Automating Finite Element Methods for Geodynamics via Firedrake

Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research.

PERFORMANCE OF SITE VELOCITY PREDICTION IN SUNDALAND

Global Positioning System (GPS) technique has been extensively implemented in determination of crustal deformation globally. With the ability of providing solution up to milimeter (mm) level, this technique has proven to provide a precise estimate of site velocity that represents the actual motion of tectonic plate over a period. Therefore, this study aims to evaluate the site velocity estimation from GPS-derived daily position of station, respective to the global plate motion model and predicted site velocity via Least-Squares Collocation (LSC) method within the tectonically active region of Sundaland. The findings have indicated that stations with precise velocity estimates were consistent with global plate model and predicted velocity, with velocity residuals of 5 mm – 10 mm. However, stations that were severely impacted by continuous earthquake events such as in Sumatra were believed to be induced by the impact with consistently large velocity residuals up to 37 mm. Following the outcomes, this study has provided an insight on the post-seismic decay period plate motion which are induced by continuous tectonic activities respective to modelled plate motion.

Numerical Modelling of Lithospheric Block-and-Fault Dynamics: What Did We Learn About Large Earthquake Occurrences and Their Frequency?

Dynamics of lithospheric plates resulting in localisation of tectonic stresses and their release in large earthquakes provides important information for seismic hazard assessments. Numerical modelling of the dynamics and earthquake simulations have been changing our view about occurrences of large earthquakes in a system of major regional faults and about the recurrence time of the earthquakes. Here, we overview quantitative models of tectonic stress generation and stress transfer, models of dynamic systems reproducing basic features of seismicity, and fault dynamics models. Then, we review the thirty-year efforts in the modelling of lithospheric block-and-fault dynamics, which allowed us to better understand how the blocks react to the plate motion, how stresses are localised and released in earthquakes, how rheological properties of fault zones exert influence on the earthquake dynamics, where large seismic events occur, and what is the recurrence time of these events. A few key factors influencing the earthquake sequences, clustering, and magnitude are identified including lithospheric plate driving forces, the geometry of fault zones, and their physical properties. We illustrate the effects of the key factors by analysing the block-and-fault dynamics models applied to several earthquake-prone regions, such as Carpathians, Caucasus, Tibet-Himalaya, and the Sunda arc, as well as to the global tectonic plate dynamics.

Visualization and Sound Measurements of Vibration Plate in a Boiling Bubble Resonator

We developed a boiling bubble resonator (BBR) as a new heat transfer enhancement method aided by boiling bubbles. The BBR is a passive device that operates under its own bubble pressure and therefore does not require an electrical source. In the present study, high-speed visualization of the flow motion of the microbubbles spouted from a vibration plate and the plate motion in the BBR was carried out using high-speed LED lighting and high-speed cameras; the sounds in the boiling chamber were simultaneously captured using a hydrophone. The peak point in the spectrum of the motion of the vibration plate and the peak point in the spectrum of the boiling sound were found to be matched near a critical heat-flux state. Therefore, we found that it is important to match the BBR vibration frequency to the condensation cycle of the boiling bubble as its own design specification for the BBR.

Eocene to Miocene tectonostratigraphic evolution of northwest New Zealand

<p>Reinga Basin is located northwest of New Zealand, along strike structurally from Northland and has a surface area of ~150,000 km². The basin contains deformed Cretaceous and Cenozoic strata, flat unconformities interpreted as sea level-modulated erosion surfaces and is intruded by volcanics. Persistent submarine conditions and moderate water depths has led to preservation of fossil-rich bathyal sedimentary records. This thesis presents the first seismic-stratigraphic analysis tied to dredged rock samples and recent International Ocean Discovery Program (IODP) drilling. The Cenozoic tectonic evolution of Reinga Basin comprises four main phases. (1) Folding and uplift from lower bathyal water depths occurred at 56-43 Ma along West Norfolk Ridge to produce wave ravinement surfaces. This phase of deformation in Reinga Basin pre-dates tectonic events onshore New Zealand. (2) Basin-wide 39-34 Ma compression and reverse faulting exposed early to middle Eocene strata at the seabed. This phase of deformation is also observed farther south in Taranaki. (3) Oligocene uplift is recorded by late Oligocene shallow-water fauna at Site U1508, and led to a 6 Myr hiatus (34-28 Ma) associated with flat wave ravinement surfaces nearby. The unconformity is temporally associated with: normal faulting near West Norfolk Ridge that created topography of Wanganella Ridge; onset of Reinga Basin volcanism; and emplacement of South Maria Allochthon. Thin-skinned deformation and volcanism post-date thick-skinned reverse faulting and folding. The end of reverse faulting near South Maria Ridge is determined from undeformed Oligocene strata that have subsided 1500-2000 m since 36-30 Ma. (4) During the final phase of Reinga Basin deformation, South Maria Ridge subsided ~900-1900 m from middle shelf to bathyal depths from 23-19 Ma. Deformation migrated southeastwards, culminating in Northland Allochthon emplacement (23-20 Ma) and onshore arc volcanism at 23-12 Ma. Eocene onset of tectonic activity in northern New Zealand is shown to be older than previously recognised and it was broadly synchronous with other events related to subduction initiation and plate motion change elsewhere in the western Pacific.</p>

Eocene to Miocene tectonostratigraphic evolution of northwest New Zealand

<p>Reinga Basin is located northwest of New Zealand, along strike structurally from Northland and has a surface area of ~150,000 km². The basin contains deformed Cretaceous and Cenozoic strata, flat unconformities interpreted as sea level-modulated erosion surfaces and is intruded by volcanics. Persistent submarine conditions and moderate water depths has led to preservation of fossil-rich bathyal sedimentary records. This thesis presents the first seismic-stratigraphic analysis tied to dredged rock samples and recent International Ocean Discovery Program (IODP) drilling. The Cenozoic tectonic evolution of Reinga Basin comprises four main phases. (1) Folding and uplift from lower bathyal water depths occurred at 56-43 Ma along West Norfolk Ridge to produce wave ravinement surfaces. This phase of deformation in Reinga Basin pre-dates tectonic events onshore New Zealand. (2) Basin-wide 39-34 Ma compression and reverse faulting exposed early to middle Eocene strata at the seabed. This phase of deformation is also observed farther south in Taranaki. (3) Oligocene uplift is recorded by late Oligocene shallow-water fauna at Site U1508, and led to a 6 Myr hiatus (34-28 Ma) associated with flat wave ravinement surfaces nearby. The unconformity is temporally associated with: normal faulting near West Norfolk Ridge that created topography of Wanganella Ridge; onset of Reinga Basin volcanism; and emplacement of South Maria Allochthon. Thin-skinned deformation and volcanism post-date thick-skinned reverse faulting and folding. The end of reverse faulting near South Maria Ridge is determined from undeformed Oligocene strata that have subsided 1500-2000 m since 36-30 Ma. (4) During the final phase of Reinga Basin deformation, South Maria Ridge subsided ~900-1900 m from middle shelf to bathyal depths from 23-19 Ma. Deformation migrated southeastwards, culminating in Northland Allochthon emplacement (23-20 Ma) and onshore arc volcanism at 23-12 Ma. Eocene onset of tectonic activity in northern New Zealand is shown to be older than previously recognised and it was broadly synchronous with other events related to subduction initiation and plate motion change elsewhere in the western Pacific.</p>

Application of Improved Stereographic Projection Method to Quantify Lithospheric Plate Motion Trajectory

The traditional method of studying plate motion still cannot be used to obtain plate motion trajectory quantitatively. In this paper, we proposed a new method to quantitative determine plate motion trajectory. Depending on the paleomagnetic data of lithosphere plate and the stereographic projection principle. We selected the Wulff net as the basic projection net, improved and transformed the traditional stereographic projection methods. Projecting the paleomagnetic data (magnetic declination, palaeolatitude and geomagnetic pole coordinate) of the lithosphere plate into the improved stereographic projection net, we can get the analysis results of lithosphere plate stereographic projection. In our study, we took the Indian plate as an example, projected the paleomagnetic data (from Cretaceous) into the stereographic projection net, got the analysis results of motion trajectory of the Indian plate from Cretaceous. This method can be applied to quantify lithospheric plate motion trajectory.