Improved full-waveform inversion for seismic data in the presence of noise based on the K-support norm

Full-waveform inversion (FWI) is known as a seismic data processing method that achieves high-resolution imaging. In the inversion part of the method that brings high resolution in finding a convergence point in the model space, a local numerical optimization algorithm minimizes the objective function based on the norm using the least-square form. Since the norm is sensitive to outliers and noise, the method may often lead to inaccurate imaging results. Thus, a new regulation form with a more practical relaxation form is proposed to solve the overfitting drawback caused by the use of the norm,, namely the K-support norm, which has the form of more reasonable and tighter constraints. In contrast to the least-square method that minimizes the norm, our K-support constraints combine the and the norms. Then, a quadratic penalty method is adopted to linearize the non-linear problem to lighten the computational load. This paper introduces the concept of the K-support norm and integrates this scheme with the quadratic penalty problem to improve the convergence and robustness against background noise. In the numerical example, two synthetic models are tested to clarify the effectiveness of the K-support norm by comparison to the conventional norm with noisy data set. Experimental results indicate that the modified FWI based on the new regularization form effectively improves inversion accuracy and stability, which significantly enhances the lateral resolution of depth inversion even with data with a low signal-to-noise ratio (SNR).Comment: 54 pages, 21 figure

Inexact Augmented Lagrangian Method-Based Full-waveform Inversion with Randomized Singular Value Decomposition

Full Waveform Inversion (FWI) is a modeling algorithm used for seismic data processing and subsurface structure inversion. Theoretically, the main advantage of FWI is its ability to obtain useful subsurface structure information, such as velocity and density, from complex seismic data through inversion simulation. However, under complex conditions, FWI is difficult to achieve high-resolution imaging results, and most of the cases are due to random noise, initial model, or inversion parameters and so on. Therefore, we consider an effective image processing and dimension reduction tool, randomized singular value decomposition (rSVD) - weighted truncated nuclear norm regularization (WTNNR), for embedding FWI to achieve high-resolution imaging results. This algorithm obtains a truncated matrix approximating the original matrix by reducing the rank of the velocity increment matrix, thus achieving the truncation of noisy data, with the truncation range controlled by WTNNR. Subsequently, we employ an inexact augmented Lagrangian method (iALM) algorithm in the optimization to compress the solution space range, thus relaxing the dependence of FWI and rSVD-WTNNR on the initial model and accelerating the convergence rate of the objective function. We tested on two sets of synthetic data, and the results show that compared with traditional FWI, our method can more effectively suppress the impact of random noise, thus obtaining higher resolution and more accurate subsurface model information. Meanwhile, due to the introduction of iALM, our method also significantly improves the convergence rate. This work indicates that the combination of rSVD-WTNNR and FWI is an effective imaging strategy which can help to solve the challenges faced by traditional FWI.Comment: 55 Pages, 21 Figure

Dispersion of flexural waves in a borehole with a tensile fracture in an anisotropic stress environment

The effect of tensile fracture in a vertical borehole under anisotropic horizontal stress conditions is numerically investigated in terms of the dispersion of flexural wave generated in dipole sonic logging. Our three-dimensional model comprises a borehole filled with water and a tensile fracture intersecting the borehole in the borehole axial direction. Two shear waves are excited individually to produce particle displacements polarized in two orthogonal radial directions using two dipole sources aligned in the two polarized directions. A vertical array of equispaced dipole sensors is placed at the centre of the borehole along the borehole axis. We assumed that the surrounding formation possesses transversally isotropic anisotropy with the isotropy plane parallel to the borehole axis due to horizontal stress anisotropy. We examined the dispersion of flexural waves travelling along a borehole in our numerical models that include either fast or slow formation with various depths of tensile fractures. Our numerical results show that the deeper the penetration depth of a tensile fracture, the higher the slowness of shear waves polarized perpendicular to the tensile fracture for both slow and fast formation models. Our results indicate that the flexural dispersion behaviour could be used to investigate the depth of penetration of a tensile fracture that can be produced by either drilling or hydraulic fracturing

Numerical Simulation of Hydraulic Fracturing in Enhanced Geothermal Systems Considering Thermal Stress Cracks

With the increasing attention to clean and economical energy resources, geothermal energy and enhanced geothermal systems (EGS) have gained much importance in recent years. For the efficient development of deep geothermal reservoirs, it is crucial to understand the mechanical behavior of reservoir rock and its interaction with injected fluid under high-temperature and high confining pressure environments for employing hydraulic stimulation technologies. In the present study, we develop a novel numerical scheme based on the distinct element method (DEM) to simulate the failure behavior of rock by considering the influence of thermal stress cracks and high confining pressure for EGS. The proposed methodology is validated by comparing uniaxial compression tests at various temperatures and biaxial compression tests at different confining pressures with laboratory experimental results. The numerical results indicate a good agreement in terms of failure models and stress-strain curves with those of laboratory experiments. We then apply the developed scheme to the hydraulic fracturing simulations under various temperatures, confining pressures, and injection fluid conditions. Based on our numerical results, the number of hydraulic cracks is proportional to the temperature. At a high-temperature and low confining pressure environment, a complex crack network with large crack width can be observed, whereas the generation of the micro-cracks is suppressed in high confining pressure conditions. In addition, high-viscosity injection fluid tends to induce more hydraulic cracks. Since the crack network in the geothermal reservoir is an essential factor for the efficient production of geothermal energy, the combination of the above factors should be considered in hydraulic fracturing treatment in EGS

Sensitivity of Deep-Towed Marine Electrical Resistivity Imaging Using Two-Dimensional Inversion: A Case Study on Methane Hydrate

Uncertain physical properties of methane hydrate (MH) above a bottom simulating reflector should be estimated for detecting MH-bearing formations. In contrast to general marine sediments, MH-bearing formations have a relatively high electrical resistivity. Therefore, marine electrical resistivity imaging (MERI) is a well-suited method for MH exploration. The authors conducted sensitivity testing of sub-seafloor MH exploration using a two-dimensional (2D) inversion algorithm with the Wenner, Pole-Dipole (PD) and Dipole-Dipole (DD) arrays. The results of the Wenner electrode array show the poorest resolution in comparison to the PD and DD arrays. The results of the study indicate that MERI is an effective geophysical method for exploring the sub-seafloor electrical structure and specifically for delineating resistive anomalies that may be present because of MH-bearing formations at a shallow depth beneath the seafloor

地震発生帯における深部掘削孔を用いた長期計測

Large earthquakes occur frequently in subduction zones. Most earthquakes are generated in the seismogenic zone, a fairly limited area confined to the shallower regions of the subduction plate boundary. To understand the processes of earthquake generation, it is essential to monitor the physical and mechanical properties of the seismogenic zone over long periods. At present, there are no deep borehole observations of the seismogenic zone more than 3km below seafloor, because it has, until now, been impossible to penetrate to such depths below the sea floor. The Integrated Ocean Drilling Program (IODP), scheduled to begin in 2003, plans to drill boreholes beneath the ocean floor using a multiple-drilling platform operation. The IODP riser-quipped drilling ship (Chikyu) enables the emplacement of boreholes up to 0km beneath the ocean floor, and will provide opportunities to conduct long-term deep borehole observations in the seismogenic zone. Long-term borehole observations in the seismogenic zone are expected to require the development of advanced sampling, monitoring, and recording technology. Here, we discuss the scientific objectives, engineering and technical challenges, and experimental design for a deep borehole, long-term deepborehole monitoring system aimed at understanding the processes of earthquake generation in the seismogenic zone of subduction plate boundaries. We focus specifically on the relationships between environmental conditions in the deep subsurface, details of monitoring and recording, and design and implementation of scientific tools and programs

High-resolution seismic reflection profiling across the Senya fault at Hanaoka, northern Honshu, Japan: Data acquisition and processing

The Senya fault, northern Honshu, Japan, which generated the Rikuu earthquake (Mj 7.2) 1896, is a typical intra-arc active thrust. Subsurface geometry provides essential information for better understanding strong ground motions and crustal deformation processes. A high-resolution seismic reflection survey was conducted along the 63km long seismic line across the toe of the thrust to reveal the subsurface geometry. The seismic source was a Mini-vibrator truck and the receiver interval was 10 m. The seismic data were processed by the standard common mid-point method. The Senya fault is clearly identified as a boundary between horizontal reflectors of the basin fill in the Yokote basin and moderately dipping reflectors beneath the Senya hills. The thrust occurred in late Miocene mudstone, and shows a flat and ramp geometry. The emergent thrust dips 30 degrees down to 500m, and changes its dip to subhorizontal following the distribution of the mudstone