Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity
Princeton University（普林斯顿大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GéoAzur Université de Nice（尼斯大学地理与地球物理实验室）；Program in Applied and Computational Mathematics Princeton University（普林斯顿大学应用与计算数学项目）
Frederik J. Simons, Ignace Loris, Guust Nolet, Ingrid C. Daubechies, S. Voronin, J. S. Judd, P. A. Vetter, J. Charlety, C. Vonesch
备注：
43 pages, 11 figures, submitted to Geophysical Journal International
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We discuss benefits and drawbacks of these constructions and apply them to analyze the information present in two published seismic wavespeed models of the mantle, for the statistics and power of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the $\ell_2$ norm of data fit and the $\ell_1$ norm on the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our new approach in future inversions of finite-frequency seismic data and show its readiness for global seismic tomography.
In the present paper, the solution of the seismic data inversion problem through multi-objective optimization with NSGA II is addressed. The seismic inversion consists of estimating the slowness of rocks in the subsurface from the travel times of the waves through the transmitters and receivers of the seismic waves. The inversion process uses the multi-objective optimization technique, in which it is necessary to estimate the trade-off between the misfit functional and the stabilizing constraint. The constraint used was the classic first-order Tikhonov. A synthetic model of inclined layers was…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.
In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with wo steps: first, wavelet estimation across all channels and second, refinement of the reflectivity estimate simultaneously in all channels using sparse deconvolution. The reflectivity update step is formulated as a basis pursuit denoising problem and a sparse solution is obtained with the spectral projected-gradient algorithm - faithfulness to the recorded traces is constrained by the measured noise level. Wavelet re-estimation has a closed form …
Ground roll suppression based on the synchrosqueezed wavelet transform and local adaptive subtraction filtering
Chengdu University of Technology（成都理工大学）；State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology（油气藏地质及开发工程国家重点实验室（成都理工大学））；College of Geophysics, Chengdu University of Technology（成都理工大学地球科学学院）；Key Laboratory of Earth Exploration and Information Technology of Ministry of Education, Chengdu University of Technology（教育部地球探测与信息技术重点实验室（成都理工大学））
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed problem. In the framework of Tikhonov regularization theory, in order to replace an ill-posed problem by a well-posed one and to get a unique and stable solution, a stabilizing functional (stabilizer) has to be introduced. The stabilizer selects the desired solution from a class of solutions with a specific physical and/or geometrical property; e.g., the exi…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a convenient way to separate the phase and the amplitude spectrum in a linear fashion. Unfortunately all surface-consistent deconvolutions make a minimum-phase assumption which is likely to be sub-optimal. Recent developments in statistical wavelet estimation demonstrate that nonminimum wavelets can be estimated directly from seismic data, thus offering promise …
Enhancing the frequency bandwidth of the seismic data is always the pursuance at the geophysical community. High resolution of seismic data provides the key resource to extract detailed stratigraphic knowledge. Here, a novel approach, based on deep learning model, is introduced by extracting reflections from well log data to broaden spectrum bandwidth of seismic data through boosting low and high frequencies. The corresponding improvement is observed from the enhancement of resolution of seismic data as well as elimination of sidelobe artifacts from seismic wavelets. During the training stage …
Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant solution to the wavelet estimation problem. Yet a successful implementation has proven difficult. Associated disadvantages like phase unwrapping and restrictions of sparsity in the reflectivity function limit its application. We explore short-time homomorphic wavelet estimation as a combination of the classical homomorphic analysis and log-spectral averagin…
Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. We show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve…
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
IFP Energies nouvelles（IFP能源新动力）；Univ. Paris-Est, LIGM UMR CNRS 8049（巴黎东大学，LIGM UMR CNRS 8049）；Aix-Marseille Univ., I2M UMR CNRS 7373（艾克斯-马赛大学，I2M UMR CNRS 7373）
The so-called "minimum uncertainty" or mu-wavelet approach has been shown to be very effective. Prior work has shown that using special algorithms based on a mu-wavelet decomposition of a seismic signal allows for arrival detection of various waves on a single-component seismogram with good precision. However, the question of interpretation of the type of wave arriving has not been addressed. The problem lies in the fact that the algorithm detects more than two arrivals even on seismograms with little noise, the peaks corresponding to P and S wave arrivals on the indicator function are not alw…
Cross-sphere Coupling and Source Inversion of Ionospheric Disturbances Associated with the 2025 Myanmar Strike-slip Earthquake from BeiDou GEO and Multi-GNSS Observations
Global Structure-Constrained 4D prestack inversion
Chengdu University of Technology（成都理工大学）；State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation（油气藏地质及开发工程国家重点实验室）；Key Laboratory of Earth Exploration & Information Techniques of Ministry of Education（教育部地球探测与信息技术重点实验室）
A new practical and effective source-independent full-waveform inversion with a velocity-distribution supported deep image prior: Applications to two real datasets
Jilin University（吉林大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿业大学）
Reliability-calibrated deep residual full-waveform inversion using geometry-invariant physics encoding: synthetic validation and zero-shot Marmousi-2 testing
Institute of Geophysics, Polish Academy of Sciences（波兰科学院地球物理研究所）；University of Allahabad（阿拉哈巴德大学）；CSIR–National Geophysical Research Institute（印度科学工业研究理事会国家地球物理研究所）
