Tomographic inversion using ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accepted dates). Corrected typ

Compression approaches for the regularized solutions of linear systems from large-scale inverse problems

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a large matrix through a sparser matrix with fewer nonzero elements, by borrowing from ideas used in wavelet image compression. Next, we describe and compare approaches based on the use of the low rank singular value decomposition (SVD), which can result in further size reductions. We describe how to obtain the approximate low rank SVD of the original matrix using the sparser wavelet compressed matrix. Some analytical results concerning the various methods are presented and the results of the proposed techniques are illustrated using both synthetic data and a very large linear system from a seismic tomography application, where we obtain significant compression gains with our methods, while still resolving the main features of the solutions.European Research Council (Advanced Grant 226837)United States. Defense Advanced Research Projects Agency (Contract N66001-13-1-4050)National Science Foundation (U.S.) (Contracts 1320652 and 0748488

An objective rationale for the choice of regularisation parameter with application to global multiple-frequency S-wave tomography

International audienceIn a linear ill-posed inverse problem, the regularisation parameter (damping) controls the balance between minimising both the residual data misfit and the model norm. Poor knowledge of data uncertainties often makes the selection of damping rather arbitrary. To go beyond that subjectivity, an objective rationale for the choice of damping is presented, which is based on the coherency of delay-time estimates in different frequency bands. Our method is tailored to the problem of global multiple-frequency tomography (MFT), using a data set of 287 078 S-wave delay times measured in five frequency bands (10, 15, 22, 34, and 51 s central periods). Whereas for each ray path the delay-time estimates should vary coherently from one period to the other, the noise most likely is not coherent. Thus, the lack of coherency of the information in different frequency bands is exploited, using an analogy with the cross-validation method, to identify models dominated by noise. In addition, a sharp change of behaviour of the model ℓ∞-norm, as the damping becomes lower than a threshold value, is interpreted as the signature of data noise starting to significantly pollute at least one model component. Models with damping larger than this threshold are diagnosed as being constructed with poor data exploitation. Finally, a preferred model is selected from the remaining range of permitted model solutions. This choice is quasi-objective in terms of model interpretation, as the selected model shows a high degree of similarity with almost all other permitted models (correlation superior to 98% up to spherical harmonic degree 80). The obtained tomographic model is displayed in the mid lower-mantle (660-1910 km depth), and is shown to be compatible with three other recent global shear-velocity models. A wider application of the presented rationale should permit us to converge towards more objective seismic imaging of Earth's mantle

Short Note Hydrophone Calibration at Very Low Frequencies

International audienceWe propose a new method to study the response of a hydrophone at very low frequencies. In our method, the hydrophone is placed in a calibration chamber filled with water and, by instantaneously changing the water height, an abrupt pressure increase of about 1000 Pa is produced. The pressure variation mathematically corresponds to an input signal close to a step function. The response is recorded after filtering and digitizing so that we obtain the response of the complete system. We also report on the development of an automatic method to determine the number of poles and zeros and their values that describe the observed response. We apply our method to the RAFOS II hydrophone, used on the Mobile Earthquake Recorder in Marine Areas by Independent Divers (MERMAID) floats. As an illustration of the method, an instrumental response in terms of poles and zeros is used to correct seis-mograms from the 7 April 2014 (M w 4.8) Barcelonnette earthquake, recorded by three MERMAIDs deployed in the Mediterranean Sea, and to express the observed signals in pascals

Finite-frequency effects in global surface-wave tomography

We compare traditional ray-theoretical surface-wave tomography with finite-frequency tomography, using 3-D Born sensitivity kernels for long-period, fundamental-mode dispersion measurements. The 3-D kernels preserve sidelobes beyond the first Fresnel zone, and fully account for the directional dependence of surface-wave scattering, and the effects of time-domain tapering and seismic source radiation. Tomographic inversions of Love and Rayleigh phase-delay measurements and synthetic checkerboard tests show that (1) small-scale S-wave velocity anomalies are better resolved using finite-frequency sensitivity kernels, especially in the lowermost upper mantle; (2) the resulting upper-mantle heterogeneities are generally stronger in amplitude than those recovered using ray theory and (3) finite-frequency tomographic models fit long-period dispersion data better than ray-theoretical models of comparable roughness. We also examine the reliability of 2-D, phase-velocity sensitivity kernels in global surface-wave tomography, and show that phase-velocity kernels based upon a forward-scattering approximation or previously adopted geometrical simplifications do not reliably account for finite-frequency wave-propagation effects. 3-D sensitivity kernels with full consideration of directional-dependent seismic scattering are the preferred method of inverting long-period dispersion data. Finally, we derive 2-D boundary sensitivity kernels for lateral variations in crustal thickness, and show that finite-frequency crustal effects are not negligible in long-period surface-wave dispersion studies, especially for paths along continent-ocean boundaries. Unfortunately, we also show that, in global studies, linear perturbation theory is not sufficiently accurate to make reliable crustal corrections, due to the large difference in thickness between oceanic and continental crust

Finite frequency whole mantle P wave tomography: Improvement of subducted slab images

We present a new whole mantle P wave tomographic model GAP_P4. We used two data groups; short-period data of more than 10 million picked-up onset times and long-period data of more than 20 thousand differential travel times measured by waveform cross-correlation. Finite frequency kernels were calculated at the corresponding frequency bands for both long- and short- period data. With respect to an earlier model GAP_P2, we find important improvements especially in the transition zone and uppermost lower mantle beneath the South China Sea and the southern Philippine Sea owing to broadband ocean bottom seismometers (BBOBS) deployed in the western Pacific Ocean where station coverage is poor. This new model is different from a model in which the full data set is interpreted with classical ray theory. BBOBS observations should be more useful to sharpen images of subducted slabs than expected from simple ray path coverage arguments

Flat versus normal subduction zones: a comparison based on 3-D regional traveltime tomography and petrological modelling of central Chile and western Argentina (29°–35°S)

Our study compares the seismic properties between the flat and normal subduction regions in central Chile, to better understand the links between the slab geometry, surface deformation and the deeper structures. In comparison with previous studies, we show the most complete 3-D regional seismic tomography images for this region, in which we use (1) a larger seismic data set compiled from several short-term seismic catalogues, (2) a denser seismic array allowing a better resolution of the subduction zone from the trench to the backarc and into the upper ∼30 km of the slab and (3) a starting 1-D background velocity model specifically calculated for this region and refined over the years. We assess and discuss our tomography results using regional seismic attenuation models and estimating rock types on the basis of pressure and temperature conditions computed from thermomechanical models. Our results show significant seismic differences between the flat and normal subduction zones. As expected, the faster seismic velocities and increased seismicity within the flat slab and overriding lithosphere are generally consistent with a cooler thermal state. Our results are also consistent with dehydration of the mantle above the subducted Juan Fernandez Ridge at the eastern tip of the flat slab segment, indicating that the latter retains some fluids during subduction. However, fluids in the upper portion of the flat slab segment are not seismically detected, since we report instead fast slab seismic velocities which contradict the argument of its buoyancy being the cause of horizontal subduction. The forearc region, above the flat slab, exhibits high Vs and very low Vp/Vs ratios, uncorrelated with typical rock compositions, increased density or reduced temperature; this feature is possibly linked with the aftershock effects of the Mw7.1 1997 Punitaqui earthquake, the flat slab geometry and/or seismic anisotropy. At the surface, the seismic variations correlate with the geological terranes. The Andean crust is strongly reduced in seismic velocities along the La Ramada–Aconcagua deformation belt, suggesting structural damage. Slow seismic velocities along the Andean Moho match non-eclogitized hydrated rocks, consistent with a previous delamination event or a felsic composition, which in turn supports the extent of the Chilenia terrane at these depths. We confirm previous studies that suggest that the Cuyania terrane in the backarc region is mafic and contains an eclogitized lower crust below 50-km depth. We also hypothesize major Andean basement detachment faults (or shear zones) to extend towards the plate interface and canalize slab-derived fluids into the continental crust

Seismic evidence for a tilted mantle plume and north–south mantle flow beneath Iceland

Post-print / lokagerð höfundaShear waves converted from compressional waves at mantle discontinuities near 410- and 660-km depth recorded by two broadband seismic experiments in Iceland reveal that the center of an area of anomalously thin mantle transition zone lies at least 100 km south of the upper-mantle low-velocity anomaly imaged tomographically beneath the hotspot. This offset is evidence for a tilted plume conduit in the upper mantle, the result of either northward flow of the Icelandic asthenosphere or southward flow of the upper part of the lower mantle in a no-net-rotation reference frame.Peer Reviewe

Imaging the mantle beneath Iceland using integrated seismological techniques

Using a combination of body wave and surface wave data sets to reveal the mantle plume and plume head, this study presents a tomographic image of the mantle structure beneath Iceland to 400 km depth. Data comes primarily from the PASSCAL-HOTSPOT deployment of 30 broadband instruments over a period of 2 years, and is supplemented by data from the SIL and ICEMELT networks. Three sets of relative teleseismic body wave arrival times are generated through cross correlation: S and SKS arrivals at 0.03–0.1 Hz, and P and PKIKP arrivals at 0.03–0.1 and 0.8–2.0 Hz. Prior to inversion the crustal portion of the travel time anomalies is removed using the crustal model ICECRTb. This step has a significant effect on the mantle velocity variations imaged down to a depth of ∼250 km. Inversion of relative arrival times only provides information on lateral velocity variations. Surface waves are therefore used to provide absolute velocity information for the uppermost mantle beneath Iceland. The average wave number for the Love wave fundamental mode at 0.020 and 0.024 Hz is measured and used to invert for the average S velocity. Combination of the body wave and surface wave information reveals a predominantly horizontal low-velocity anomaly extending from the Moho down to ∼250 km depth, interpreted as a plume head. Below the plume head a near-cylindrical low-velocity anomaly with a radius of ∼100 km and peak VP and VS anomalies of −2% and −4%, respectively, extends down to the maximum depth of resolution at 400 km. Within the plume head, in the uppermost mantle above the core of the plume, there is a relatively high velocity with a maximum VP and VS anomaly of +2%. This high-velocity anomaly may be the result of the extreme degree of melt extraction necessary to generate the thick (46 km) crust in central Iceland. Comparison of the plume volumetric flux implied by our images, the crustal generation rate, and the degree of melting suggested by rare earth element inversions, suggests that (1) mantle material must be flowing horizontally away from the plume core faster than the overlying lithosphere and (2) the bulk of the plume material does not participate in melting beneath Iceland