Browsing by Subject "Inversion"
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Item Acoustic full-waveform to elastic pre-stack seismic inversion of the Yakutat Terrane, Gulf of Alaska(2018-08-16) Alqatari, Hala; Sen, Mrinal K.The Yakutat-North American collision in the Gulf of Alaska has developed a complex subduction zone followed by major deformations such as the Chugach-St Elias mountain range creation, intensified exhumation, fold and thrust-fault formation. I generate a compressional velocity model of the Yakutat microplate using two-dimensional acoustic and isotropic time-domain full waveform inversion (FWI) of marine seismic reflection and refraction data from the STEEP project (ST. Elias Erosion/tectonics Project). FWI is a non-linear data-fitting algorithm that aims to recover subsurface parameters from the recorded seismic wavefield. Seismic wave propagation along the Yakutat terrane is simulated using a staggered-grid finite difference modeling scheme. Drawbacks associated with FWI is cycle skipping during the minimization process, which results in converging to the wrong velocity model. Starting with a good initial model that contains the low-frequency information can help mitigate this issue. The starting velocity model input to FWI in this case is generated by a traveltime tomographic inversion of ocean-bottom seismometer and streamer seismic data. Data preconditioning includes muting, filtering, noise removal and amplitude rescaling of the field seismic data to match the corresponding amplitudes of the synthetic traces. The forward model is able to produce a good match between the observed and the modeled wavefield within half the propagated wavelength. I use the FWI result, which shows good correlation with the industry well, as an input to two additional seismic inversion methods: acoustic post-stack and elastic pre-stack seismic inversion in order to recover shear impedance and density models along the seismic line. Extending the problem to the elastic medium is important to support more advanced seismic interpretation. Both techniques were able to produce higher-resolution images of the Yakutat terrane that are well correlated with the well response. Structural complexities identified in the generated models include the northwest-dipping Pamplona fault system, the offshore folding zone, thickening of the Yakutat basement and, lastly, significantly lower velocities in the Poul Creek formation compared to the younger Yakataga formation, which may be attributed to high-fluid pressure within that formation.Item Arc-related Mesozoic basins of northern Mexico : their origin, tectonic inversion and influence on ore localization(2016-05) Lyons, James Irwin, 1948-; Kyle, J. Richard; Lawton, Timothy Frost; Cloos, Mark; Horton, Brian K; Elliott, BrentNew structural mapping and radiometric dating in northern Mexico integrated with previous studies indicate the need for revision of current regional tectonic models. The Mezcalera Marginal Basin, an autochthonous Jurassic-Lower Cretaceous basin exposed from southern Arizona to Guerrero replaces accreted terrane models. The lack of significant documentable offsets of this marginal basin provides evidence that contradict proposed major Mexican transform faults in northern Mexico. A left-lateral Cenomanian transpressional fault along which the Caborca and related terranes and offset Bisbee Group strata were displaced is documented by east-directed thrusting of the translated basement and supracrustal strata over the autochthonous Mezcalera Basin strata. Oxfordian (149 Ma) submarine volcanic domes at Batopilas, Chihuahua indicates the Nazas arc of central Mexico migrated across the Mezcalera Marginal Basin, and 124 to 138 Ma dates on Bisbee Group Morita Formation tuffs indicate Alisitos arc volcanism to the west. The well documented Late Cretaceous through Miocene arc migration can thus be projected to the Early Jurassic. Oceanic plate rollback toward the Pacific from the Jurassic through the Early Cretaceous explains the observed arc migration as well as the resulting extension of the Mexican continent. A previously unrecognized intracratonic basin, the Carrizal Basin, a probable northern extension of the Mexican Basin, is documented west of the Chihuahua Basin. The older usage Aldama Platform is divided into the Casas Grandes Platform to the west and the Florida-Aldama Ridge to the east of the Carrizal Basin. Basin inversion as defined by mapping of bivergent out-of-the-basin thrusting along both sides of both the Carrizal and Mexican Intracratonic Basins suggests inversion as the principal tectonic process that produced the Sierra Madre Oriental fold belts. Stratigraphic relationships document the inception of tectonic shortening as Late Cenomanian and a folded 43.7 Ma rhyolite flow at Division de Norte, Chihuahua documents continuing basin inversion well into the Eocene. Previous observations of spatial correlations between structurally complex basin margins and numerous major Cretaceous through Miocene mineral deposits are enhanced by the discovery of the large Cinco de Mayo polymetallic carbonate deposit hosted in stacked west-directed out-of-the-basin thrusting on the west margin of the Carrizal Basin.Item Autoencoders for seismic model upscaling and facies identification(2022-08-12) DeFabry, Cameron Mark; Sen, Mrinal K.; Cardenas, Meinhard B; Spikes, Kyle TThe research presented here focuses on the resolution enhancement of inverted seismic volumes and geological facies identification. In the first section I utilize a regularized neural network in the form of an autoencoder to improve the resolution of seismic models which were inverted for compressional wave impedance. In the second section, I focus on the utilization of autoencoders to classify spatially small geologic facies with inverted seismic models and a computed facies map. In section one I focus on the processing and inversion of seismic data from the 3D Penobscot field on the Scotian shelf to produce models for compressional wave impedance. The dataset is inverted using two different approaches, first using a deterministic method, and secondly using a stochastic method. The stochastically derived models have higher frequency content than the deterministic models and are used as the target for the task of resolution enhancement. An autoencoder is trained to recreate the stochastic models with a set of randomly chosen starting weights. During training the network attempts to create a feature map that correlates the low-resolution deterministic model to the high-resolution stochastic model by using the deterministic models as input data and the stochastic models as target data. Once training is complete the network is given the deterministic model as an input and asked to predict an output with the convolution filters learned by recreating the stochastic models. The result is a model of higher resolution than the original deterministic model, but lower resolution than the original stochastic model. In section two I characterize a seismic volume from the Marco Polo field collected in the Gulf of Mexico and then classify five distinct facies, a shale member, an oil sand member, a gas sand member, and discrete brine sand members corresponding to the sand units. The brine sand members were simulated through fluid substitution and then have their probabilistic properties derived through a rock physics template. Bayesian classification is used to create an initial facies map with the brine sands predicted with rock physics templates, and the remaining units predicted directly from the distributions inherent to the well log. Geologic units less than 600 meters in any direction were specifically targeted by converting the standard facies map into a binary facies map. This binary facies map was used as an input in an autoencoder along with two seismic volumes inverted for compressional wave impedance and Vp/Vs. The result is a trained network that can take inverted model inputs and produce a probabilistic output predicting the location of a given facies. Additionally, when provided with smoothed inputs, the autoencoder can produce outputs of a similar resolution to that of the original data, with a loss of performance noted in the probabilities displayed. This result, along with the result from section one are used to justify the claim that autoencoders can be effectively used for the tasks of seismic model upscaling and facies identification without the direct use of well log data as a network input. Convolutional layers provide a way of processing these data in a manner often seen in image recognition and enhancement problems. These networks are limited to the data they were trained on, so additional training would be required for use on separate datasets. The utilized methods though, should maintain their efficacy provided the appropriate training has taken place.Item Determining seafloor sediment geoacoustic and ripple parameters from simulated transmission loss data through Bayesian parallel tempering inference(2021-12-06) Albritton, James Andrew; Wilson, Preston S.; Gunderson, Aaron M.Geoacoustic inversion of shallow water transmission loss (TL) measurements can be a more convenient way to characterize the seafloor compared to coring or other direct measurements. The Bayesian inversion method of parallel tempering was applied to high-fidelity simulated TL data to determine the viability of inverting for a small parameter set characterizing a rippled seafloor. The algorithm inverts for bulk sediment density, sound speed, attenuation, and sediment ripple amplitude and wavelength. Ripple wavelengths ranging from 1–3.5 m were considered due to their impact on acoustic waves in the kilohertz frequency range. Parallel tempering overcame local entrapment issues encountered by traditional Markov Chain Monte Carlo Metropolis-Hastings sampling with multimodal solutions. Parallel tempering prevents entrapment through state-swapping between parallel inversion chains, which improves parameter space sampling while remaining unbiased. The ray-based model Bellhop was used to evaluate the forward solution. To evaluate the algorithm’s performance, simulated data sets were created using both finite element models and Bellhop, and were then inverted. The algorithm yielded marginal posterior probability distributions for each of the parameters, as well as information about parameter resolvability. It performed well for a range of ripple parameters, acoustic frequencies, waveguide ranges, and source locations. The specific results of each test case and potential ways to improve the overall accuracy and efficiency of the algorithm are discussedItem Development of a new analytical model to interpret inter-well poroelastic pressure transient data(2020-07-17) Elliott, Brendan Michael; Sharma, Mukul M.Pressure interference data between fractured wells in unconventional formations during fracturing has been shown to yield great insights into the geometry of propagating fractures. Interpretation of this pressure response data can be used to estimate key unknown fracture parameters such as azimuth, height, width, and length. This pressure interference is ascribed to the poroelastic impact of the propagating fracture’s stress shadow. Numerical modeling of these measurements using fully coupled geomechanical simulators has been shown to history match field observations. Numerical modeling, however, can be time-consuming and not feasible for application in on-the-fly solutions during the frac treatment. There is a need for simple, high-speed tools that can guide the staff and engineers on location with insight into the position and geometry of the propagating fractures. This work presents a new analytical model that provides a method for quick analysis of the fracture responses from downhole pressure gauges during treatment, validation with fully 3-D coupled numerical modeling, and successful application to field cases. This new analytical model uses the fundamental stress equations for simple fracture geometries (KGD, PKN, and radial fractures) and captures critical characteristics observed in field pressure interference observations. Multiple field stages with offset pressure responses were captured with bottom-hole gauges, interpreted, and detailed in this body of work. A Python code for these analytical stress predictions was developed to make the process user-friendly and adaptable to ever-changing industry needs. The model closely ties these observed field responses to predicted stresses reported from the model and allows for timely interpretation of the pressure data. To further validate the characteristic stress responses observed in the field, fully coupled 3-D poroelastic simulations were also performed with results showing less than 2% error relative to the analytical predictions. Insights into well spacing, fracture geometry, fracture overlap, and stress shadow with varying distances are obtained from the results. This workflow can be employed for near real-time analysis and yield estimates of fracture geometry to greatly advance the field capabilities for on-the-fly fracture design optimization. In an industry with increasing complexity in nearly every model, this work shows that simple ground truth physics and analytical results can be extremely useful tools to make quick, effective decisions with minimal computational resourcesItem Estimation of in-situ fluid properties from the combined interpretation of nuclear, dielectric, optical, and magnetic resonance measurements(2018-12) Lee, Hyungjoo; Torres-Verdín, Carlos; Daigle, Hugh; Heidari, Zoya; Okuno, Ryosuke; Raizen, MarkDuring the last few decades, the quantification of hydrocarbon pore volume from borehole measurements has been widely studied for reservoir descriptions. Relatively less effort has been devoted to estimating in-situ fluid properties because (1) acquiring fluid samples is expensive, (2) reservoir fluids are a complex mixture of various miscible and non-miscible phases, and (3) they depend on environmental factors such as temperature and pressure. This dissertation investigates the properties of fluid mixtures based on various manifestations of their electromagnetic properties from the MHz to the THz frequency ranges. A variety of fluids, including water, alcohol, alkane, aromatics, cyclics, ether, and their mixtures, are analyzed with both laboratory experiments and numerical simulations. A new method is introduced to quantify in-situ hydrocarbon properties from borehole nuclear measurements. The inversion-based estimation method allows depth-continuous assessment of compositional gradients at in-situ conditions and provides thermodynamically consistent interpretations of reservoir fluids that depend greatly on phase behavior. Applications of this interpretation method to measurements acquired in two field examples, including one in a gas-oil transition zone, yielded reliable and verifiable hydrocarbon compositions. Dielectric properties of polar liquid mixtures were analyzed in the frequency range from 20 MHz to 20 GHz at ambient conditions. The Havriliak-Negami (HN) model was adapted for the estimation of dielectric permittivity and relaxation time. These experimental dielectric properties were compared to Molecular Dynamics (MD) simulations. Additionally, thermodynamic properties, including excess enthalpy, density, number of hydrogen bonds, and effective self-diffusion coefficient, were computed to cross-validate experimental results. Properties predicted from MD simulations are in excellent agreement with experimental measurements. The three most common optical spectroscopy techniques, i.e. Near Infrared (NIR), Infrared, and Raman, were applied for the estimation of compositions and physical properties of liquid mixtures. Several analytical techniques, including Principal Component Analysis (PCA), Radial Basis Functions (RBF), Partial Least-Squares Regression (PLSR), and Artificial Neural Networks (ANN), were separately implemented for each spectrum to build correlations between spectral data and properties of liquid mixtures. Results show that the proposed methods yield prediction errors from 1.5% to 22.2% smaller than those obtained with standard multivariate methods. Furthermore, the errors can be decreased by combining NIR, Infrared, and Raman spectroscopy measurements. Lastly, the ¹H NMR longitudinal relaxation properties of various liquid mixtures were examined with the objective of detecting individual components. Relaxation times and diffusion coefficients obtained via MD simulations for these mixtures are in agreement with experimental data. Also, the ¹H-¹H dipole-dipole relaxations for fluid mixtures were decomposed into the relaxations emanate from the intramolecular and intermolecular interactions. The quantification of intermolecular interactions between the same molecules and different molecules reveals how much each component contributes to the total NMR longitudinal relaxation of the mixture as well as the level of interactions between different fluids. Both experimental and numerical simulation results documented in this dissertation indicate that selecting measurement techniques that can capture the physical property of interest and maximize the physical contrasts between different components is important for reliable and accurate in-situ fluid identificationItem Estimation of static and dynamic petrophysical properties from well logs in multi-layer formations(2011-08) Heidari, Zoya; Torres-Verdín, Carlos; Sepehrnoori, Kamy; Peters, Ekwere J.; Preeg, William E.; Schneider, Erich A.Reliable assessment of static and dynamic petrophysical properties of hydrocarbon-bearing reservoirs is critical for estimating hydrocarbon reserves, identifying good production zones, and planning hydro-fracturing jobs. Conventional well-log interpretation methods are adequate to estimate static petrophysical properties (i.e., porosity and water saturation) in formations consisting of thick beds. However, they are not as reliable when estimating dynamic petrophysical properties such as absolute permeability, movable hydrocarbon saturation, and saturation-dependent capillary pressure and relative permeability. Additionally, conventional well-log interpretation methods do not take into account shoulder-bed effects, radial distribution of fluid saturations due to mud-filtrate invasion, and differences in the volume of investigation of the various measurements involved in the calculations. This dissertation introduces new quantitative methods for petrophysical and compositional evaluation of water- and hydrocarbon-bearing formations based on the combined numerical simulation and nonlinear joint inversion of conventional well logs. Specific interpretation problems considered are those associated with (a) complex mineral compositions, (b) mud-filtrate invasion, and (c) shoulder-bed effects. Conventional well logs considered in the study include density, photoelectric factor (PEF), neutron porosity, gamma-ray (GR), and electrical resistivity. Depending on the application, estimations yield static petrophysical properties, dynamic petrophysical properties, and volumetric/weight concentrations of mineral constituents. Assessment of total organic carbon (TOC) is also possible in the case of hydrocarbon-bearing shale. Interpretation methods introduced in this dissertation start with the detection of bed boundaries and population of multi-layer petrophysical properties with conventional petrophysical interpretation results or core/X-Ray Diffraction (XRD) data. Differences between well logs and their numerical simulations are minimized to estimate final layer-by-layer formation properties. In doing so, the interpretation explicitly takes into account (a) differences in the volume of investigation of the various well logs involved, (b) the process of mud-filtrate invasion, and (c) the assumed rock-physics model. Synthetic examples verify the accuracy and reliability of the introduced interpretation methods and quantify the uncertainty of estimated properties due to noisy data and incorrect bed boundaries. Several field examples describe the successful application of the methods on (a) the assessment of residual hydrocarbon saturation in a tight-gas sand formation invaded with water-base mud (WBM) and a hydrocarbon-bearing siliciclastic formation invaded with oil-base mud (OBM), (b) estimation of dynamic petrophysical properties of water-bearing sands invaded with OBM, (c) estimation of porosity and volumetric concentrations of mineral and fluid constituents in carbonate formations, and (d) estimation of TOC, total porosity, total water saturation, and volumetric concentrations of mineral constituents in the Haynesville shale-gas formation. Comparison of results against those obtained with conventional petrophysical interpretation methods, commercial multi-mineral solvers, and core/XRD data confirm the advantages and flexibility of the new interpretation techniques introduced in this dissertation for the quantification of petrophysical and compositional properties in a variety of rock formations.Item Fast methods to model the response of fluid-filled fractures and estimate the fracture properties(2018-11-21) Alulaiw, Badr Abdullah; Sen, Mrinal K.; Spikes, Kyle T; Fomel, Sergey; Grand, Stephen P; Foster, DouglasEstimation of fracture orientation and properties has become an important part of seismic reservoir characterization especially in unconventional reservoirs because of the crucial role of fractures in enhancing the permeability in tight reservoirs. The presence of fluid inside the fractures affects their seismic response. Using equivalent medium theories, seismic wave signatures such as Amplitude Variation with Offset and azimuth (AVOz), Normal Moveout (NMO) correction and shear waves splitting have been used to detect the presence of gas-filled and fluid-filled fractures. These methods, however, are unable to specify the type of fluid inside the fractures and cannot be used for thin beds and complex geology where the subsurface properties change laterally. Hence, modeling the seismic waveform using numerical methods is inevitable. The main limitation of those methods is their high computation costs. In this dissertation, I focus on developing two fast numerical methods to model the response of fluid-filled fractures as well as one fast global optimization method to estimate the fracture properties. Although local optimization methods are computationally cheap, the probability of being trapped in a local minimum becomes high when the initial model is not close to the global minimum especially when applied to highly nonlinear problems. Quantum Annealing (QA) is a recent global optimization method that was shown to be faster than Simulated Annealing (SA) in many situations. QA has been recently applied to geophysical problems. In this research, I modify QA by proposing using a new kinetic term that helps QA converge faster to the global minimum. With a synthetic dataset, I illustrate that QA is faster than Very Fast Simulated Annealing (VFSA) using a highly non-linear forward model that computes the response of seismic Amplitude Variation with Angle (AVA) for spherical waves. Most AVA inversion algorithms are based on plane wave solutions whereas seismic surveys use point sources to generate spherical waves. Although the plane wave solution is an excellent approximation for spherical waves, this approximation breaks down in the vicinity of the critical angle. Here, I implement an AVA inversion method for three parameters (P-wave velocity, S-wave velocity and density) based on analytical approximation for spherical waves. In addition, I apply this algorithm to a 2D seismic dataset from Cana field, Oklahoma with the primary objective of resolving the Woodford formation. I compare the results with those obtained by a local optimization method. The results clearly demonstrate superior performance of the proposed inversion method over that of local optimization. Specifically, the inverted images show clear delineation of the Woodford formation. For a reservoir containing vertical and rotationally invariant fractures, the linear slip model characterizes the reservoir using four properties: two elastic properties describing the isotropic host rock and two fracture properties – normal ΔN and tangential ΔT fracture weaknesses. This model, however, ignores the pore porosity effect on the anisotropy and hence the fracture properties might be inaccurate. In this work, I estimate the fracture properties as well as pore porosity using a new expression for the stiffness tensor for a porous fractured medium. I use the ray-Born approximation to calculate the seismic response of a laterally varying porous reservoir and QA to estimate the fracture properties. Using numerical experiments, I compare the inversion results from both unconstrained and constrained simultaneous (PP and PSV components) seismic inversion as well as constrained inversion using only the PP component. I explain the importance of including a constraint to mitigate the effect of the equivalence problem between ΔN and porosity. Unlike the unconstrained inversion, the estimated properties from the constrained inversion are acceptable. Also, I illustrate that the simultaneous constrained inversion is more robust than using the PP component alone. I apply this algorithm to a 3D multicomponent seismic dataset acquired in Saudi Arabia. The estimated fracture orientation agrees with those obtained in previous studies using borehole image logs, oriented cores, drilling observation and seismic in the same area. Also, the computed porosity using available well logs matches the inverted porosity very well. Computationally cheap analytical methods and equivalent medium theories available to model seismic wavefields diffracted by multiple fluid-filled fractures are not capable of handling complex fracture models or wave multi-scattering. Hence, using expensive numerical methods is inevitable. The advantages of boundary element method (BEM) over domain methods, such as finite difference and finite element methods, include the ease of handling irregular fracture geometry and reduction of the problem dimensions making the computation fast. Moreover, BEM models the complete wavefield including multiples, reverberations and refracted waves inside the fractures. The downside of BEM is that the computation cost increases rapidly whenever we increase the number of boundary elements making these methods computationally inefficient to model a large number of 2D cracks or 3D fractures. By combining the Indirect Boundary Element Method (IBEM) and a Generalized Born Series (GBS), I propose a new algorithm that can compute the response of 3D fluid-filled fracture sets effectively. In addition, when I consider equally spaced fractures that have the same geometry within a fracture set, computation can be performed even more rapidly. I compare the wavefield obtained using this approximation in five numerical experiments with those obtained from IBEM and show that the results are accurate in many situations.Item Feasibility of isotropic inversion in orthorhombic media : the Barrett unconventional model(2016-05) Yanke, Andrew James; Spikes, Kyle; Sen, Mrinal K; Fomel, Sergey BGeophysicists often relegate shale reservoirs as having higher symmetries (e.g., transversely isotropic (TI) or isotropic) than what reality demonstrates. Routine application of TI (or even isotropic) algorithms to orthorhombic media neglects the associated errors because we never know the true model in practice. This thesis evaluates the viability of isotropic post-stack and pre-stack seismic inversion to orthorhombic media using the SEAM Barrett Unconventional Model, the most realistic depositional model to date. The Barrett Model contains buried topography, simulated stratigraphy, and designated reservoir zones with orthorhombic anisotropy. I inverted the Barrett data volume for isotropic elastic property cubes, which I compared to the model volume in each symmetry-plane of an orthorhombic medium. If the stacked seismic data contained only the near offsets, post-stack inversion resolved acoustic impedances that closely matched the true model both within and outside of the reservoir zones at all well locations. Anisotropy most affected the far offsets, so muting them predictably enhanced the post-stack inversion. I maintained all offsets for pre-stack inversion, but a parabolic radon filter eliminated nonhyperbolic behavior (rather than nonhyperbolic moveout analysis) at far offsets. The pre-stack impedance attributes adequately described the vertical heterogeneity of the true model at a cross-validation well, but the inverted values increasingly relied on the initial model with depth. The inverted density estimates experienced notable oscillations relative to the initial model, particularly where steep contrasts in elastic properties occurred. Mismatch of the inverted elastic properties at the well locations can be attributed to noise, thin layering effects, band limitation, steep contrasts in elastic properties, AVO behavior stacked into the data, an inaccurate starting model, and the effects of anisotropy. The most significant sources of error include small-scale reflectivity and comprehensive filtering of nonhyperbolic phenomena. Away from the well locations, the isotropic inversion gave no visual indication of reservoir geobodies, but it sufficiently described the elastic property variations near reservoir mid-sections. Moreover, I showed that the inverted elastic properties differ from their orthorhombic models by no more than 35%. The greatest misfits occurred near reservoir contacts and geobody locations. The computed impedance models in each symmetry-plane have distinctive differences, but isotropic inversion dismisses these variations entirely. I conclude that isotropic inversion should not be a surrogate for orthorhombic methods in data preconditioning and quantitative reservoir characterization.Item Fluid Characterization at the Cranfield CO₂ Injection Site : Quantitative Seismic Interpretation from Rock-Physics Modeling and Seismic Inversion(2014-12) Carter, Russell Wirkus; Spikes, KyleThis dissertation focuses on quantitatively interpreting the elastic properties of the Cranfield reservoir for CO₂ saturation. In this work, quantitative interpretation starts by examining the relationship between CO₂ saturation and the elastic properties of the reservoir. This relationship comes from a rock-physics model calibrated to measured well data. Seismic data can then be inverted using a model for CO₂ saturation and rock-property estimates. The location and saturation of injected CO₂ are important metrics for monitoring the long-term effectiveness of carbon capture utilization and storage. Non-uniform CO₂ saturation is a contributing factor to both lateral and time-lapse changes in the elastic properties of the Cranfield reservoir. In the Cranfield reservoir, CO₂ saturation and porosity can be estimated from the ratio of P-wave velocity (Vp) to S-wave velocity (Vs) and P-impedance (Ip), respectively. Lower values of Ip for a given rock matrix often correlate to higher porosity. Similarly, for a given area of the reservoir, lower Vp/Vs frequently can be associated with higher CO₂ saturation. If a constant porosity from the baseline to the time-lapse survey is assumed, changes in Ip over time can be attributed to changes in CO₂ saturation in lieu of using Vp/Vs. Decreases in Ip between the baseline and time-lapse survey can be attributed to increases in CO₂ saturation. With a rock-physics model calibrated to the reservoir, Ip and Is from a vertical seismic profile were correlated to statistical ranges of porosity and CO₂ saturations. To expand the lateral interpretation of reservoir porosity and CO₂ saturation, the time-variant changes in Ip between baseline and time-lapse surface seismic datasets were compared to changes in CO₂ saturation calculated from the rock-physics model. Characterizing the CO₂ saturation of the Tuscaloosa sandstones helped to establish a workflow for estimating reservoir properties and fluid saturation from multiple types of geophysical data. Additionally, this work helped establish an understanding for how CO₂ injected into a reservoir alters and changes the elastic properties of the reservoir and the degree to which those changes can be detected using geophysical methods.Item Improving resolution of NMO stack using shaping regularization(2016-05) Regimbal, Kelly Alaine; Fomel, Sergey B.; Zahm, Christopher Kent; Spikes, KyleCommon midpoint (CMP) stacking is one of the major steps in seismic data processing. Traditional CMP stacking sums a combination of normal moveout (NMO) corrected traces across a CMP gather to produce a single trace with a higher signal-to-noise (S/N) ratio than that of individual traces within the gather. Several problems arise with the assumptions and principles of conventional NMO and stack. NMO correction causes undesirable distortions of signals on a seismic trace known as "NMO stretch", which lowers the frequency content of the corrected reflection event at far offsets. This violates the assumption of a uniform distribution of phase and frequency of seismic reflections across the corrected gather. Common procedures to eliminate this stretching effect involve muting all of the samples with severe distortions. This causes a decrease in fold and can destroy useful far-offset information essential for amplitude variation with offset (AVO) analysis. Inaccuracy in stretch muting with residual "stretching" effects produces a lower amplitude and lower resolution stack. I present two methods that eliminate the effects of "NMO stretch" and restore a wider frequency band by replacing conventional NMO and stack with a regularized inversion to zero offset. The resulting stack is a model that best fits the data using additional constraints imposed by the method of shaping regularization. Shaping regularization implies a mapping of the input model to a space of acceptable models. The shaping operator is integrated in an iterative inversion algorithm and provides an explicit control on the estimated stack. I use shaping regularization to achieve a stack that has a denser time sampling and contains higher frequencies than the conventional stack. In the first approach, I define the backward operator of shaping regularization using the principles of conventional NMO correction and stack. In the second approach, I introduce a recursive stacking scheme using plane-wave construction in the backward operator of shaping regularization. The advantage of using recursive stacking along local slopes in the application to NMO and stack is that it avoids "stretching" effects caused by NMO correction and is insensitive to non-hyperbolic moveout in the data. Numerical tests demonstrate each algorithm's ability to attain a higher frequency stack with a denser temporal sampling interval compared to those of the conventional stack and to minimize stretching effects caused by NMO correction. I apply both methods to two 2-D marine datasets from the North Sea and achieve noticeable resolution improvements in the stacked sections compared with that of conventional NMO and stack. By treating NMO and stack as an iterative inversion using shaping regularization, resolution is enhanced by utilizing signal from different offsets and minimizing stretching effects to reconstruct a high resolution stack.Item Invasion-consistent interpretation of multi-dimensional magnetic resonance measurements(2013-12) Lee, Hyungjoo; Torres-Verdiń, CarlosThis thesis introduces a workflow to accomplish invasion-consistent Nuclear Magnetic Resonance (NMR) measurement interpretations. Magnetic resonance measurements are affected by mud-filtrate invasion because the radial depth of investigation (DOI) of NMR logging tools is very shallow (approximately 1 to 4 inches). This characteristic indicates that identification of in-situ fluid saturations from NMR measurements is uncertain. Calculation of fluid saturations from apparent electrical resistivities and nuclear logs does not guarantee a precise estimation of the fluid distributions. Free water in the reservoir displaced by oil based mud (OBM) poses more challenges in the estimation of in-situ fluid saturations. To mitigate this ambiguity, I construct layer-by-layer static and dynamic reservoir models. The common stratigraphic framework (CSF) proposed by Voss et al. (2009) was used to construct the earth model. Appraisal of static petrophysical properties is based on the iterative adjustments to minimize the discrepancy between available well logs and their numerical simulations. Evaluation of dynamic petrophysical properties can be achieved with the simulation of mud-filtrate invasion. This simulation can assess accurate fluid saturations at specific radial distances. In addition, numerically simulated apparent resistivity and nuclear logs are in agreement with measured logs. Algorithms are also developed to cross-validate NMR measurements based on the assumption of spherically shaped water-wet pores. The algorithms need all petrophysical parameters and fluid saturations yielded from the dynamic model as inputs. Various NMR parameter changes were tested to validate this algorithm. Examples of NMR responses include wettability change and kerogen contained in nano-scale pores. For the field case examples, two 15 meter-thick depth intervals in oil- and gas-bearing siliciclastic formations were selected. Two-dimensional (2D) NMR simulations were performed with petrophysical parameters provided from the numerical simulation of mud-filtrate invasion. The 2D NMR maps are more favorable in fluid typing than conventional NMR T₂ distributions because they contrast fluid diffusion coefficient. Comparisons of simulation results to inversion results confirm the validity of the workflow introduced in this thesis for the quantification of virgin reservoir fluids and mud-filtrate saturations. Finally, forward modeling and inversion processes are applied to 2D NMR data. The reconstructed echo decay sequences are more advantageous than raw measurements because of their higher signal to noise ratio (SNR). Linear inversion using these echo decay sequences provides proton density distribution functions of D-T₂ and T₁-T₂ maps. Application of inversion to the two field cases measured from two different radial depths verifies the validity of the NMR interpretations.Item Inversion-based petrophysical interpretation of logging-while-drilling nuclear and resistivity measurements(2013-08) Ijasan, Olabode; Torres-Verdín, CarlosUndulating well trajectories are often drilled to improve length exposure to rock formations, target desirable hydrocarbon-saturated zones, and enhance resolution of borehole measurements. Despite these merits, undulating wells can introduce adverse conditions to the interpretation of borehole measurements which are seldom observed in vertical wells penetrating horizontal layers. Common examples are polarization horns observed across formation bed boundaries in borehole resistivity measurements acquired in highly-deviated wells. Consequently, conventional interpretation practices developed for vertical wells can yield inaccurate results in HA/HZ wells. A reliable approach to account for well trajectory and bed-boundary effects in the petrophysical interpretation of well logs is the application of forward and inverse modeling techniques because of their explicit use of measurement response functions. The main objective of this dissertation is to develop inversion-based petrophysical interpretation methods that quantitatively integrate logging-while-drilling (LWD) multi-sector nuclear (i.e., density, neutron porosity, photoelectric factor, natural gamma ray) and multi-array propagation resistivity measurements. Under the assumption of a multi-layer formation model, the inversion approach estimates formation properties specific to a given measurement domain by numerically reproducing the available measurements. Subsequently, compositional multi-mineral analysis of inverted layer-by-layer properties is implemented for volumetric estimation of rock and fluid constituents. The most important prerequisite for efficient petrophysical inversion is fast and accurate forward models that incorporate specific measurement response functions for numerical simulation of LWD measurements. In the nuclear measurement domain, first-order perturbation theory and flux sensitivity functions (FSFs) are reliable and accurate for rapid numerical simulation. Albeit efficient, these first-order approximations can be inaccurate when modeling neutron porosity logs, especially in the presence of borehole environmental effects (tool standoff or/and invasion) and across highly contrasting beds and complex formation geometries. Accordingly, a secondary thrust of this dissertation is the introduction of two new methods for improving the accuracy of rapid numerical simulation of LWD neutron porosity measurements. The two methods include: (1) a neutron-density petrophysical parameterization approach for describing formation macroscopic cross section, and (2) a one-group neutron diffusion flux-difference method for estimating perturbed spatial neutron porosity fluxes. Both methods are validated with full Monte Carlo (MC) calculations of spatial neutron detector FSFs and subsequent simulations of neutron porosity logs in the presence of LWD azimuthal standoff, invasion, and highly dipping beds. Analysis of field and synthetic verification examples with the combined resistivity-nuclear inversion method confirms that inversion-based estimation of hydrocarbon pore volume in HA/HZ wells is more accurate than conventional well-log analysis. Estimated hydrocarbon pore volume from conventional analysis can give rise to errors as high as 15% in undulating HA/HZ intervals.Item Issues related to site property variability and shear strength in site response analysis(2015-08) Griffiths, Shawn Curtis; Cox, Brady Ray, 1976-; Rathje, Ellen M.; Stokoe, Kenneth; Ghannoum, Wassim; Wilson, ClarkNonlinear site response analyses are generally preferred over equivalent linear analyses for soft soil sites subjected to high-intensity input ground motions. However, both nonlinear and equivalent linear analyses often result in large induced shear strains (3-10%) at soft sites, and these large strains may generate unusual characteristics in the predicted surface ground motions. One source of the overestimated shear strains may be attributed to unrealistically low shear strengths implied by commonly used modulus reduction curves. Therefore, modulus reduction and damping curves can be modified at shear strains greater than 0.1% to provide a more realistic soil model for site response. However, even after these modifications, nonlinear and equivalent linear site response analyses still may generate unusual surface acceleration time histories and Fourier amplitude spectra at soft soil sites when subjected to high-intensity input ground motions. As part of this work, equivalent linear and nonlinear 1D site response analyses for the well-known Treasure Island site demonstrate the challenges associated with accurately modeling large shear strains, and subsequent surface response, at soft soil sites. Accounting for the uncertainties associated with the shear wave velocity profile is an important part of a properly executed site response analyses. Surface wave data from Grenoble, France and Mirandola, Italy have been used to determine shear wave velocity (Vs) profiles from inversion of surface wave data. Furthermore, Vs profiles from inversion have been used to determine boundary, median and statistically-based randomly generated profiles. The theoretical dispersion curves from the inversion analyses as well as the boundary, median and randomly generated Vs profiles are compared with experimentally measured surface wave data. It is found that the median theoretical dispersion curve provides a satisfactory fit to the experimental data, but the boundary type theoretical dispersion curves do not. Randomly generated profiles result in some theoretical dispersion curves that fit the experimental data, and many that do not. Site response analyses revealed that the greater variability in the response spectra and amplification factors were determined from the randomly generated Vs profiles than the inversion or boundary Vs profiles.Item Machine learning approaches for solving subsurface inverse problems(2023-07-28) Crocker, Jodie Amberly; Kumar, Krishna (Engineering geologist); Cox, Brady R; Rathje, Ellen M; Stokoe, Kenneth H; Pyrcz, Michael JA necessary component of geotechnical engineering design is the assessment of the physical properties of the subsurface, such as a site’s subsurface shear stiffness or shear-wave velocity (Vs). To obtain this information, various invasive and non-invasive methods may be used to perform seismic site characterization. Typically, non-invasive techniques, such as surface wave methods, are preferred due to being relatively inexpensive, quick, and easy to perform compared to invasive methods. Generally, surface wave methods involve three steps: (1) data acquisition; (2) data processing; and (3) inversion. While the first two steps are straightforward, the third step is particularly challenging due to the ill-posedness and non-uniqueness of the inverse problem. Additionally, traditional inversion may be time-consuming to perform, as it is computationally expensive and requires a high degree of domain expertise. Therefore, there has been a recent push to find non-traditional alternatives to performing inversion, particularly through the use of machine learning (ML) tools. These ML-driven tools, such as neural networks, allow users without domain expertise to quickly perform inversion, although care must be taken to ensure the tools adequately address the surface wave inverse problem. This dissertation discusses three possible ML-driven solutions to the inverse problem, beginning with a physics-aware convolutional neural network (CNN) that takes surface wave dispersion data as input and provides two-dimensional (2D) subsurface Vs profiles as output. To ensure the network learns the physical relationship between surface wave dispersion data and subsurface Vs, methods from the field of explainable artificial intelligence (XAI) are used during the network development process to perform hyperparameter tuning. Next, an ML-driven framework is presented that combines a CNN with a differentiable programming (DP) algorithm to provide one-dimensional (1D) velocity profile predictions. In this case, the CNN generates 1D velocity starting models for inversion. These velocity models are then passed through the DP algorithm, which uses a wave propagation simulator to solve the governing acoustic wave equation and perform inversion, leading to an optimized velocity profile. Finally, a comparison between a non-physical CNN and a simulation-based CNN is presented. The simulation-based CNN uses the previous DP algorithm as a layer to incorporate the physics of the acoustic wave equation into the network’s training process. This network takes 1D waveforms as input and provides 1D subsurface Vs profiles as output while ensuring the results are physically consistent.Item Mechanistic numerical simulation and interpretation of borehole measurements of spontaneous electrical potential acquired in complex petrophysical environments(2021-04-07) Bautista-Anguiano, Joshua Christopher; Torres-Verdín, Carlos; Prodanovic, Masa; Sepehrnoori, Kamy; Heidari, Zoya; Yilmaz, Ali; Katz, LynnBorehole measurements of spontaneous electrical potential (SP) are routinely acquired in wells drilled with water-based mud. However, to this day, the interpretation of borehole SP measurements is chiefly limited to imprecise calculations of formation water resistivity and qualitative assessments of volumetric concentration of shale and permeability. This dissertation develops new methods to numerically simulate borehole SP measurements and improve their quantitative interpretation. Interpretation products are water saturation, water resistivity, and radius of invasion of mud-filtrate invasion in permeable rocks, together with their uncertainty. The calculation of formation water resistivity from borehole SP measurements is commonly performed via Nernst’s equation under the assumptions of shallow mud-filtrate invasion, negligible streaming potentials, and water as the only rock-saturating fluid. To circumvent these limitations while honoring the governing physics of coupled mass transport associated with SP phenomena, a three-dimensional finite-difference algorithm is developed to incorporate electrochemical, membrane, and electrokinetic SP phenomena in the simulation of borehole SP measurements. The algorithm implements a mechanistic description of non-equilibrium thermodynamics, which is coupled to a fluid-flow simulator to quantify the effects of time-varying conditions within permeable formations due to mud-filtrate invasion. Simulations indicate that the best spatial resolution of rock properties possible with SP borehole measurements occurs when rock beds are perpendicular to the well; deviated wells or dipping beds give rise to extended and pronounced shoulder-bed effects on SP measurements. It is also found that the simplifying assumption of perpendicular beds relative to the borehole does not cause significant errors in the numerical simulation of borehole SP measurements acquired in well trajectories with a relative dip less than 30°, thereby reducing CPU time by a factor of at least 1.76. Furthermore, electrokinetic effects on SP measurements become negligible for commonly used pressure overbalance ranges. For the interpretation of borehole SP measurements acquired in hydrocarbon-bearing rocks, this dissertation explores whether the difference between borehole SP measurements and Nernst-equation predictions enables the estimation of in situ hydrocarbon saturation of porous rocks. A new petrophysical model is advanced and successfully verified to establish the limits of detectability of hydrocarbon saturation solely from borehole SP measurements. It is found that optimal conditions for the quantification of hydrocarbon saturation from borehole SP measurements take place when (1) capillary forces dominate the process of mud-filtrate invasion, (2) the matrix-pore interface region, known as the electrical double layer, has a relevant impact on the diffusion of counter-ions, and (3) the electrolyte concentration of drilling mud is greater than that of formation water. Three blind tests show that the developed petrophysical model and the mechanistic SP simulation algorithm enable the estimation of hydrocarbon saturation from SP borehole measurements without the need of electrical resistivity measurements or porosity calculations. The estimation is reliable when (a) the volumetric concentration of shale is negligible, (b) the pore network structure is constant throughout the reservoir, and (c) radial invasion profiles are similar to those observed in calibration key wells used to adjust the parameters of the new petrophysical model. Finally, this dissertation develops a new inversion-based method for the interpretation of borehole SP measurements, which concomitantly mitigates shoulder-bed and mud-filtrate invasion effects on SP logs via fast numerical simulations based on Green’s functions. The method delivers layer-by-layer estimates of (a) equivalent NaCl concentration, (b) radius of mud-filtrate invasion, and (c) sodium macroscopic transport number, together with their uncertainty, by progressively matching borehole SP measurements with their numerical simulations. Successful examples of implementation include noisy borehole SP measurements acquired in aquifers with various degrees of petrophysical complexity. Results confirm the possibility of accurately and reliably estimating the electrical resistivity of formation water resistivity solely from borehole SP measurements, i.e., without the need of porosity calculations or fitting parameters from independent core measurements (as is the case with borehole resistivity measurements). Inversion-based interpretation results (a) compare well to those obtained from resistivity and nuclear porosity logs, (b) provide estimates of uncertainty, and (c) can assimilate a priori knowledge of aquifer petrophysical properties in the estimation.Item On the development of uncertainty-consistent one-dimensional shear wave velocity profiles from inversion of surface wave dispersion data(2021-11-19) Vantassel, Joseph Philip; Kumar, Krishna (Engineering geologist); Cox, Brady R.; Stokoe II, Kenneth H.; Spikes, Kyle T.Characterization of a site’s subsurface shear stiffness is of critical importance to many areas of geotechnical engineering, such as site characterization and seismic hazard analysis. The site’s subsurface shear stiffness, more specifically referred to as the site’s small-strain shear modulus (G₀), is most commonly determined through measurements of the site’s shear wave velocity (Vs), as G₀ and the square of Vs are linearly related through mass density (ρ) (i.e., G₀=ρ Vs²). Due to their advantages in terms of speed of acquisition and versatility in challenging geologic environments, non-invasive characterization methods are increasingly being preferred over invasive methods for assessing a site’s Vs. Of the non-invasive techniques, surface wave methods are becoming the technique of choice for near-surface characterization due to their ability to be used to characterize arbitrary subsurface conditions, even those which are challenging to other non-invasive techniques (e.g., soft layers beneath stiff layers), and their ability to accurately infer Vs at both the near-surface as well as at depth through the combined use of active-source and passive-wavefield approaches to measuring surface wave propagation. However, surface wave methods, as with all site characterization techniques (invasive and non-invasive), contain uncertainties that need to be quantified and propagated through the data acquisition and processing into the resulting Vs measurements. Non-invasive techniques, such as surface wave methods, are particularly challenging due to the ill-posedness of the inverse problem and the non-uniqueness that it implies. The presence of non-uniqueness in the solution of the inverse problem results in a compounding of the apparent uncertainties. As a result, it is imperative that uncertainties in surface wave testing be quantified not only in regard to the acquisition and processing of the data but in the inversion process itself. This dissertation presents a comprehensive approach that documents the process of quantifying experimental dispersion data uncertainty, stemming from aleatory and epistemic sources, and the rigorous propagation of that uncertainty through the inversion process and into suites of Vs profiles that more realistically quantify the expected distribution of Vs. Because the resulting suites of Vs profiles propagate both epistemic and aleatory uncertainty, as well as the uncertainty associated with the inverse problem’s ill-posedness, the profiles are referred to as uncertainty-consistent. The development of uncertainty-consistent Vs profiles has been the interest of much research over the past two decades, however, the approach detailed in this dissertation is the first to quantitatively show that such profiles could be obtained from experimental surface wave dispersion data.Item Pre-injection reservoir evaluation at Dickman Field, Kansas(2011-08) Phan, Son Dang Thai; Sen, Mrinal K.; Srinivasan, Sanjay; Grand, StephenI present results from quantitative evaluation of the capability of hosting and trapping CO₂ of a carbonate brine reservoir from Dickman Field, Kansas. The analysis includes estimation of some reservoir parameters such as porosity and permeability of this formation using pre-stack seismic inversion followed by simulating flow of injected CO₂ using a simple injection technique. Liner et at (2009) carried out a feasibility study to seismically monitor CO₂ sequestration at Dickman Field. Their approach is based on examining changes of seismic amplitudes at different production time intervals to show the effects of injected gas within the host formation. They employ Gassmann's fluid substitution model to calculate the required parameters for the seismic amplitude estimation. In contrast, I employ pre-stack seismic inversion to successfully estimate some important reservoir parameters (P- impedance, S- impedance and density), which can be related to the changes in subsurface rocks due to injected gas. These are then used to estimate reservoir porosity using multi-attribute analysis. The estimated porosity falls within a reported range of 8-25%, with an average of 19%. The permeability is obtained from porosity assuming a simple mathematical relationship between porosity and permeability and classifying the rocks into different classes by using Winland R35 rock classification method. I finally perform flow simulation for a simple injection technique that involves direct injection of CO₂ gas into the target formation within a small region of Dickman Field. The simulator takes into account three trapping mechanisms: residual trapping, solubility trapping and mineral trapping. The flow simulation predicts unnoticeable changes in porosity and permeability values of the target formation. The injected gas is predicted to migrate upward quickly, while it migrates slowly in lateral directions. A large amount of gas is concentrated around the injection well bore. Thus my flow simulation results suggest low trapping capability of the original target formation unless a more advanced injection technique is employed. My results suggest further that a formation below our original target reservoir, with high and continuously distributed porosity, is perhaps a better candidate for CO₂ storage.Item Quantitative interpretation of pulsed neutron capture logs : fast numerical simulation and inversion in thinly-bedded formations(2010-08) Mimoun, Jordan Gilles Attia; Torres-Verdín, Carlos; Preeg, William E.Pulsed neutron capture (PNC) logs are commonly used for formation evaluation behind casing and to assess time-lapse variations of hydrocarbon pore volume. Because conventional interpretation methods for sigma logs assume homogeneous formations, errors may arise, especially in thinly-bedded formations, when appraising petrophysical properties of hydrocarbon-bearing beds. There exist no quantitative interpretation methods to account for shoulder-bed effects on sigma logs acquired in sand-shale laminated reservoirs. Because of diffusion effects between dissimilar beds, sigma logs acquired in such formations do not obey mixing laws between the sigma responses of pure-sand and pure-shale end members of the sedimentary sequence. We introduce a new numerical method to simulate rapidly and accurately PNC logs. The method makes use of late-time, thermal-neutron flux sensitivity functions (FSFs) to describe the contribution of multi-layer formations toward the measured capture cross section. It includes a correction procedure based on 1D neutron diffusion theory that adapts the transport-equation-derived, base-case FSF of a homogeneous formation to simulate the response of vertically heterogeneous formations. Benchmarking exercises indicate that our simulation method yields average differences smaller than 2 c.u. within seconds of CPU time with respect to PNC logs simulated with rigorous Monte Carlo methods for a wide range of geometrical, petrophysical, and fluid properties. We develop an inversion method to reduce shoulder-bed effects on pulsed neutron capture (PNC) logs in the estimation of layer-by-layer capture cross sections, Σ. The method is based on the previously developed rapid approximation of PNC logs. Tests performed on synthetic examples that include a variety of lithology, saturating-fluid, and bed-thickness configurations confirm the efficiency, reliability, and stability of the inversion procedure. Inversion consistently improves the vertical resolution and Σ definition of PNC logs across beds thinner than 45 cm. Our fast, iterative algorithm inverts sigma logs in seconds of CPU time, and is therefore suitable for joint petrophysical interpretation with other open- and cased-hole logs.Item Rapid modeling and inversion-based interpretation of borehole acoustic measurements acquired in isotropic and vertical transversely isotropic formations(2017-12-08) Maalouf, Elsa; Torres-Verdín, Carlos; Daigle, Hugh; Heidari, Zoya; Sepehrnoori, Kamy; Spikes, KyleBorehole acoustic measurements are often affected by instrument noise, motion and eccentricity, environmental conditions, and spatial averaging that can compromise the accuracy of elastic properties of rock formations calculated with conventional interpretation methods. Forward and inverse modeling can be used to improve the interpretation of acoustic logs acquired in the presence of spatially complex rock formations and adverse borehole conditions. However, forward modeling of acoustic modes often requires time-consuming numerical algorithms. The main objective of this dissertation is to develop fast-forward modeling and inversion-based interpretation procedures of borehole acoustic logs for isotropic and vertical transversely isotropic (VTI) formations. Fast-forward modeling is achieved with spatial sensitivity functions which are calculated from frequency-domain linear perturbation theory of borehole acoustic modes. Spatial sensitivity functions quantify both the dependence of measured slowness on elastic properties and the spatial averaging introduced by acoustic tools. Fast-forward modeling using spatial sensitivity functions is applied to synthetic examples that include thin layers, anisotropy, and dipping layers, and is successfully validated with numerical simulations performed with finite-difference and finite-element methods. Two inversion-based interpretation methods are then developed: (1) a physics-based inversion method to reduce noise and spatial averaging effects on acoustic logs acquired in horizontally layered formations penetrated by vertical wells, and (2) a sequential inversion method to estimate stiffness coefficients of VTI formations from multi-frequency flexural/quadrupole, Stoneley, and compressional logs. The physics-based inversion method is applied to mitigate measurement noise and spatial averaging effects of acoustic logs acquired in two hydrocarbon reservoirs. Results confirm the accuracy and reliability of the estimated layer-by-layer elastic properties compared to conventional numerical filters and are obtained in less than 14 CPU seconds for a 100 ft-depth log. In VTI formations penetrated by vertical wells, sequential inversion is applied to estimate layer-by-layer stiffness coefficients of synthetic formations from borehole acoustic logs. Results indicate that mitigating spatial averaging of frequency-dependent slowness logs prior to inversion improves the layer-by-layer estimation of slownesses by a factor of 2, and that sequential inversion yields accurate and reliable estimates of rock stiffness coefficients. Finally, in high-angle wells fast-forward modeling yields flexural slownesses measured with orthogonal dipoles with 2% relative errors and in 3 CPU minutes for a log consisting of 50 measured-depth samples, compared to 15 CPU hours when using finite-difference simulation methods. Analysis of field and synthetic examples confirms that inversion-based interpretation methods yield more accurate estimations of elastic properties than conventional sonic-log interpretation procedures. Spatial sensitivity functions constitute a fast, reliable, and efficient alternative for interpreting acoustic logs acquired in isotropic and VTI formations.