Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods

We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by ‘banana–doughnut’ kernels which exhibit large, path-dependent variations and even sign changes. P-wave travel-times appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation travel-time anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation travel-time anomaly, and the second a generalized ‘splitting intensity’. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver

Spectral-Element and Adjoint Methods in Seismology

We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem

Adjoint centroid-moment tensor inversions

We determine centroid-moment tensor (CMT) solutions by minimizing waveform differences between observed and simulated seismograms based on an adjoint method. Synthetic seismograms and Fréchet derivatives are calculated based on a spectral-element method. The non-linear adjoint CMT inversion algorithm requires three simulations for each iteration: one ‘forward’ simulation to obtain synthetics for the current source parameters, one ‘adjoint’ simulation which involves injecting time-reversed differences between observed and simulated seismograms as simultaneous virtual sources at each of the receivers, and an extra forward simulation to compute the step length in the conjugate-gradient direction. Whereas the vertical component of the adjoint wavefield reflects the radiation pattern near the centroid location, the components of the adjoint strain tensor capture the elements of the moment tensor. We use the method to determine adjoint CMT solutions for two representative southern California earthquakes using recent 3-D crustal model CVM-6.2. The adjoint CMT solutions are in good agreement with classical Hessian-based CMT solutions involving 3-D Green's functions. In general, adjoint CMT inversions require fewer numerical simulations than traditional Hessian-based inversions. This faster convergence holds promise for multiple moment-tensor and kinematic rupture inversions in 3-D earth models

Spectral-Element Moment Tensor Inversions for Earthquakes in Southern California

We have developed and implemented an automated moment tensor inversion procedure to determine source parameters for southern California earthquakes. The method is based upon spectral-element simulations of regional seismic wave propagation in an integrated 3D southern California velocity model. Sensitivity to source parameters is determined by numerically calculating the Fréchet derivatives required for the moment tensor inversion. We minimize a waveform misfit function, and allow limited time shifts between data and corresponding synthetics to accommodate additional 3D heterogeneity not included in our model. The technique is applied to three recent southern California earthquakes: the 9 September 2001, M_L 4.2 Hollywood event, the 22 February 2003, M_L 5.4 Big Bear event, and the 14 December 2001, M_L 4.0 Diamond Bar event. Using about half of the available three-component data at periods of 6 sec and longer, we obtain focal mechanisms, depths, and moment magnitudes that are generally in good agreement with estimates based upon traditional body-wave and surface-wave inversions

Seismic tomography of the southern California crust based on spectral-element and adjoint methods

We iteratively improve a 3-D tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3-D model is provided by the Southern California Earthquake Center. The data set comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2–30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations. The new crustal model, m_(16), is described in terms of independent shear (V_S) and bulk-sound (V_B) wave speed variations. It exhibits strong heterogeneity, including local changes of ±30 per cent with respect to the initial 3-D model. The model reveals several features that relate to geological observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment

Finite-Frequency Kernels Based on Adjoint Methods

We derive the adjoint equations associated with the calculation of Fréchet derivatives for tomographic inversions based upon a Lagrange multiplier method. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ = ∫ K_m(x) δ ln m(x) d^3x, where δ ln m = δm/m denotes the relative model perturbation and K_m the associated 3D sensitivity or Fréchet kernel. Complications due to artificial absorbing boundaries for regional simulations as well as finite sources are accommodated. We construct the 3D finite-frequency “banana-doughnut” kernel K_m by simultaneously computing the so-called “adjoint” wave field forward in time and reconstructing the regular wave field backward in time. The adjoint wave field is produced by using time- reversed signals at the receivers as fictitious, simultaneous sources, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field, saved by a previous forward simulation, backward in time. The approach is based on the spectral-element method, and only two simulations are needed to produce the 3D finite-frequency sensitivity kernels. The method is applied to 1D and 3D regional models. Various 3D shear- and compressional-wave sensitivity kernels are presented for different regional body- and surface-wave arrivals in the seismograms. These kernels illustrate the sensitivity of the observations to the structural parameters and form the basis of fully 3D tomographic inversions

Time reversal location of glacial earthquakes

In 2003, Ekström et al. reported the detection and location of a new class of earthquakes occurring in the polar regions of the Earth. The proposed source mechanism involves large and sudden sliding motions of glaciers, which gave the name “glacial earthquakes” to these events. In this study we localize some of these earthquakes with a time reversal mirror (TRM) algorithm, which, contrary to ordinary back projection methods, does not involve testing each possible source location. In TRM localization, an earthquake is located on the basis of only one 3-D spectral element simulation of seismic wave propagation by using the full complexity of recorded data as simultaneous time-reversed sources. We show that on the basis of this approach, even glacial earthquakes with a faint signal can be correctly localized and that the pattern of the time-reversed wavefield is coherent with the motion of glaciers down their valley

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the $K_\alpha$ sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels

Toward Waveform-Based Characterization of Slab & Mantle Wedge (SAM) Earthquakes

Earthquakes in subduction zones occur in the slab mantle, in the subducting crust, on the subduction plate interface, and, in some cases, in the mantle wedge–regions that are separated by strong seismic discontinuities. These discontinuities are typically imaged with techniques using teleseismic waves, while local earthquakes are located based on arrival times. While this combination of imaging and earthquake location provides a good initial overview of where the earthquakes are located, the uncertainties associated with the two approaches are too large (i.e., few kilometers) to robustly identify on which side of a discontinuity (with thickness urn:x-wiley:21699313:media:jgrb55116:jgrb55116-math-0001100 m) the earthquakes occurred. Here we investigate how the waveforms of local earthquakes, which contain secondary phases arising from wave scattering at discontinuities, can be exploited to determine the source region of subduction zone earthquakes more robustly. Our investigation involves a three-step approach and includes an application to data from western Greece. First, to identify characteristic secondary phases, we analyzed synthetic seismograms from a generic 2-D subduction zone. Second, to enhance the visibility of secondary phases in field data, we implemented a workflow to process three-component seismograms. Third, to identify individual secondary phases in the data, we matched their timing to arrivals computed in a 3-D velocity model. We identified on average two to three secondary arrivals per station. These include P- and S-reflections from the plate interface which indicate hypocenters in the mantle wedge, and P-reflections from the slab Moho which indicate hypocenters on the plate interface and in the subducting crust.publishedVersio

Simulations of Ground Motion in the Los Angeles Basin Based upon the Spectral-Element Method

We use the spectral-element method to simulate ground motion generated by two recent and well-recorded small earthquakes in the Los Angeles basin. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum-industry well logs and more than 20,000 km of seismic reflection profiles. The numerical simulations account for 3D variations of seismic-wave speeds and density, topography and bathymetry, and attenuation. Simulations for the 9 September 2001 M_w 4.2 Hollywood earthquake and the 3 September 2002 M_w 4.2 Yorba Linda earthquake demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 sec and longer inside the basin model and 6 sec and longer in the regional model. Peak ground displacement, velocity, and acceleration maps illustrate that significant amplification occurs in the basin