM, with the greatest variation occurring in ScS, reflecting strong heterogeneity along the core‐mantle boundary. Together, these observations require that the East Pacific Rise spreading ridge cannot be actively supplied from the local lower mantle and that tomographically imaged lateral variation beneath the ridge likely reflects lateral smearing of outlying velocity gradients. Dynamically, the transition zone therefore appears vertically decoupled from the overlying East Pacific Rise spreading system

Results on open charm from NA50

NA5

Transverse momentum distributions of J/ψ\psi, ψ′\psi^{\prime}, Drell-Yan and continuum dimuons produced in Pb-Pb interactions at the SPS

Muon pairs produced in Pb-Pb interactions at 158~GeV/$c$ per nucleon are used to study the transverse momentum distributions of the J/$\psi$, $\psi^{\prime}$ and dimuons in the mass continuum. In particular, the dependence of these distributions on the centrality of the Pb-Pb collision is investigated in detail

Low mass dimuon production in proton and ion induced interactions at SPS

The low mass dimuon spectra collected in $p$-U collisions by the NA38 experiment significantly exceeds the total cross section expected from previous analysis, done by other experiments. The 'excess' events have a harder $p_{T}$ distribution than the muon pairs from $\eta$ and $\omega$ Dalitz decays, expected to dominate the mass window 0.4—0.65~GeV/$c^2$. We conjecture that the excess events might be due to $q\bar{q}$ annihilations, negligible at low $p_{T}$ but made visible by the $m_{T}$ cut applied in the NA38 data. Taking this assumption to parametrise the $p$-U spectra, we proceed with the analysis of the S-Cu, S-U and Pb-Pb data, collected by the NA38 and NA50 experiments, where we find that the measured mass spectra does not seem to exceed the expected low mass `cocktail' by more than 20%

Scaling of charged particle multiplicity in Pb-Pb collisions at SPS energies

The charged particle multiplicity distribution $dN_{ch}/d\eta$ has been measured by the NA50 experiment in Pb--Pb collisions at the CERN SPS. Measurements were done at incident energies of 40 and 158 GeV per nucleon over a broad impact parameter range. The multiplicity distributions are studied as a function of centrality using the number of participating nucleons ($N_{part}$), or the number of binary nucleon--nucleon collisions ($N_{coll}$). Their values at midrapidity exhibit a power law scaling behaviour given by $N_{part}^{1.00}$ and $N_{coll}^{0.75}$ at 158 GeV. Compatible results are found for the scaling behaviour at 40 GeV. The width of the $dN_{ch}/d\eta$ distributions is larger at 158 than at 40 GeV/nucleon and decreases slightly with centrality at both energies. Our results are compared to similar studies performed by other experiments both at the CERN SPS and at RHIC.

Transverse momentum distributions of J/ψ,ψ′J/\psi,\psi', Drell-Yan and continuum dimuons produced in Pb-Pb interactions at the SPS

NA50Muon pairs produced in Pb-Pb interactions at 158~GeV/$c$ per nucleon are used to study the transverse momentum distributions of the \jpsi, \psip\ and dimuons in the mass continuum. In particular, the dependence of these distributions on the centrality of the Pb-Pb collision is investigated in detail