ALBERT

Description: Global-scale tomographic models should aim at satisfying the full seismic spectrum. For this purpose, and to better constrain isotropic 3-D variations of shear velocities in the mantle, we tackle a joint inversion of spheroidal normal-mode structure coefficients and multiple-frequency S -wave delay times. In all previous studies for which normal modes were jointly inverted for, with body and/or surface waves, the mantle was laterally parametrized with uniform basis functions, such as spherical harmonics, equal-area blocks and evenly spaced spherical splines. In particular, spherical harmonics naturally appear when considering the Earth's free oscillations. However, progress towards higher resolution joint tomography requires a movement away from such uniform parametrization to overcome its computational inefficiency to adapt to local variations in resolution. The main goal of this study is to include normal modes into a joint inversion based upon a non-uniform parametrization that is adapted to the spatially varying smallest resolving length of the data. Thus, we perform the first joint inversion of normal-mode and body-wave data using an irregular tomographic grid, optimized according to ray density. We show how to compute the projection of 3-D sensitivity kernels for both data sets onto our parametrization made up of spherical layers spanned with irregular Delaunay triangulations. This approach, computationally efficient, allows us to map into the joint model multiscale structural informations from data including periods in the 10–51 s range for body waves and 332–2134 s for normal modes. Tomographic results are focused on the 400–2110 km depth range, where our data coverage is the most relevant. We discuss the potential of a better resolution where the grid is fine, compared to spherical harmonics up to degree 40, as the number of model parameters is similar. Our joint model seems to contain coherent structural components beyond degree 40, such as those related to the Farallon subduction. Assessing their robustness is postponed to a future work. A wider application of this tomographic workflow, holding promise to better understand mantle dynamics at various spatial scales, should primarily consist in adding surface-wave data and extending our sets of normal-mode and body-wave data.

Description: The appraisal of tomographic models, of fundamental importance towards better understanding the Earth's interior, consists in analysing their resolution and covariance. The discrete theory of Backus–Gilbert, solving all at once the linear problems of model estimation and appraisal, aims at evaluating weighted averages of the true model parameters. Contrary to damped least-squares techniques, one key advantage of Backus–Gilbert inversion is that no subjective regularization is needed to remove the non-uniqueness of the model solution. Indeed, it is often possible to identify unique linear combinations of the parameters even when the parameters themselves are not uniquely defined. In other words, the non-uniqueness can be broken by averaging rather than regularizing. Over the past few decades, many authors have considered that, in addition to a high computational cost, it could be a clumsy affair in the presence of data errors to practically implement the Backus–Gilbert approach to large-scale tomographic applications. In this study, we introduce and adapt to seismic tomography the Subtractive Optimally Localized Averages (SOLA) method, an alternative Backus–Gilbert formulation which retains all its advantages, but is more computationally efficient and versatile in the explicit construction of averaging kernels. As a leitmotiv, we focus on global-scale S -wave tomography and show that the SOLA method can successfully be applied to large-scale, linear and discrete tomographic problems.

Description: 〈span〉〈div〉SUMMARY〈/div〉We investigate the influence of crust on time residual measurements made by cross-correlation in the 10–51 s filtering period range on a global scale, considering two crustal models: CRUST2.0 and CRUST1.0. This study highlights, in a quantitative way, crust-related time corrections. One part of this correction is directly linked to the body wave traveltime through the crust as predicted by the ray theory, whereas a second part is related to interferences with multiple crustal reflections. This second component, called finite-frequency (FF) crustal correction, is frequency-dependent unlike the ray-theory based correction. We show that if this frequency-dependent crust-related correction is not taken into account in cross-correlation measurements, it may lead to a dispersive effect in S-wave delay-times that could ultimately bias tomographic models. On average, this FF correction increases with the filtering period. Comparisons between the two crustal models highlight the significant dispersive effect of the crust, which has complex patterns depending on geological contexts, with an important role of the sediment thickness. Although ray crustal corrections remain important, FF crustal effects may lead to a bias in measurements if not properly taken into account; on average they may reach 0.9–1.6 s for CRUST2.0 and 0.5–1.6 s for CRUST1.0, for period ranging from 10 to 51 s, respectively.〈/span〉

Description: Global seismic tomography suffers from uncertainties in earthquake parameters routinely published in seismic catalogues. In particular, errors in earthquake location and origin-time may lead to strong biases in measured body wave delay-times and significantly pollute tomographic models. Common ways of dealing with this issue are to incorporate source parameters as additional unknowns into the linear tomographic equations, or to seek combinations of data to minimize the influence of source mislocations. We propose an alternative, physically-based method to desensitize direct S -wave delay-times to errors in earthquake location and origin-time. Our approach takes advantage of the fact that mislocation delay-time biases depend to first order on the earthquake-receiver azimuth, and to second order on the epicentral distance. Therefore, for every earthquake, we compute S -wave differential delay-times between optimized receiver pairs, such that a large part of their mislocation delay-time biases cancels out (for example origin-time fully subtracts out), while the difference of their sensitivity kernels remains sensitive to the model parameters of interest. Considering realistic, randomly distributed source mislocation vectors, as well as various levels of data noise and different synthetic Earths, we demonstrate that mislocation-related model errors are highly reduced when inverting for such differential delay-times, compared to absolute ones. The reduction is particularly rewarding for imaging the upper-mantle and transition zone. We conclude that using optimized receiver pairs is a suitable, low cost alternative to get rid of errors on earthquake location and origin-time for teleseismic direct S -wave traveltimes. Moreover, it can partly remove unilateral rupture propagation effects in cross-correlation delay-times, since they are similar to mislocation effects.

Description: 〈span〉〈div〉SUMMARY〈/div〉This proof-of-concept study presents a parameter-free, linear Backus–Gilbert inversion scheme, tractable for seismic tomography problems. It leads to efficient computations of unbiased tomographic images, accompanied by meaningful resolution and uncertainty informations. Moreover, as there is no need to parametrize the model space in this parameter-free approach, it enables numerically accurate data sensitivity kernels to be effectively exploited in tomographic inversions. This is a major benefit over discrete tomographic methods, for which data sensitivity kernels are often inaccurate, as they are projected on a given model parametrization prior to be exploited in the inversion, and these parametrizations are usually coarse to limit the number of parameters and keep tractable the problems of model estimation and/or appraisal. Therefore, this new tomographic scheme fuels great hopes on better constraining multiscale seismic heterogeneities in the Earth’s interior by exploiting accurate data sensitivity kernels, that is, taking full advantage of known wave-propagation physics, and enabling quantitative appraisals of tomographic features. As a remark, since its computational cost grows as a function of the total number of data squared, it may be better suited to handle moderate-size data sets, typically encountered in regional-scale tomography. Theoretical developments are illustrated within a finite-frequency physical framework. A set of $27\, 070$ teleseismic 〈span〉S〈/span〉-wave time residuals is inverted, with focus on imaging and appraising shear-wave velocity anomalies lying in the mantle below Southeast Asia, in the 350–1410 km depth range.〈/span〉

Description: We study wavefield effects of direct P - and S -waves in elastic and isotropic 3-D seismic structures derived from the temperature field of a high-resolution mantle circulation model. More specifically, we quantify the dispersion of traveltime residuals caused by diffraction in structures with dynamically constrained length scales and magnitudes of the lateral variations in seismic velocities and density. 3-D global wave propagation is simulated using a spectral element method. Intrinsic attenuation (i.e. dissipation of seismic energy) is deliberately neglected, so that any variation of traveltimes with frequency can be attributed to structural effects. Traveltime residuals are measured at 15, 22.5, 34 and 51 s dominant periods by cross-correlation of 3-D and 1-D synthetic waveforms. Additional simulations are performed for a model in which 3-D structure is removed in the upper 800 km to isolate the dispersion signal of the lower mantle. We find that the structural length scales inherent to a vigorously convecting mantle give rise to significant diffraction-induced body-wave traveltime dispersion. For both P - and S -waves, the difference between long-period and short-period residuals for a given source–receiver pair can reach up to several seconds for the period bands considered here. In general, these ‘differential-frequency’ residuals tend to increase in magnitude with increasing short-period delay. Furthermore, the long-period signal typically is smaller in magnitude than the short-period one; that is, wave-front healing is efficient independent of the sign of the residuals. Unlike the single-frequency residuals, the differential-frequency residuals are surprisingly similar between the ‘lower-mantle’ and the ‘whole-mantle’ model for corresponding source–receiver pairs. The similarity is more pronounced in case of S -waves and varies between different combinations of period bands. The traveltime delay acquired in the upper mantle seems to cancel in these differential signals depending on the associated wavelengths and the length scales of structure at shallow depth. Differential-frequency residuals may thus prove useful to precondition tomographic inversions for the lower-mantle structure such as to reduce the influence of the upper mantle for certain length scales. Overall, standard deviations of the diffraction-induced traveltime dispersion between the longest (51 s) and the shortest (15 s) period considered here are 0.6 and 1.0 s for P - and S -waves, respectively. For comparison, the corresponding standard deviations of the 15 s residuals are 1.0 s and 2.8 s. In the lower-mantle model, standard deviations are 0.3 and 0.6 s, respectively, which gives an average lower-mantle contribution to the total dispersion of 50 per cent for P -waves and 60 per cent for S -waves.

Description: 〈span〉〈div〉Summary〈/div〉This proof-of-concept study presents a parameter-free, linear Backus–Gilbert inversion scheme, tractable for seismic tomography problems. It leads to efficient computations of unbiased tomographic images, accompanied by meaningful resolution and uncertainty informations. Moreover, as there is no need to parameterize the model space in this parameter-free approach, it enables numerically accurate data sensitivity kernels to be effectively exploited in tomographic inversions. This is a major benefit over discrete tomographic methods, for which data sensitivity kernels are often inaccurate, as they are projected on a given model parameterization prior to be exploited in the inversion, and these parameterizations are usually coarse to limit the number of parameters and keep tractable the problems of model estimation and/or appraisal. Therefore, this new tomographic scheme fuels great hopes on better constraining multi-scale seismic heterogeneities in the Earth’s interior by exploiting accurate data sensitivity kernels, i.e., taking full advantage of known wave-propagation physics, and enabling quantitative appraisals of tomographic features. As a remark, since its computational cost grows as a function of the total number of data squared, it may be better suited to handle moderate-size data sets, typically encountered in regional-scale tomography. Theoretical developments are illustrated within a finite-frequency physical framework. A set of 27 070 teleseismic 〈span〉S〈/span〉-wave time residuals is inverted, with focus on imaging and appraising shear-wave velocity anomalies lying in the mantle below Southeast Asia, in the 350–1410 km depth range.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉We investigate the influence of crust on time residual measurements made by cross-correlation in the 10–51 s filtering period range on a global scale, considering two crustal models: CRUST2.0 and CRUST1.0. This study highlights, in a quantitative way, crust-related time corrections. One part of this correction is directly linked to the body wave travel time through the crust as predicted by the ray theory , whereas a second part is related to interferences with multiple crustal reflections. This second component, called finite-frequency crustal correction, is frequency-dependent unlike the ray-theory based correction. We show that if this frequency-dependent crust-related correction is not taken into account in cross-correlation measurements, it may lead to a dispersive effect in S-wave delay-times that could ultimately bias tomographic models. On average, this finite-frequency correction increases with the filtering period. Comparisons between the two crustal models highlight the significant dispersive effect of the crust, which has complex patterns depending on geological contexts, with an important role of the sediment thickness. Although ray crustal corrections remain important, finite-frequency crustal effects may lead to a bias in measurements if not properly taken into account; on average they may reach 0.9–1.6 s for CRUST2.0 and 0.5–1.6 s for CRUST1.0, for period ranging from 10–51 s, respectively.〈/span〉

Description: In 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, 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 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 the Earth's mantle.