Yuancheng Gung

Crustal magnetization equivalent source model of Mars constructed from a hierarchical multiresolution inversion of the Mars Global Surveyor data

[1] Several magnetic field models of Mars have been constructed since the Mars Global Surveyor data became available. Three distinct schemes formulated through spherical harmonic functions, discrete equivalent dipoles, and the continuous magnetic field kernels have yielded results that are grossly compatible but with very different details. Models of internal potential function in terms of spherical harmonics tend to yield divergent high-degree Mauersberger-Lowes spectra, whereas crustal magnetization models exhibit flat but still significant spectra up to high degrees. To have a better fitting to the observed data seems to have dominated previous efforts that have yielded fine details with wavelengths shorter than the lateral track spacing. The variance-reduction versus model-variance tradeoff analysis is invoked in this study for the determination of the appropriate regularization. Taking advantage of the recently developed multiscale inversion, we are able to conservatively retain only the model components that are robustly constrained by the data rather than unilaterally pushing for a higher degree of fitting. With the variance reduction around 82%, we find that to reach a reasonably fair data fitting without high model variance, the high-degree power spectra of our preferred model exhibit an obvious decaying trend, implying that a lot of the short-wavelength energy embedded within established models is either not robustly resolvable or is of external origin or is simply reflecting the nonuniform distribution of sampling at short scales. The reason that models based on spherical harmonics have greater high-degree power is attributed to the spectral leakage due to the truncated representation. Citation: Chiao, L.-Y., J.-R. Lin, and Y.-C. Gung (2006), Crustal magnetization equivalent source model of Mars constructed from a hierarchical multiresolution inversion of the Mars Global Surveyor data, J. Geophys. Res., 111, E12010, doi:10.1029/ 2006JE002725.

Multiscale Ambient Noise Tomography of Short-Period Rayleigh Waves across Northern Taiwan

Abstract Using the ambient noise cross-correlation technique, we derived empirical Green’s functions (EGFs) of short-period Rayleigh waves from the continuous vertical component of data recorded by 34 seismic stations in northern Taiwan. We measured the group velocity of the EGFs in the frequency range of 0.2–0.5xa0Hz. The derived EGFs and group velocity measurements were carefully examined, and only quality results were used for the tomographic inversion. We implemented a wavelet-based multiscale inversion technique to construct the group velocity map for 0.35-Hz Rayleigh waves in northern Taiwan. The resulting model shows excellent correlation to the surface topography and geological units. To compare with models derived from traditional body-wave tomography, we calculated the group velocity maps and their fit to the noise-derived EGFs for two recent body-wave models. The comparison indicates that body-wave velocities, particularly V S , at shallow depth in the west coast plain are overestimated in two recent body-wave-derived models, and/or a much higher V P / V S ratio may exist for this area. Our results suggest that the noise-derived short-period EGFs may provide important constraints on shallow Earth structure, in complement to that provided by body waves.

Broad‐band Rayleigh wave tomography of Taiwan and its implications on gravity anomalies

[1]xa0We construct the first broad-band surface wave group velocity dispersion maps for the entire island of Taiwan using the ambient seismic noise tomography. Continuous data from three island-wide broad-band networks are used. In particular, taking advantage of the temporary arrays deployed by the TAiwan Integrated GEodynamics Research project (TAIGER), we have collected an unprecedented data amount for the noise tomography in Taiwan. We construct 2D group velocity maps for Rayleigh waves from 4 to 20 seconds using a wavelet-based multi-scale inversion technique. Patterns of lateral variations of our shorter period (<10 seconds) model demonstrate very good correlation with the surficial geology, whereas the overall structure, albeit with much better resolution in the shallow depth, is generally consistent with previously established body wave models. Besides seismic structure, our model also provides vital constraint on resolving the long-lasting controversy about most prominent Bouguer gravity anomaly in central Taiwan, implying that it is likely caused by a deeper mountain root. With regard to various scenarios of the tectonic evolution of Taiwan, our results seem to favor the lithospheric collision model that invokes significant crustal thickening during the collisional orogeny.

Characteristics of short period secondary microseisms (SPSM) in Taiwan: The influence of shallow ocean strait on SPSM

Taking advantage of a unique opportunity provided by a dense array of coastal short-period seismic stations and the diverse bathymetry around Taiwan, we examine how the long-range coherent ambient noises are influenced by surrounding ocean settings using the cross-correlation functions (CCFs) between pairs of stations. The effective energy of the CCFs derived from three components of short-period seismometer data falls within the frequency range of the short period secondary microseism (SPSM). The spatial variations mapped from the amplitude asymmetry of CCFs and source migration images evidently demonstrate that the SPSM strengths are closely linked to the drastic changes in offshore ocean characteristics and result in much stronger SPSM in the shallow and narrow Taiwan Strait than in deep open seas of eastern Taiwan. The temporal variations of the CCF strengths exhibit very good correlations with the wind speeds and wave heights, explicitly indicating the observed SPSM is dominated by local sources generated from wind-driven ocean waves around offshore Taiwan.

Comparative appraisal of linear inverse models constructed via distinctive parameterizations (comparing distinctly inverted models)

[1] Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus-Gilberts theory demonstrates that the resolvable model variation is the truth viewed through the resolution kernel that is woven by the data kernels. The actual numerical resolution amounts to the inversion of the Gram matrix formed by the inner products among data kernels. However, due to the usually sizable amount of data constraints and/or imperfection of the forward theory, the practical implementations are usually tackled through certain a priori finite parameterizations based on rather arbitrary choices of bases such as spatial voxels, splines, spherical harmonics, or spherical wavelets. The cross assessment on the consistency among inverse models parameterized or regularized differently has long been downplayed. It is shown in this study that straightforward conversions among different model representations also enable the direct conversions of the Gram matrices. This leads to significant flexibility in formulating the forward data rule in one representation and then carrying out the actual inversion in an alternate domain. Furthermore, it is also fairly easy to convert both the model covariance and resolution matrices across different representations. These conversions thus enable direct assessments across inverse models obtained via different parameterizations and different regularization schemes. An example utilizing preliminary results of an experiment of ambient noise tomography of a plate boundary region of complex tectonics for the northeast coast and offshore area of Taiwan is shown to demonstrate such comparisons.

Multiscale waveform tomography with two‐step model parameterization

[1]xa0In geophysical tomography, a proper model parameterization scheme for forward modeling is not necessarily a suitable one for the inversion stage, and vice versa. To take full advantage of the merits of parameterization in both stages, we propose a two-step model parameterization approach, in which different model bases for forward computation and inversion are adopted and the basis change is achieved by applying a spatial projection directly to the sensitivity matrix. We demonstrate this approach through an experimental study of waveform tomography for the Pacific upper mantle shear wave structure using first-orbit long-period Rayleigh waves. In the forward modeling, a normal-mode-based nonlinear asymptotic coupling theory is used for the computation of the synthetics and sensitivity matrix, and the model is parameterized in terms of spherical harmonics which provide efficient analytical solutions for path integrals in the forward modeling. Prior to the inversion, the model basis of the sensitivity matrix is transformed to local functions within the study region. After mapping, only local bases around the data sampling path receive effective sensitivities. Accordingly, the computation cost in the inversion is significantly reduced. Furthermore, the two-step model parameterization also adds flexibility to the inversion schemes. In particular, a wavelet-based multiscale inversion is implemented, and its results are compared to simple damping solutions. The general concept and applications of the two-step model parameterization are not restricted to the forwarding modeling technique or model parameterization schemes employed in this experimental study. This approach benefits any inverse problems wherever transformation of model bases helps to better constrain the results.

Constructing empirical resolution diagnostics for kriging and minimum curvature gridding

Resolution analysis is a crucial appraisal procedure in solving general estimation problems, especially for correctly interpreting the results of spatial analysis schemes. Resolution analyses based on the resolving kernels are typically applied to small inverse problems only when the inverse operators are explicitly accessible. Stochastic simulation schemes have been proposed to extract empirical resolution information for solving large inverse problem. In this study, we generalize the formulation of the empirical resolution length and derive the characteristic length of the point spread function for general estimation methods such as minimum curvature gridding and kriging interpolation schemes that are not equipped with explicitly accessible resolving kernels. The implementation of these resolution diagnostics has not been possible in the past and is demonstrated in this study to facilitate clarifying the advantages and limitations of these widely used methods. In addition, we compare these schemes, based on the resolution appraisal, with a multiscale gridding algorithm in the spatial analysis of the Pacific seafloor heat flow observations. By depicting the pattern of the resolution length variations of both the empirical averaging function and the point spread function for each of the estimated models, we demonstrate that schemes equipped with multiscale capability are more favorable for accommodating sparse, nonuniform data distribution than stationary schemes, such as the kriging method. Furthermore, the empirical resolution pattern constructed in this study facilitates the selection of an appropriate reference function and radii of influence for fitting the variogram, which is difficult but critical when using the kriging method.