## Research

### Global Seismology

Recent advances in high-performance computing and numerical techniques have facilitated fully 3D simulations of global and regional seismic wave propagation at unprecedented resolution and accuracy. The spectral-element method (SEM) has been used for more than two decades in computational ﬂuid dynamics, but it has only recently gained popularity in seismology. Initially the method was applied to 2D seismic wave propagation problems, but currently the SEM is widely used for 3D regional and global simulations. Like a classical ﬁnite-element method, the SEM is based upon an integral or weak formulation of the equation of motion. It combines the accuracy of the global pseudospectral method with the ﬂexibility of the ﬁnite-element method. It has been validated against normal-mode and discrete wavenumber methods and can be used with conﬁdence to simulate global seismic wave propagation in 3D Earth models.

For global and regional simulations, the Theoretical & Computational Seismology research group has developed the open-source SEM package SPECFEM3D_GLOBE.

**Selected publications:**

- Chen, M. and Tromp, J., 2006. "Theoretical and numerical investigations of global and regional seismic wave propagation in weakly anisotropic Earth models."
*Geophys. J. Int.*, 168(3):1130–1152. - Dahlen, F.A., and Tromp, J., 1998. "Theoretical Global Seismology." 1025 pages,
*Princeton University Press*, Princeton, NJ. - Komatitsch, D., and Tromp, J., 2002. "Spectral-element simulations of global seismic wave propagation -II. 3-D models, oceans, rotation, self-gravitation."
*Geophys. J. Int.*, 150, 303–318. - Komatitsch, D., and Tromp, J., 2002. "Spectral-element simulations of global seismic wave propagation -I." Validation,
*Geophys. J. Int.*, 149, 390–412. - Maggi, A., Tape, C., Chen, M., Chao, D., and Tromp, J., 2009. "An automated time window selection algorithm for seismic tomography."
*Geophys. J. Int.*, 178, 257-281. - Tromp, J., Komatitsch, D., and Liu, Q., 2008. "Spectral-element and adjoint methods in seismology."
*Commun. in Comput. Phys.*, 3, 1–32. top

### Regional Seismology

For regional and local earthquake studies, the research group uses the spectral-element method (SEM) to simulate the influence of 3D upper-mantle and crustal structure upon seismic wave propagation. Effects on local-scale wave propagation due to lateral variations in compressional-wave speed, shear-wave speed and density are studied using the software package SPECFEM3D. It was originally developed to simulate southern California seismic wave propagation based upon the spectral-element method, including a 3D crustal model with sedimentary layers, topography and bathymetry.

**Selected publications:**

- Komatitsch, D., and Tromp, J., 1999. "Introduction to the spectral-element method for 3-D seismic wave propagation."
*Geophys. J. Int.*, 139(3):806–822. - Komatitsch, D., Liu, Q., Tromp, J., Süss, P., Stidham, C., and Shaw, J., 2004. "Simulations of strong ground motion in the Los Angeles Basin based upon the spectral-element method."
*Bull. Seismol. Soc. Am.*, 94(1):187–206. - Lovely, P., Shaw, J., Liu, Q., and Tromp, J., 2006. "A structural model of the Salton Trough and its implications for seismic hazard."
*Bull. Seismol. Soc. Am.*, 96:1882–1896. -
Peter, D., D. Komatitsch, Y. Luo, R. Martin, N. Le Goff, E. Casarotti, P. Le Loher, F. Magnoni, Q. Liu, C. Blitz, T. Nissen-Meyer, P. Basini and J. Tromp, 2011. "Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes."
*Geophys. J. Int.*, doi: 10.1111/j.1365-246X.2011.05044.x. top

### Exploration Seismology

The overarching goal of exploration geophysics is to map or “image” geological structures. This involves solving the forward problem for complex seismic models, including acoustic, elastic and poroelastic domains. The ﬁrst stage in such a spectral-element simulation involves the construction of a suitable mesh. One needs to resolve at least ﬁve grid points per shortest wavelength, honor all major discontinuities, and satisfy the Courant stability condition for the time integration scheme. To accomplish this, we divide the model into different regions. The spectral-element mesh honors all ﬁrst-order discontinuities, and based upon this unstructured mesh we simulate the propagation of seismic waves using the spectral-element method (SEM) (Komatitsch and Vilotte. 1998; Komatitsch and Tromp. 1999; Morency and Tromp. 2008). As an example, we use the open-source 2D spectral-element package, SPECFEM2D for our forward (and adjoint) simulations in the SEG/EAGE salt dome model. Current applications involve 3D simulations of seismic wave propagation in complexgeological domains. These developments open the door to tackling then the full 3D inverse problem, i.e., the problem of using the remaining differences between data and synthetics to improve seismic imaging.

**Selected publications:**

- Luo, Y., Zhu, H., Nissen-Meyer, T., Morency, C., and Tromp, J., 2009. "Seismic modeling and imaging based upon spectral-element and adjoint methods."
*The Leading Edge*, May 2009, 568-574. - Morency, C., Luo, Y., and Tromp, J., 2008. "Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels based upon Adjoint Methods."
*Proceedings of the Fourth Biot Conference on Poromechanics.* - Morency, C., Tromp, J., 2008. "Spectral-element simulations of wave propagation in poroelastic media."
*Geophys. J. Int.*, 175, 301-345. top

### Helioseismology

Near-surface supersonic turbulence drives acoustic oscillations in the Sun, whose properties may be utilized to image the opaque solar interior. Techniques of local helioseismology allow us to extract seismic information from the observed noisy solar wavefield. The nature of solar dynamo action and convective turbulence, subsurface structure and dynamics of sunspots, meridional circulation belts, convective penetration at the base of the solar convection zone, rotation anomalies etc. are some of the aspects we wish to image using these helioseismic measurements. The adjoint method in conjunction with modern numerical and inverse methods facilitate tomography of the solar interior. Apart from the interest in precision estimation of exotic stellar physics, a useful practical application is to develop the ability to forecast the emergence of magnetically active regions using helioseismic signatures.

**Selected publications:**

- Gizon, L. and Birch, A. C. 2002. "Time-Distance Helioseismology: The Forward Problem for Random Distributed Sources."
*Astrophysical Journal*, 571, 966. - Gizon, L., Birch, A. C., and Spruit, H. 2011. "Local Helioseismology: Three-Dimensional Imaging of the Solar Interior."
*Annual Review of Astronomy and Astrophysics*, 48, 289. - Hanasoge, S. M., Birch, A. C., Gizon, L., and Tromp, J. 2011. "The Adjoint Method Applied to Time-Distance Helioseismology." Accepted
*Astrophysical Journal*, arXiv eprint 1105.4263. Stable URL: http://arxiv.org/abs/1105.4263. top

### Tomography

The research group's goal is to use the remaining differences between observed and seismograms to improve models of Earth's subsurface and kinematic representations of earthquakes. The objective is to minimize some measure of the remaining differences between data and synthetics. There are numerous ways in which to characterize such differences, e.g., cross-correlation travel-time and amplitude anomalies, multi-taper phase and amplitude measurements, or waveform differences. Thus, for a given model, we are free to consider objective functions that minimize differences between waveforms, travel-times or amplitudes. For tomographic inversions we then calculate the corresponding Fréchet derivatives of such objective functions using our SEM codes.

How does the research group use these ﬁnite-frequency kernels to address the inverse problem? To reduce the computational burden, the adjoint approach is to measure as many arrivals as possible in three component seismograms from all available stations for any given earthquake. Ideally, every component at every station will have a number of arrivals suitable for measurement, for example in terms of frequency-dependent phase and amplitude anomalies. During an adjoint simulation, each component of every receiver will transmit simultaneously its measurements in reverse time, and the interaction between the so generated adjoint waveﬁeld and the forward waveﬁeld results in a misﬁt kernel for that particular event. This earthquake-speciﬁc "event kernel" is essentially a sum of weighted banana-donut kernels, with weights determined by the corresponding measurement, and is obtained based upon just two 3D simulations. In combination with conjugate gradient methods, we are then able to minimize the total misfit in an iterative procedure using all available event kernels, thereby successively increasing the level of detail in our tomographic models.

**Selected publications:**

- Savage, B., Peter, D., Covellone, B., Rodgers, A., and Tromp, J., 2009. "Progress towards next generation, waveform based three-dimensional models and metrics to improve nuclear explosion monitoring in the Middle East."
*Proceedings of the 31th Monitoring Research Review of Ground-Based Nuclear Explosion Monitoring Technologies*, LLNL-PROC-414451, 9 pages. - Tape, C., Liu, Q., Maggi, A., and Tromp, J., 2010. "Seismic tomography of the Southern California crust based upon spectral-element and adjoint methods."
*Geophys. J. Int.*, 180, 433-462. - Tape, C., Liu, Q., Maggi, A., and Tromp, J., 2009. "Adjoint tomography of the Southern California crust."
*Science*, 325, 988-992. top

### Noise Tomography

In the past decade, seismologists have begun using ground perturbations from ocean waves, industrial activity, and storms — collectively known as "noise" — to produce seismic velocity maps of the Earth's interior. What makes this development exciting is that, in many cases, it allows us to resolve Earth structure in finer detail than has been possible through the traditional approach of inverting of earthquake travel times or waveforms. To improve upon existing noise methods, we have developed forward and inverse techniques for noise tomography similar to ones already in place for classical __tomography__. Our approach accounts for the difference between noise cross-correlations and impulse response and avoids simplifying assumptions with regard to ray theory or uniformity of noise sources. We are in the process of applying this new noise tomography technique to both the Earth and the Sun.

**Selected Publications:**

- Tromp, J., Y. Luo, S. Hanasoge, D. Peter, 2010, "Noise cross-correlation sensitivity kernels."
*Geophys. J. Int.*,**183**, 791–819. top

### Imaging

Modern numerical methods and computers have facilitated the accurate and efﬁcient simulation of 3D acoustic, anelastic and poroelastic wave propagation. We have determined how such waveform simulations may be harnessed to improve onshore and offshore seismic imaging strategies and capabilities. We have found that the density sensitivity kernel in adjoint tomography is related closely to the "imaging principle" in exploration seismology, and that in elastic modeling the impedance kernel actually is a better diagnostic tool for reﬂector identiﬁcation. The shear-and compressional-wave speed sensitivity kernels in adjoint tomography are related closely to ﬁnite-frequency banana-doughnut kernels, and these kernels are well suited for mapping larger-scale structure, i.e., for transmission tomography. These ideas have been substantiated by addressing problems in subsalt time-lapse migration.

**Selected publications:**

- Liu, Q., and Tromp, J., 2008. "Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods."
*Geophys. J. Int.*, 174, 265–286. - Luo, Y., Zhu, H., Nissen-Meyer, T., Morency, C., and Tromp, J., 2009. "Seismic modeling and imaging based upon spectral-element and adjoint methods."
*The Leading Edge*, May 2009, 568-574. - Morency C., Luo, Y., and Tromp, J., 2009. "Finite-Frequency Kernels for Wave Propagation in Porous Media based upon Adjoint Methods."
*Geophys. J. Int.*, 179, 1148-1168 - Sieminski, A., Trampert, J., and Tromp, J., 2009. "Principal component analysis of anisotropic finite-frequency sensitivity kernels."
*Geophys. J. Int.*,179, 1186-1198. - Tromp, J., Tape, C., and Liu, Q., 2005. "Seismic tomography, adjoint methods, time reversal, and banana-donut kernels."
*Geophys. J. Int.*, 160, 195–216. - Zhu, H., Luo, Y., Nissen-Meyer, T., Morency, C., and Tromp, J., 2009. "Imaging and Time-Lapse Migration based upon Adjoint Methods."
*Geophysics*, 74, WCA167-WCA177. top

### Time-lapse migration and CO_{2} sequestration monitoring

The research group study time-lapse experiments in which the properties of particular regions of the model change between two subsequent surveys. Time-lapse migration is referred to also as 4D seismic imaging, because it involves not only the spatial distribution of reﬂection coefﬁcients, but also temporal change (the fourth dimension) caused by the ﬂow of ﬂuids. Time-lapse migration is an important tool for carbon sequestration monitoring and for imaging and monitoring induced ﬂuid injections in reservoirs.

**Selected publications:**

- Morency, C., Luo, Y., and Tromp, J., 2011. "Acoustic, elastic and poroelastic simulations of CO
_{2}sequestration crosswell monitoring based on spectral-element and adjoint methods."*Geophys. J. Int.*, 185, 955-966. top

### Global Shakemovie

The research group has developed a near real-time system for the simulation of global earthquakes. Prompted by a trigger from the Global Centroid Moment Tensor (CMT) Project, the system automatically calculates normal-mode synthetic seismograms for the Preliminary Reference Earth Model, and spectral-element synthetic seismograms for 3D mantle model S362ANI in combination with crustal model Crust 2.0. The 1D and 3D synthetics for more than 1800 seismographic stations operated by members of the International Federation of Digital Seismograph Networks are made available through the Global Shakemovie website (shakemovie.princeton.edu) and the Incorporated Research Institutions for Seismology Data Management Center website (IRIS: iris.edu).

**Selected publications:**

- Tromp, J., Komatitsch, D., Hjörleifsdóttir, V., Liu, Q., Zhu, H.,Peter, D., Bozdag, E., McRitchie, D., Friberg, P., Trabant, C., and Hutko, A., 2010. Near real-time simulations of global CMT earthquakes, Geophys. J. Int., in press. top

### Cluster Computing

Research in the group relies heavily on numerical simulations. Currently, they use the Dell cluster Sesame for this purpose. Sesame has 3584 cores, each with 3 GB of memory, for a total of 11 TB of distributed memory. The machine has an Infiniband interconnect and 20 TB of storage.