The analysis of seismological observations (e.g., seismic waves, Earth normal modes – the vibrational pattern due to large earthquakes) is a key component to inferring the structure and dynamic processes of the Earth. My research interests include the quantitative study of Earth structure and dynamic processes by inversion of seismological observations and the development of computational methods to elucidate Earth structure. Currently, my specific focus is on developing and applying probabilistic (Bayesian) inversion to achieve better understanding of the structure, composition, and dynamics of the solid Earth interior. While increased data quality, new inference techniques, and increased computational power have improved our understanding of the Earth’s interior, the interpretation of inversion results remains challenging because of inherent nonuniqueness (many models explain the data equally well) and nonlinearities. I assert that rigorous model parameter estimates and uncertainties are required for meaningful physical interpretation. In Bayesian inversion, parameters are considered as random variables and their values are represented by probability densities that express degrees of belief. Parameters are assigned prior information which is independent of the data and updated by data information to produce the inversion result (posterior probability density) from which rigorous parameter values and uncertainties can be inferred.

Core-reflected waves (i.e., PcP and ScP) have been extensively utilized to constrain small-scale structures that exhibit a strong decrease in shear (S)- and compressional (P)- wave velocity above the CMB, known as Ultra Low Velocity Zones (ULVZs). However, the details of extent and fine structure are poorly understood because of the nonuniqueness and nonlinearity of the inverse problem. Therefore, I developed a novel Bayesian approach to constrain ULVZ parameter values and uncertainties. I applied this method to ScP waves recorded by the Hi-Net array (Japan) that sample the CMB beneath the east of Philippines. This study found a complex ULVZ with dense material sitting at the bottom of two layers. An extension of this study generalizes the inversion to consider an unknown model parameterization (i.e. the number of layers and data noise are unknown — a trans-dimensional model). The new study produces more general, but consistent, results than our previous work and, in particular, more meaningful uncertainties which improves comparisons between data sets. Recently, I also applied the trans-dimensional (trans-D) approach to additional waveforms recorded by the Australian transportable array WOMBAT to study an extensive CMB area beneath the east of Australia.

Another project improves the measurement of splitting functions (a visualization of the radial average of the normal-mode sensed structure) for inner core sensitive modes, which are relatively well isolated in frequency, by inversion of normal mode data. Splitting functions depend linearly on isotropic and anisotropic velocities in the Earth. Inner core structure has been extensively studied using normal modes and body waves but is still controversial because of strong non-linearity. Therefore, my project applies nonlinear optimization (neighborhood algorithm — NA) to compute the splitting functions of the 13S2 (spheroidal mode with radial order 13 and angular order 2) mode. For the observed data, the splitting functions of this mode are dominated by zonal structure with positive frequency anomalies near the poles and negative frequency anomalies along the equator. One of the main benefits of the NA approach is that the splitting functions of this mode can be constrained with significantly fewer events in comparison to those using traditional approaches. Limitations of the NA approach are under sampling for higher orders (billions of samples are required) and lack of rigorous uncertainty estimation. To address the limitations, I have adapted the Bayesian ULVZ inversion to this problem and successfully applied for 19 inner-core sensitive modes. I am currently working on the application of this approach to the mantle sensitive modes.

I am also working on the crustal and mantle structure using both radial and transverse components of receiver functions and surface wave dispersions, mainly focused on Himalaya, Afar, and Iran.

Not only the deep Earth structure, I am also involved in the estimation of subsurface structure using spatial autocorrelation (SPAC) of ambient noise. SPAC represents the azimuthal average of normalized cross-correlation of a station at the center of the circle to the stations at the circumference of a circle. The 2-D shape of station geometry is preferred to reduce the directionality of noise. The SPAC method helps to constrain high-resolution subsurface structures (top 10s of meters) depending on the size of the array. In addition to the estimation of the S-wave velocity structure, I am also working on the modeling of electrical resistivity and gravity data to estimate the resistivity and density, respectively. I mostly develop and apply Bayesian inversion of these geophysical measurements to not only constrain the structure but also its uncertainties. Estimation of rigorous uncertainty in the Bayesian framework allows us to make meaningful interpretations of the results.