Nonlinear Frechet derivative and its De Wolf approximation

We introduce and derive the nonlinear Frechet derivative for the acoustic wave equation. It turns out that the high order Frechet derivatives can be realized by consecutive applications of the scattering operator and a zero-order propagator to the source. We prove that the higher order Frechet derivatives are not negligible and the linear Frechet derivative may not be appropriate in many cases, especially when forward scattering is involved for large scale perturbations. Then we derive the De Wolf approximation (multiple forescattering and single backscattering approximation) for the nonlinear Frechet derivative. We split the linear derivative operator (i.e. the scattering operator) onto forward and backward derivatives, and then reorder and renormalize the nonlinear derivative series before making the approximation by dropping the multiple backscattering terms. Numerical simulations for a Gaussian ball model show significant difference between the linear and nonlinear Frechet derivatives.University of California, Santa Cruz (Wavelet Transform on Propagation and Imaging for seismic exploration Research Consortium); Massachusetts Institute of Technology. Earth Resources Laborator

Flexible Spatio-Temporal Hawkes Process Models for Earthquake Occurrences

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space-time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.Comment: 53 page

Crazyseismic: A MATLAB GUI‐Based Software Package for Passive Seismic Data Preprocessing

We introduce an open‐source MATLAB software package, named Crazyseismic, for passive seismic data preprocessing. Built‐in core functions such as seismic phase travel‐time calculation and multichannel cross correlation significantly improve the efficiency of data processing. Compared with conventional command‐line‐style toolboxes, all functions in Crazyseismic are embedded in one single graphic user interface (GUI). The human–machine interactive nature of GUI facilitates data quality control. The simplicity of the software allows users to process Seismic Analysis Code format seismic data with great ease and also provides a means by which users can tailor the software for their specific needs. We demonstrate the power of our software through two field examples: one for P‐wave arrival‐time picking and the other for receiver function calculation. The software can essentially be used for analyzing all major body‐wave phases in seismology

Fracture clustering effect on amplitude variation with offset and azimuth analyses

Traditional amplitude variation with offset and azimuth (AVOAz) analysis for fracture characterization extracts fracture properties through analysis of reflection AVOAz to determine anisotropic parameters (e.g., Thomsen’s parameters) that are then related to fracture properties. The validity of this method relies on the basic assumption that a fractured unit can be viewed as an equivalent anisotropic medium. As a rule of thumb, this assumption is taken to be valid when the fracture spacing is less than λ/10. Under the effective medium assumption, diffractions from individual fractures destructively interfere and only specular reflections from boundaries of a fractured layer can be observed in seismic data. The effective medium theory has been widely used in fracture characterization, and its applicability has been validated through many field applications. However, through numerical simulations, we find that diffractions from fracture clusters can significantly distort the AVOAz signatures when a fracture system has irregular spacing even though the average fracture spacing is much smaller than a wavelength (e.g., ≪λ/10). Contamination by diffractions from irregularly spaced fractures on reflections can substantially bias the fracture properties estimated from AVOAz analysis and may possibly lead to incorrect estimates of fracture properties. Additionally, through Monte Carlo simulations, we find that fracture spacing uncertainty inverted from amplitude variation with offset (AVO) analysis can be up to 10%–20% when fractures are not uniformly distributed, which should be the realistic state of fractures present in the earth. Also, AVOAz and AVO analysis gives more reliable estimates of fracture properties when reflections at the top of the fractured layer are used compared with those from the bottom of the layer

Target-oriented Time-lapse Waveform Inversion using Virtual Survey

Time-lapse seismic data are widely used for monitoring time-variant subsurface changes. Conventional analysis provides qualitative information by comparing results from consecutive surveys, whereas waveform inversion can retrieve quantitative estimates of reservoir properties through seismic waveform fitting. The quantitative evaluation of the physical parameters obtained by waveform inversion allows for better interpretation of fluid substitution and migration during processes like oil and gas production, and carbon sequestration. Since reservoir changes are localized and only part of the data are of interest, the time-lapse waveform inversion can be optimized in terms of computational cost and convergence rate. In this study, we propose a scheme of localized waveform inversion with computed datasets we refer to as virtual surveys. Both the model domain and trace duration in forward modeling are reduced by the reorganization of the data. We show a numerical example in which the recovery of the reservoir change is computationally faster and more robust to source-receiver locations than inversion with original survey