Preliminary reference earth model

Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

/pdf/an-overview-of-full-waveform-inversion-in-exploration-59sei7fzvh.pdf

An overview of full-waveform inversion in exploration geophysics

▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isos...

GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2) Model and GRACE

GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2)

The conventional magnitude scale M suffers saturation when the rupture dimension of the earthquake exceeds the wavelength of the seismic waves used for the magnitude determination (usually 5–50 km). This saturation leads to an inaccurate estimate of energy released in great earthquakes. To circumvent this problem the strain energy drop W (difference in strain energy before and after an earthquake) in great earthquakes is estimated from the seismic moment M_0. If the stress drop Δσ is complete, W = W_0 = (Δσ/2μ)M_0 ∼ M_0/(2×10^4), where μ is the rigidity; if it is partial, W_0 gives the minimum estimate of the strain energy drop. Furthermore, if Orowan's condition, i.e., that frictional stress equal final stress, is met, W_0 represents the seismic wave energy. A new magnitude scale M_w is defined in terms of W_0 through the standard energy-magnitude relation log W_0 = 1.5M_w + 11.8. M_w is as large as 9.5 for the 1960 Chilean earthquake and connects smoothly to M_s (surface wave magnitude) for earthquakes with a rupture dimension of about 100 km or less. The M_w scale does not suffer saturation and is a more adequate magnitude scale for great earthquakes. The seismic energy release curve defined by W_0 is entirely different from that previously estimated from Ms. During the 15-year period from 1950 to 1965 the annual average of W_0 is more than 1 order of magnitude larger than that during the periods from 1920 to 1950 and from 1965 to 1976. The temporal variation of the amplitude of the Chandler wobble correlates very well with the variation of W_0, with a slight indication of the former preceding the latter. In contrast, the number N of moderate to large earthquakes increased very sharply as the Chandler wobble amplitude increased but decreased very sharply during the period from 1945 to 1965, when W_0 was largest. One possible explanation for these correlations is that the increase in the wobble amplitude triggers worldwide seismic activity and accelerates plate motion which eventually leads to great decoupling earthquakes. This decoupling causes the decline of moderate to large earthquake activity. Changes in the rotation rate of the earth may be an important element in this mechanism.

/pdf/the-energy-release-in-great-earthquakes-27rg7m8mky.pdf

The energy release in great earthquakes

We present tomographic evidence for the existence of deep-mantle thermal convection plumes. P-wave velocity images show at least six well-resolved plumes that extend into the lowermost mantle: Ascension, Azores, Canary, Easter, Samoa, and Tahiti. Other less well-resolved plumes, including Hawaii, may also reach the lowermost mantle. We also see several plumes that are mostly confined to the upper mantle, suggesting that convection may be partially separated into two depth regimes. All of the observed plumes have diameters of several hundred kilometers, indicating that plumes convey a substantial fraction of the internal heat escaping from Earth.

https://science.sciencemag.org/content/sci/303/5656/338.full.pdf

Finite-Frequency Tomography Reveals a Variety of Plumes in the Mantle

Summary

We use body wave ray theory in conjunction with the Born approximation tocompute 3-D Frechet kernels for finite-frequency seismic traveltimes, measured by cross-correlation of a broad-band waveform with a spherical earth synthetic seismogram. Destructive interference among adjacent frequencies in the broad-band pulse renders a cross-correlation traveltime measurement sensitive only to the wave speed in a hollow banana-shaped region surrounding the unperturbed geometrical ray. The Frechet kernel expressing this sensitivity is expressed as a double sum over all forward-propagating body waves from the source and backward-propagating body waves from the receiver to every single scatterer in the vicinity of this central ray. The kernel for a differential traveltime, measured by cross-correlation of two phases at the same receiver, is simply the difference of the respective single-phase kernels. In the paraxial approximation, an absolute or differential traveltime kernel can be computed extremely economically by implementing a single kinematic and dynamic ray trace along each source-to-receiver ray.

/pdf/frechet-kernels-for-finite-frequency-traveltimes-i-theory-2a6ijylcmv.pdf

Fréchet kernels for finite-frequency traveltimes—I. Theory

New finite-frequency tomographic images of S-wave velocity confirm the existence of deep mantle plumes below a large number of known hot spots. We compare S-anomaly images with an updated P-anomaly model. Deep mantle plumes are present beneath Ascension, Azores, Canary, Cape Verde, Cook Island, Crozet, Easter, Kerguelen, Hawaii, Samoa, and Tahiti. Afar, Atlantic Ridge, Bouvet(Shona), Cocos/Keeling, Louisville, and Reunion are shown to originate at least below the upper mantle if not much deeper. Plumes that reach only to midmantle are present beneath Bowie, Hainan, Eastern Australia, and Juan Fernandez; these plumes may have tails too thin to observe in the lowermost mantle, but the images are also consistent with an interpretation as “dying plumes” that have exhausted their source region. In the tomographic images, only the Eifel and Seychelles plumes are unambiguously confined to the upper mantle. Starting plumes are visible in the lowermost mantle beneath South of Java, East of Solomon, and in the Coral Sea. All imaged plumes are wide and fail to show plumeheads, suggesting a very weakly temperature-dependent viscosity for lower mantle minerals, and/or compositional variations. The S-wave velocity images show several minor differences with respect to the earlier P-wave results, including plume conduits that extend down to the core-mantle boundary beneath Cape Verde, Cook Island, and Kerguelen. A more substantial disagreement between P-wave and S-wave images reopens the question on the depth extent of the Iceland plume. We suggest that a pulsating behavior of the plume may explain the shape of the conduit beneath Iceland.

A catalogue of deep mantle plumes: New results from finite‐frequency tomography

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology, and numerical analysis. The spherical Slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap, the spatiospectral projection operator commutes with a Sturm--Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth, the spherical concentration problem reduces to its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.

https://www.jstor.org/stable/pdfplus/20453835.pdf

Spatiospectral Concentration on a Sphere

We use a coupled surface wave version of the Born approximation to compute the 3-D sensitivity kernel K-T(r) of a seismic body wave traveltime T measured by crosscorrelation of a broad-band waveform with a spherical earth synthetic seismogram. The geometry of a teleseismic S wave kernel is, at first sight, extremely paradoxical: the sensitivity is zero everywhere along the geometrical ray! The shape of the kernel resembles that of a hollow banana; in a cross-section perpendicular to the ray, the shape resembles a doughnut. The cross-path extent of such a banana-doughnut kernel depends upon the frequency content of the wave. The kernel for a very high-frequency wave is a very skinny hollow banana; wave-speed heterogeneity wider than this banana affects the traveltime, in accordance with ray theory. We also use the Born approximation to compute the sensitivity kernel K-Delta T(T) Of a differential traveltime Delta T measured by crosscorrelation of two phases, such as SS and S, at the same receiver. The geometries of both an absolute SS wave kernel and a differential SS-S kernel are extremely complicated, particularly in the vicinity of the surface reflection point and the source-to-receiver and receiver-to-source caustics, because of the minimax character of the SS wave. Heterogeneity in the vicinity of the source and receiver exerts a negligible influence upon an SS-S differential traveltime Delta T only if it is smooth

F. A. Dahlen

Papers

Finite-Frequency Tomography Reveals a Variety of Plumes in the Mantle

Fréchet kernels for finite-frequency traveltimes—I. Theory

A catalogue of deep mantle plumes: New results from finite‐frequency tomography

Spatiospectral Concentration on a Sphere

Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana–doughnut paradox