# Browsing by Subject "Seismic imaging"

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Item A generalized model to estimate the elastic stiffness tensor of mudrocks based on the full strain tensor(2021-05-07) Wiggs, David McLean; Flemings, Peter Barry, 1960-Show more I develop a three-step framework to model the anisotropic elastic properties of a mechanically compacted mudrock based on the full strain tensor. I model the microstructure as an effective medium representative of locally aligned domains of clay grains and fluid filled porosity with isolated quartz. Then I predict the orientation of these building blocks due to the application of any strain field. Finally, the previous two steps are combined to determine an effective medium model for the entire mudrock that predicts the elastic stiffness matrix. I focus on the relationship of deformation to porosity reduction and grain alignment in mudrocks. My results show that the application of axial loading leads to the development of elastic anisotropy with stiffnesses increasing more rapidly in the direction perpendicular to loading. These stiffness predictions closely match experimental data on a mudrock specimen from Eugene Island – Gulf of Mexico. I further apply my three-step framework to predict elastic stiffnesses in a synthetic salt basin based on the full strain tensor predicted by an evolutionary poromechanical model. This coupling allows us to predict elastic stiffnesses and anisotropy due to sediment deposition and non-uniaxial salt loading. Accurate estimation of elastic stiffnesses for mudrocks based on the full strain tensor holds immense potential to improve pressure prediction, seismic imaging in complex geologic environments, and prospect evaluationShow more Item Depth-registration of 9-component 3-dimensional seismic data in Stephens County, Oklahoma(2014-05) Al-Waily, Mustafa Badieh; Hardage, Bob Adrian, 1939-Show more Multicomponent seismic imaging techniques improve geological interpretation by providing crucial information about subsurface characteristics. These techniques deliver different images of the same subsurface using multiple waveforms. Compressional (P) and shear (S) waves respond to lithology and fluid variations differently, providing independent measurements of rock and fluid properties. Joint interpretation of multicomponent images requires P-wave and S-wave events to be aligned in depth. The process of identifying P and S events from the same reflector is called depth-registration. The purpose of this investigation is to illustrate procedures for depth-registering P and S seismic data when the most fundamental information needed for depth-registration – reliable velocity data – are not available. This work will focus on the depth-registration of a 9-component 3-dimensional seismic dataset targeting the Sycamore formation in Stephens County, Oklahoma. The survey area – 16 square miles – is located in Sho-Vel-Tum oilfield. Processed P-P, SV-SV, and SH-SH wave data are available for post-stack analysis. However, the SV-data volume will not be interpreted because of its inferior data-quality compared to the SH-data volume. Velocity data are essential in most depth-registration techniques: they can be used to convert the seismic data from the time domain to the depth domain. However, velocity data are not available within the boundaries of the 9C/3D seismic survey. The data are located in a complex area that is folded and faulted in the northwest part of the Ardmore basin, between the eastern Arbuckle Mountains and the western Wichita Mountains. Large hydrocarbon volumes are produced from stratigraphic traps, fault closures, anticlines, and combination traps. Sho-Vel-Tum was ranked 31st in terms of proved oil reserves among U.S. oil fields by a 2009 survey. I will interpret different depth-registered horizons on the P-wave and S-wave seismic data volumes. Then, I will present several methods to verify the accuracy of event-registration. Seven depth-registered horizons are mapped through the P-P and SH-SH seismic data. These horizons show the structural complexity that imposes serious challenges on well drilling within the Sho-Vel-Tum oil field. Interval Vp/Vs – a seismic attribute often used as lithological indicator – was mapped to constrain horizon picking and to characterize lateral stratigraphic variations.Show more Item Diffraction imaging by path-summation migration(2018-08-07) Merzlikin, Dmitrii; Fomel, Sergey B.; Foster, Douglas J; Ghattas, Omar; Meckel, Timothy A; Sen, Mrinal KShow more Unconventional reservoir characterization requires accurate and high-resolution subsurface images to detect small-scale geological features controlling the production efficiency. Diffraction imaging techniques provide higher lateral resolution images in comparison with the results of conventional reflection imaging and highlight direct responses of such subsurface discontinuities as faults, channel edges, fracture swarms and pinch-outs, distribution of which can be crucial for reservoir development decisions. There are three major challenges in diffraction imaging: reflection/diffraction separation, imaging of diffractions, and de-noising of diffractions. I develop a diffraction imaging workflow based on least-squares inversion and path-summation migration to address these challenges and to improve the robustness of diffraction imaging. Conventional reflection images are dominated by high-energy reflections, which mask diffractions. The challenge of diffraction/reflection separation is to extract diffracted energy by suppressing reflections. Diffraction on an edge has both reflective and diffractive components. Both components should be preserved to generate a diffraction image. I develop azimuthal plane-wave destruction workflow (AzPWD) to account for edge diffraction signatures. The method suppresses high-energy reflections and preserves edge diffractions by orienting plane wave destruction (PWD) filter perpendicular to the edge. Edge orientations are also determined and can be utilized for the interpretation. Diffraction imaging is based on conventional imaging operators tailored towards reflections. I develop analytical expressions for path-summation integral diffraction imaging, which naturally incorporates diffraction apex stationarity under time migration velocity perturbation. This approach allows for determining diffraction likelihood distribution with the approximate cost of only two fast Fourier transforms in a velocity-model-independent fashion. I also develop double-path-summation framework for automatic migration velocity analysis based on diffractions, which does not require picking. Diffraction images are prone to noise and contain reflection remainders after application of reflection-diffraction separation procedure. I address this problem using least-squares migration. I define the inverted forward modeling operator as the chain of three operators: Kirchhoff modeling, plane-wave destruction and path-summation integral filter. This chain of operators accounts for diffraction energy contribution to the least-squares migration misfit dominated by reflections. I propose to use sparsity constraints to penalize diffractions with spiky and intermittent distributions. Reflections are regularized using smoothing along the dominant local slopes in the image domain. I use a shaping regularization framework. The approach decomposes input data into diffractions, reflections and noise. I extend the proposed chain inversion approach to 3D to account for edge diffraction responses by replacing PWD with AzPWD in forward modeling. I penalize edge diffractions using both sparsity constraints and anisotropic diffusion. The first regularization extracts diffractive component of the edge response whereas the second one enforces continuity along the edge to account for the reflective component. Proposed inversion schemes address the challenge of diffraction de-noising and can be treated as imaging operators tailored towards diffractions and extracting edge diffractions in an iterative fashion. The developed workflows allow for diffraction extraction from reflections and noise and for accurate focusing of diffracted energy. Numerous synthetic and field data examples are used to test the performance of the proposed methods. The tests confirm their effectiveness.Show more Item Diffraction imaging for seal evaluation using ultra high resolution 3D seismic data(Marine and Petroleum Geology, 2017-04-01) Klokov, Alexander; Trevino, Ramon H.; Meckel, Timothy A.Show more Item Efficient seismic imaging with the double plane wave data(2015-12-04) Zhao, Zeyu; Sen, Mrinal K.; Stoffa, Paul L., 1948-; Frohlich, Clifford A; Grand, Stephen P; Tatham, Robert H; Nakamura, YosioShow more Seismic imaging is critical in providing the image of the Earth’s subsurface, and it plays an important role in hydrocarbon explorations. Obtaining high resolution images with accurate reflectivities and accurate positions of subsurface structures is the goal for exploration geophysicists. Reverse time migration (RTM), which solves the two-way wave equation, can resolve all wavefield propagation phenomena. In geologically complex regions, RTM has been proven to outperform other imaging methods in correctly revealing the subsurface structures. However, implementing the traditional pre-stack shot profile RTM is computationally expensive. Time consuming wavefield propagation processes need to be performed for each shot gather to obtain high resolution images. The traditional RTM can become extremely expensive with increasing shot numbers. In this dissertation, I focus on improving the migration efficiency of the RTM using the double plane wave (DPW) data, which are the fully decomposed plane wave data. Three RTM methods are developed to migrate the DPW data, all of which can improve the migration efficiency comparing to the traditional shot profile RTM. Two of the methods utilize the adjoint state method, and they are known as the time domain DPW-based RTM and the frequency domain DPW-based RTM. A third migration method using the DPW data is derived under the Born approximation. This method employs the frequency domain plane wave Green’s functions for imaging, and it is named as frequency domain DPW RTM. Among the three proposed RTM methods, the frequency domain DPW RTM is the most efficient. Comparing to the traditional shot profile pre-stack RTM, the frequency domain DPW RTM can increase migration efficiency of RTM by an order of magnitude, making the frequency domain DPW RTM a preferable option for migrating large seismic datasets. All of the three proposed migration methods can image subsurface structures with given dips, which makes them target-oriented imaging methods. The proposed methods are beneficial to migration velocity analysis. To improve the resolution of migration results, a least squares RTM method using the DPW data is proposed. A Born modeling operator that predict the DPW data at the surface and its adjoint operator, which is a migration operator, are derived to implement the least squares RTM. Both of the operators require only a limited number of plane wave Green’s functions for the modeling and the migration processes. The proposed least squares RTM substantially increases the efficiency of the least squares migration. In the DPW domain, the applicability of the reciprocity principle is also investigated. The reciprocity principle can be applied to the seismic data that are processed with proper seismic processing flow. Utilizing the reciprocity principle, a DPW dataset transformed from one-sided shot gathers can approximate a DPW dataset transformed from split-spread shot gathers. Therefore, I suggest that one-sided acquisition geometries should be extended to the largest possible offsets, and the reciprocity principle should be invoked to improve subsurface illumination. Migration efficiency can be further improved with the help of the reciprocity principle.Show more Item Mechanisms of lithospheric failure during late continental rifting and early subduction(2021-08-13) Shuck, Brandon Douglas; Van Avendonk, Harm J. A.; Gulick, Sean P. S.; Bangs, Nathan L.B.; Becker, Thorsten W.; Lavier, Luc L.; Shillington, Donna J.Show more Two fundamental components of plate tectonics are the separation of continents, leading to new ocean basins, and the initiation of subduction zones, which facilitate recycling of the Earth's outer shell into its interior. In order for continental rifting and subduction initiation to succeed, tectonic driving forces must overcome resisting forces and strength of the lithosphere. If achieved, the lithosphere undergoes failure and a new plate boundary is established, wherein subsequent strain is localized along a narrow weak zone, such as a subduction zone megathrust or seafloor spreading center. Though these processes are conceptually straightforward, many aspects remain elusive. In particular, intact lithospheric strength is thought to be far greater than available tectonic forces, yet observationally continental breakup and subduction initiation occur frequently throughout Earth's history. The goal of this dissertation is to further investigate this force paradox by exploring the weakening mechanisms that assist lithospheric failure during late continental rifting and early subduction. Active-source seismic data are used to image geologic processes and the tectonic evolution along two study areas - the Eastern North American Margin and the Puysegur Margin, New Zealand. Along the Eastern North American Margin, I show that new mafic crust was emplaced above a thinning subcontinental mantle lithosphere that resisted breakup despite abundant magmatism. I propose a new model in which continental crust separated before the lithosphere and complete breakup was not achieved for ~25 Myrs after the arrival of melts. I then image mantle dynamics near the lithosphere-asthenosphere boundary during final stages of rifting and show that rupture was enabled by highly organized crystallographic textures that focused melt and deformation into a narrow weak zone. At the Puysegur Margin, I argue that subduction initiation was aided by previous phases of continental rifting and strike-slip. Rifting stretched continental crust of Zealandia and later dextral strike-slip translated thin and dense oceanic crust from farther south and juxtaposed it with thick continental crust at a collisional restraining bend. Ideal conditions ensued, where buoyancy contrasts and pre-existing fault zones weakened the lithosphere and facilitated subduction nucleation. Since initial underthrusting, subduction initiation became more efficient as the trench propagated southward over time. I conclude with a novel 4D model where subduction initiation is resisted at the site of nucleation but followed by mechanically easier and faster initiation and lateral propagation as the plate boundary develops along-strike. Inherited lithospheric heterogeneities and weak zones are the dominant mechanism allowing the plate tectonic cycle to persist on Earth.Show more Item Optimal transport for seismic inverse problems(2018-07-27) Yang, Yunan; Engquist, Björn, 1945-; Fomel, Sergey; Ghattas, Omar; Ren, Kui; Tsai, Yen-Hsi RichardShow more Seismic data contains interpretable information about subsurface properties, which are important for exploration geophysics. Full waveform inversion (FWI) is a nonlinear inverse technique that inverts the model parameters by minimizing the difference between the synthetic data from numerical simulations and the observed data at the surface of the earth. The least-squares norm of this difference is the traditional objective function for FWI, but it is sensitive to the initial model, the data spectrum, the noise in the measurement, and other issues related to optimization. The least-squares norm is a point-by-point comparison. Other misfit functions with a global feature have been proposed in the literature to achieve better convexity, but none of them is technically a metric. Here we apply the quadratic Wasserstein metric of the optimal transport theory to FWI. Both the amplitude differences and the phase mismatches are considered in this new misfit function. Mathematically, we prove the convexity of the quadratic Wasserstein metric concerning shift, dilation, and partial amplitude changes of data as well as its insensitivity to noise. Despite these good properties of the quadratic Wasserstein metric, solving optimal transport problem in higher dimension is challenging. We first compute the misfit globally by regarding it as a 2D optimal transport problem. Since the Monge-Ampère equation is rigorously related to the quadratic Wasserstein metric, we solve the 2D optimal transport problem by solving a fully nonlinear Monge-Ampère equation based on a monotone finite difference solver which has been proved to converge to the viscosity solution. To increase the resolution of the inversion, we further develop another method to compute the quadratic Wasserstein metric: trace-by-trace comparison based on the 1D optimal transport. The 1D technique can be solved accurately and efficiently and thus is more robust to handle more complicated problems with less computational cost. We also explore the connections between optimal transport and other misfit functions and explain the intrinsic features of the transport-based idea. Since optimal transport problem concerns nonnegative measures, we will also investigate the critical data normalization step which transforms the sign-changing wavefields into probability densities. This is the most important topic to address in applying optimal transport to seismic inversion. With the least-squares norm being the misfit function, FWI using the reflection data often results in migration-like features in the model updates. We argue that it is the inherent nonconvexity that prevents it from updating the kinematics with high-frequency data. Through numerical examples and discussions, we demonstrate that the better convexity of the quadratic Wasserstein metric can tackle the local minima generated by the high-wavenumber update which appears in addition to the known cycle-skipping issues caused by phase mismatches.Show more Item Phase-space imaging of reflection seismic data(2014-08) Bashkardin, Vladimir; Fomel, Sergey B.; Stoffa, Paul L., 1948-Show more Modern oil and gas exploration depends on a variety of geophysical prospect tools. One of them is reflection seismology that allows to obtain interwell information of sufficient resolution economically. This exploration method collects reflection seismic data on the surface of an area of prospect interest and then uses them to build seismic images of the subsurface. All imaging approaches can be divided into two groups: wave equation-based methods and integral schemes. Kirchhoff migration, which belongs to the second group, is an indispensable tool in seismic imaging due to its flexibility and relatively low computational cost. Unfortunately, the classic formulation of this method images only a part of the surface data, if so-called multipathing is present in it. That phenomenon occurs in complex geologic settings, such as subsalt areas, when seismic waves travel between a subsurface point and a surface location through more than one path. The quality of imaging with Kirchhoff migration in complex geological areas can be improved if multiple paths of ray propagation are included in the integral. Multiple arrivals can be naturally incorporated into the imaging operator if it is expressed as an integral over subsurface take-off angles. In this form, the migration operator involves escape functions that connect subsurface locations with surface seismic data values through escape traveltime and escape positions. These escape quantities are functions of phase space coordinates that are simply related to the subsurface reflection system. The angle-domain integral operator produces output scattering- and dip-angle image gathers, which represent a convenient domain for subsurface analysis. Escape functions for angle-domain imaging can be simply computed with initial-value ray tracing, a Lagrangian computational technique. However, the computational cost of such a bottom-up approach can be prohibitive in practice. The goal of this work was to construct a computationally efficient phase space imaging framework. I designed several approaches to computing escape functions directly in phase space for mapping surface seismic reflection data to the subsurface angle domain. Escape equations have been introduced previously to describe distribution of escape functions in the phase space. Initially, I employed these equations as a basis for building an Eulerian numerical scheme using finite-difference method in the 2-D case. I show its accuracy constraints and suggest a modification of the algorithm to overcome them. Next, I formulate a semi-Lagrangian approach to computing escape functions in 3-D. The second method relies on the fundamental property of continuity of these functions in the phase space. I define locally constrained escape functions and show that a global escape solution can be reconstructed from local solutions iteratively. I validate the accuracy of the proposed methods by imaging synthetic seismic data in several complex 2-D and 3-D models. I draw conclusions about efficiency by comparing the compute time of the imaging tests with the compute time of a well-optimized conventional initial-value ray tracing.Show more Item Seismic imaging and velocity model building with the linearized eikonal equation and upwind finite-differences(2014-05) Li, Siwei, 1987-; Fomel, Sergey B.Show more Ray theory plays an important role in seismic imaging and velocity model building. Although rays are the high-frequency asymptotic solutions of the wave equation and therefore do not usually capture all details of the wave physics, they provide a convenient and effective tool for a wide range of geophysical applications. Especially, ray theory gives rise to traveltimes. Even though wave-based methods for imaging and model building had attracted significant attentions in recent years, traveltime-based methods are still indispensable and should be further developed for improved accuracy and efficiency. Moreover, there are possibilities for new ray theoretical methods that might address the difficulties faced by conventional traveltime-based approaches. My thesis consists of mainly four parts. In the first part, starting from the linearized eikonal equation, I derive and implement a set of linear operators by upwind finite differences. These operators are not only consistent with fast-marching eikonal solver that I use for traveltime computation but also computationally efficient. They are fundamental elements in the numerical implementations of my other works. Next, I investigate feasibility of using the double-square-root eikonal equation for near surface first-break traveltime tomography. Compared with traditional eikonal-based approach, where the gradient in its adjoint-state tomography neglects information along the shot dimension, my method handles all shots together. I show that the double-square-root eikonal equation can be solved efficiently by a causal discretization scheme. The associated adjoint-state tomography is then realized by linearization and upwind finite-differences. My implementation does not need adjoint state as an intermediate parameter for the gradient and therefore the overall cost for one linearization update is relatively inexpensive. Numerical examples demonstrate stable and fast convergence of the proposed method. Then, I develop a strategy for compressing traveltime tables in Kirchhoff depth migration. The method is based on differentiating the eikonal equation in the source position, which can be easily implemented along with the fast-marching method. The resulting eikonal-based traveltime source-derivative relies on solving a version of the linearized eikonal equation, which is carried out by the upwind finite-differences operator. The source-derivative enables an accurate Hermite interpolation. I also show how the method can be straightforwardly integrated in anti-aliasing and Kirchhoff redatuming. Finally, I revisit the classical problem of time-to-depth conversion. In the presence of lateral velocity variations, the conversion requires recovering geometrical spreading of the image rays. I recast the governing ill-posed problem in an optimization framework and solve it iteratively. Several upwind finite-differences linear operators are combined to implement the algorithm. The major advantage of my optimization-based time-to-depth conversion is its numerical stability. Synthetic and field data examples demonstrate practical applicability of the new approach.Show more