44468-G9
Characterizing Uncertainty Distribution of Ground Surface Responses Caused by an Impulse Excitation
PROGRESS REPORT This research aims at advancing existing inversion methods by establishing a unified, rigorous theoretical framework for complete inversion of surface seismic wave that incorporate uncertainty into elastodynamic inversion via Bayesian inference and genetic algorithm. The need for ground physical properties (velocity, density, stiffness, thickness, Poisson’s ratio) as input for petroleum exploration and engineering design has been well established. Seismic methods have been extensively used in petroleum exploration and engineering design. The principal of seismic methods is to exert an artificial seismic energy source to the ground so that seismic waves can be excited and measured using sensors. The seismic energy source may be a hammer, a drop weight, a harmonic oscillator, or an explosive. The sensor receiving seismic energy is the geophone, either accelerometer or velocity transducers. The experimentally recorded seismic signals are matched with theoretical ground response predicted from elastodynamics for layered media in such a way that the different between the measurement and prediction become minimized in some sense. This matching process is termed inversion or reconstruction, and is implemented via the least square estimation using nonlinear optimization. Site velocity and density profiles are important information obtained from petroleum seismic exploration. Low stiffness soils are associated with the amplification of ground motion during earthquake, and often result in structure damage of great concern to earthquake engineer. The thickness and stiffness of different layers of a pavement system are critical parameters in pavement design and nondestructive evaluation. Seismic methods are the most widely used of all geophysical methods used in petroleum exploration. The main advantage is that it provides the most accurate rendition of the geometry of subsurface layers. Seismic methods measure seismic velocity of rock layers to detect both lateral and depth variations, and to further determine the lithology and geometry of the layers. Commonly used seismic methods include cross-borehole and down hole seismic methods for wave velocity and Young’s modulus, and spectral analysis of surface wave or multi-channel analysis of surface wave for wave velocity profiles. While the former requires drilling, the latter is less expansive, non-invasive and environmental-friendly and will be the focus of this project because it avoids drilling and sampling disturbance and unrepresentative sampling and testing. There exist several shortcomings associated with many of the current inversion methods. First, some inversion methods only utilize phase velocity information and ignore amplitudes of wave propagation. As a result, they are sensitive to only shear velocity because of incomplete use of measured seismic signals. Second, physical models used to represent the earth are assumed to be multilayered media with deterministic layer thickness, isotropic and homogeneous physical properties. In reality, uncertainty arises due to primarily heterogeneity inherent in material and geometric properties. Such uncertainty needs to be quantitatively described in order to improve the accuracy and reliability of the inversion result. Third, nonlinear optimization algorithms used in many existing inversion algorithms are often trapped to local extrema as they rely heavily on gradient information, leading to less effective inversion results. The project consists of four major tasks: (1) establish a physical model to capture dynamic response of a multilayered medium to dynamic excitation; (2) experimentally generate impulsive load to excite ground motion; (3) solve Navier’s equation for surface displacement response of the medium; (4) match the predicted displacement response with the measured displacement response through nonlinear optimization algorithm under the framework of parameter estimation. The research team has completed most of these tasks. Two journal publications have been produced from this project. Four other papers are under preparation or review. Thomson-Haskell transfer matrix method is used for dealing with multiple layers, while fast Fourier transform (FFT) algorithm is used to efficiently compute multifold Laplace transform and Hankel transform. The research team uses a hybrid gradient-based and non-gradient-based (direct search) algorithms to find parameters of the multilayered medium in the framework of least square error in both the time domain and the frequency domain. A sound theoretical foundation for complete inversion of surface seismic wave that takes into account not only the phase but also the amplitude of the received surface seismic response is establishing. It is evident that both the time domain and the frequency domain inversion algorithms show very good performance in terms of estimation accuracy and robustness. The result of the proposed method is reliable and repeatable and has been compared against field test data. The research team plan to conduct a field data collection to investigate variability of layer thickness and modulus by taking samples from highway pavements and construction sites. The field test will be conducted in some newly built highways in China. The principal investigator has made a few connections with colleagues in Chine to arrange such trip and data collection activities.
