ALBERT

Description: 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 α 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.

Description: The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.

Description: The study of acoustic emissions (AEs) is of paramount importance to understand rock deformation processes. AE recorded during laboratory experiments mimics, in a controlled geometry and environment, natural and induced seismicity. However, these experiments are destructive, time consuming and require a significant amount of resources. Lately, significant progresses have been made in numerical simulations of rock failure processes, providing detailed insights into AE. We utilized the 2-D combined finite-discrete element method to simulate the deformation of Stanstead Granite under varying confining pressure ( P c ) and demonstrated that the increase of confining pressure, P c , (i) shifts failures from tensile towards shear dominated and (ii) enhance the macroscopic ductility. We quantitatively describe the AE activity associated with the fracturing process by assessing the spatial fractal dimension (D-value), the temporal distribution (AE rate) and the slope of the frequency–magnitude distribution (b-value). Based on the evaluation of D-value and AE rate, we defined two distinct deformation phases: Phase I and Phase II. The influence of P c on the spatial distribution of AE varies according to the deformation phase: for increasing P c , D-value decreases and increases during Phases I and II, respectively. In addition, b-value decreases with increasing P c during the entire experiment. Our numerical results show for the first time that variations of D- and b-values as a function of in situ stress can be simulated using the combined finite-discrete element approach. We demonstrate that the examination of seismicity should be carried out carefully, taking into consideration the deformation phase and in situ stress conditions.

Description: The aim of this study is to improve the temporal resolution of seismic wave velocity variations measured using ambient noise correlations. We first reproduce the result obtained by Chen et al. using a network of 21 broad-band stations ideally located around the fault system activated during the Wenchuan earthquake.We measure a velocity drop of 0.07 per cent that was associated with the main shock, with a temporal resolution of 30 days. To determine whether this velocity drop is co-seismic or post-seismic, we attempt to increase the temporal resolution of our observations. By taking advantage of the properties of the curvelet transform, we increase the signal-to-noise ratio of the daily correlations computed between each station pair. It is then possible to measure the velocity drop associated with the Wenchuan earthquake with a temporal resolution of 1 day. This shows that the velocity drop started on 2008 May 12, which was the day of the earthquake, and the velocity reached its lowest value 2 days after the main shock. Moreover, there was a second velocity drop on 2008 May 27, which might relate to strong aftershocks.

Description: We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation ( t 0 , x s ) and the resulting traveltime residual t of a particular seismic phase, represented by the traveltime sensitivity kernel K ( t 0 , x s ) with respect to the earthquake location ( t 0 , x s ), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K ( t 0 , x s ) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake–receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.

Description: We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation ( t 0 , x s ) and the resulting traveltime residual t of a particular seismic phase, represented by the traveltime sensitivity kernel K ( t 0 , x s ) with respect to the earthquake location ( t 0 , x s ), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K ( t 0 , x s ) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake–receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.

Description: In view of significant discrepancy between the slip models of the 2009 April 6 L'Aquila, (Italy) earthquake based on seismic waveforms or geodetic data, a new inversion strategy is proposed to constrain the coseismic rupture model and early post-seismic afterslip model of this earthquake. Both models were jointly inverted simultaneously from the near-source strong ground motion recordings, teleseismic P waves, long-period Rayleigh waves, GPS displacement vectors and InSAR line-of-sight displacement image. The deformations are mapped onto the fault with strike 140° and dip 50° to the southwest. The coseismic period here represents the first 10 s after the rupture initiation, when over 99 per cent of our total seismic moment (3.07 10 18 Nm) is already released in our preferred coseismic model. Most coseismic slip occurs in a small rupture area of approximately 16 km along strike and in a depth range of 3–10 km. The average slip is 0.45 m; peak slip reaches about 0.90 m. Our result reveals that L'Aquila rupture has a lag of 0.6 s before it first propagates updip to break an asperity equivalent to an M w 5.7. And then the rupture propagates along strike to break a large patch located about 8.0 km along strike and 4.0 km updip from the hypocentre. The weighted average of the rise time and slip velocity are 0.71 s and 0.77 m s –1 , respectively. Our estimate of radiated seismic energy is 1.67 10 13 J, yielding an energy to seismic moment ratio of 0.55 10 –5 , considerably smaller than the global average for shallow earthquakes. The early post-seismic period here represents the time window from 10 s to about first day. During this period, our preferred post-seismic model has an accumulated seismic moment of 6.0 10 17 Nm, equivalent to an M w of 5.8. The afterslip distribution features two separated high slip fault patches, locating either near the hypocentre or the region with peak coseismic slip. Their locations only partially overlap with the fault patches with significant afterslip after the first day. In particular, the slip distribution of the shallower patch is quantitatively consistent with the Amoruso and Crescentini’ diffusive afterslip model. Therefore, the coseismic rupture of the 2009 L'Aquila earthquake was following by a slow-slip event with significant moment release in first hour.

Description: The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of the structured grid. This is similar to the situation for the FDTD method in electromagnetics when it is applied to model a curved perfect conductor surface, where the conformal FDTD methods have been recently developed to avoid this error. In this work a stable and second-order accurate 2-D FDTD method for elastic wave modelling on a curved free surface is presented based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the meantime, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability even for small irregular cells. This method is verified by several 2-D numerical examples. Results show that the method is second-order accurate and stable at the Courant stability limit for a regular FDTD grid.