Inversion Stage Research Articles

WUS324: Multiscale Full Waveform Inversion Approaching Convergence Improves Waveform Fits While Imaging Seismic Structure of the Western United States

AbstractWe report a new model of radially anisotropic crustal and upper mantle structure of the western United States (WUS324) obtained from full waveform inversion of earthquake data. We ran three multiscale inversion stages beyond model WUS256 (Rodgers et al., 2022, https://doi.org/10.1029/2022jb024549) allowing them to approach convergence to fit a larger data set to a shorter minimum period of 16 s. WUS324 is based on 324 total iterations from its starting model, significantly more (16 times) than previous studies. Waveform misfit reductions are 66%–70% for both the inversion data and an independent validation data set providing confidence in the predictive power of the model. WUS324 provides much better fits and reveals shear wavespeed, vS, structure of this large region with more detail than previous waveform tomography models. We show representative images demonstrating the resolution of diverse seismic structure across this highly heterogeneous region including oceanic lithosphere, subducting slabs and continental magmatism.

Combining BioTRIZ and Multi-Factor Coupling for Bionic Mechatronic System Design

To realize the design process of bionic mechatronic systems, involving mapping from engineering to biology and inversion from biology to engineering, a novel design paradigm is introduced that integrates BioTRIZ with multi-factor coupling bionics. In the mapping stage from engineering to biology, BioTRIZ is employed to frame the concrete engineering issue as a general conflicting problem. The biological solution is refined by amalgamating the BioTRIZ solution derived from the contradiction matrix with biological instances. In the inversion stage of biology to engineering, a novel approach is proposed for constructing a bionic multi-factor coupling model, drawing inspiration from the establishment of biological multi-factor coupling model. This allows for a seamless correspondence between biological elements, such as morphology and behavior, and their respective engineering counterparts, including structure and algorithms. This correspondence ultimately achieves the engineering conceptual model that is rooted in biological principles. The practical application of this methodology is exemplified through a multi-biometric fusion bionic active vision system, underscoring its feasibility and efficacy.

Impedance Response and Phase Angle Determination of Metal-Semiconductor Structure with N-Doped Diamond Like Carbon Interlayer

With their superior properties over p-n barriers, Schottky Barrier Diodes have a wide usage area, especially as a test tool to produce better-performance devices. The main performance parameter of these devices is measured by their conduction, which can develop with an interlayer addition through the sandwich design. Regarding the DLC, which also has outstanding specifications under thermal, chemical, and physical conditions, is a good candidate for interlayer tailoring, specifically when used with doping atoms. Thus, this study investigates the impedance response of the fabricated device with an N-doped DLC interlayer by employing the electrochemical technique as a combination of electrolysis, RF magnetron sputtering, and thermal evaporation. The measurements were conducted for broad scales of voltage and frequency corresponding between (-3V) and (+4V) and 1kHz and 1MHz, respectively. According to the impedance analysis, complex impedance decreases by rising bias and frequency, from 1.8 MΩ to 2 k Ω at 1MHZ due to the additional insulating layer. At the same time, the phase angle indicates the quality of the dielectric layer with an average of 81.36  for the sample logarithmic frequency values with an almost constant-like trend in the inversion stage. In comparison, it reduces to an average of 30.25  after the depletion stage by showing the rising conductivity. Moreover, it has some unexpected rising values at the strong accumulation stage, possibly due to the deposited thin film's unique structure. The supported results by phase angle changes, showing frequency-adjustable working conditions, may offer that selective electrical conduction can be tuned.

Experimental Results of Underwater Sound Speed Profile Inversion by Few-Shot Multi-Task Learning

Underwater Sound Speed Profile (SSP) distribution is crucial for the propagation mode of acoustic signals, so fast and accurate estimation of SSP is of great importance in building underwater observation systems. The state-of-the-art SSP inversion methods include frameworks of matched field processing (MFP), compressive sensing (CS), and feed-forward neural networks (FNNs), among which the FNN shows better real-time performance while maintaining the same level of accuracy. However, the training of FNN needs quite a lot historical SSP samples, which is difficult to satisfy in many ocean areas. This situation is called few-shot learning. To tackle this issue, we propose a multi-task learning (MTL) model with partial parameter sharing among different training tasks. By MTL, common features could be extracted, which accelerates the learning process on given tasks, and reduces the demand for reference samples, enhancing the generalization ability in few-shot learning. To verify the feasibility and effectiveness of MTL, a deep-ocean experiment was held in April 2023 in the South China Sea. Results show that MTL outperforms the other mainstream methods in terms of accuracy for SSP inversion, while inheriting the real-time advantage of FNN during the inversion stage.

Evaluation of solubility parameters and relative energy difference (RED) on the preparation of polysulfone/polyethylene glycol membrane: A study on the casting solution and coagulation bath

Solubility parameters are effective factors for controlling membrane preparation based on hydrophilic/hydrophobic polymers. Hansen solubility parameters (HSPs) of a polysulfone/polyethylene glycol (PSU/PEG) in increasing PEG molecular weights and binary coagulation bath of solvent/non-solvent mixtures are investigated. The results revealed that with increased PEG molecular weight in the casting solution, the relative energy difference (RED) of the solution increases, and subsequently its instability increases too. On the other hand, by increasing the solvent in the coagulation bath, RED decreases. Findings demonstrated that by increasing PEG molecular weight to 15,000 g/mol and increasing solvent to 60 wt% in the coagulation bath, an interconnected sponge-like structure with maximum mean pore size (120 nm) was achieved. With increased PEG molecular weight, membrane morphology tended toward to a sponge-like structure due to delayed demixing in the phase inversion stage. Furthermore, pure water permeability and rejection capability of membranes exhibited that with increasing RED of casting solution and reducing RED of coagulation bath, the highest permeability (2199 L/m2h and the lowest rejection capability (33%) of the membrane were attained. This study confirmed that, for the PSU/PEG system, by controlling the solubility parameters, RED value of casting solution and coagulation bath, membrane characteristics can be controlled.

Methodology of elastic full‐waveform inversion of multicomponent ocean‐bottom data for anisotropic media

AbstractFull‐waveform inversion of multicomponent data can provide an improved estimation of medium parameters using both compressional‐ and shear‐wave information. However, most earlier studies that involved a full‐waveform inversion of ocean‐bottom data are based on acoustic anisotropic or elastic isotropic approximations. Here, we consider realistic elastic anisotropic media and develop an efficient full‐waveform inversion framework for estimating model parameters. We simulate seismic wavefields using a previously developed coupled acoustic/elastic wave propagator that implements a mimetic finite‐difference method with fully staggered grids to accurately handle the fluid/solid boundary conditions. The algorithm employs a multiscale approach starting from low frequencies and incorporating higher frequency bands in the later inversion stages. We analyse the influence of different types of input data on the accuracy of the inverted anisotropy parameters for hard and soft water bottoms. The employed misfit function incorporates information from both hydrophones and ocean‐bottom geophones. Numerical examples indicate that injecting multiple data components simultaneously increases the complexity of the objective function and often degrades the quality of the estimated medium parameters. Thus, we propose a sequential strategy using a single data component at a time. Pressure (hydrophone) data alone can provide satisfactory results if long offsets (i.e., with the offset/depth ratio ≥ 3) are available. Adding the horizontal particle‐displacement or ‐velocity components increases the accuracy of the estimated shear‐wave vertical velocity () and P‐wave normal‐moveout () velocity, especially for strongly heterogeneous sub‐water‐bottom models.

The control of curved faults on structural trap formation: Tiantai slope belt, Xihu Sag, East China Sea

Mesoscale (tens of kilometers) curved faults are a common fault geometry in plan view. These types of faults are commonly hydrocarbon traps or sand body controlling faults that play a key role in hydrocarbon exploration. However, restricted by the high-resolution requirements for basic research data, studies of mesoscale curved faults are not as sufficient as those of basin boundary curved faults. Based on high-resolution 3D seismic and well data, through structural interpretation, fault activity analysis, and balanced cross-sections, we investigated the structural characteristics of mesoscale curved normal faults in the Tiantai slope belt of the Xihu Sag, East China Sea, and further revealed the controlling effect on structural trap formation. Our results show a significant association between curved fault evolution and structural trap formation. (a) The curved fault evolution process can be divided into the fault segment stage, hard-linked stage, weak activity stage, fault segment stage Ⅱ, and positive inversion stage, resulting in several east-dipping curved faults. The difference in the fault geometry between different typical curved faults is because they experienced different evolution stages. (b) The formation of curved normal faults is controlled by preexisting sag-controlling faults. In the early Cenozoic, the sag-controlling faults underwent oblique extension, forming segments of curved faults; in the Middle Eocene, the regional extension direction changed to be orthogonal to the curved faults, resulting in the hard linking of fault segments, and the curved normal fault zone formed. This process can be summarized as an accommodation model of mesoscale curved faults. (c) Four types of structural traps have been identified in the curved fault zone. The half-anticlinal trap in the footwall was formed in the hard-linked stage (∼32 Ma) according to the tilting fault block model; the half-anticlinal trap in the hanging wall is a transverse anticline that was formed in the fault segment stage Ⅱ (∼23 Ma) due to the differential subsidence of the strata in the hanging wall; and the faulted anticlinal and the anticlinal traps were controlled by the compression of the Longjing movement and formed at approximately 13 Ma.

Circulating current suppression for ground tied variable frequency to constant frequency converter system in aircraft

This paper presents a solution to the circulating current fault of aircraft power supply. The DC-link type Variable Frequency to Constant Frequency (VFCF) converter system is the preferred scheme to feed the constant 400 Hz load in an aircraft with a variable frequency power supply. Due to the requirement of aircraft standards, both grounds of the rectification and inversion stage are tied to the metal frame of the aircraft. With such a tied ground, the DC bus voltage rises greatly, and a large circulating current appears in the casing as the ground, which leads to equipment failure and potential safety hazards. According to the existing methods of circulating current fault suppression, this paper analyzes the causes of the above faults and the harmonic components of circulating current and points out the limitations of the existing methods. Therefore, a Common-Mode (CM) choke-based method is proposed to provide a high impedance in the path of the CM circulating current. By doing so, the circulating current can be suppressed without the additional burden of the hardware and control algorithm, which is quite friendly for quality control of mass-production aircraft. Moreover, a simplified mathematic model of the VFCF converter system is derived to calculate the minimum inductance value reference of the CM choke, which saves the weight of passive devices to the greatest extent. Finally, simulation and experimental results are studied to verify the effectiveness of the proposed method.

Research on Seismic Velocity Inversion Method Based on Deep Learning

Methods for obtaining seismic velocity include offset velocity analysis, tomography velocity inversion and full waveform. inversion, but these methods all share common problems: As the amount of seismic data increases, the time required to process the data to obtain the seismic velocity increases exponentially, and the latter two methods are more dependent on the initial seismic velocity. To address the problems of the above methods, this paper improves a seismic velocity inversion method based on deep learning. At the same time, a method that can generate a large number of velocity models randomly with geological features (undulation layer, faults, anomalies, etc. ) similar to those of real subsurface structures is also proposed. The generated velocity model and fluctuation equation for forward modeling are used to perform. the forward modeling, which allows for the efficient establishment of data set. The basic principle of the improved deep learning inversion method in this paper is as follows: the characteristic information of the training data is extracted by convolution neural network, which is trained with large data to obtain a nonlinear mapping relationship between seismic record and seismic velocity. In the inversion stage, the seismic velocity can be inversed quickly by inputting the seismic records into the trained network. In order to make the network give full play to the advantages of processing seismic data, the authors obtained the dominant network structure by means of numerical simulation, and achieved satisfactory inversion results. Finally, through comparative experiments, this paper verifies the advantages and applicability of the method.

Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data

Context.The internal structures of small solar system bodies (SSSBs) are still poorly understood. In this paper, we find an experimental tomographic reconstruction of coarse high-contrast details inside a complex-structured target object using multipoint full-wave radar data.Aims.Our aim is to advance the development of inversion techniques to be used in potential planetary scientific radar investigations targeting SSSBs, which have complex shapes and whose internal structure is largely unknown. Finding out the structure is an important scientific objective of Solar System research in order to understand its history and evolution.Methods.This is the second part (Paper II) of a joint study considering the methods to analyse and invert quasi-monostatic microwave measurement data of an asteroid analogue. We focused on incorporating advanced, full-wave, forward simulation in time domain with experimental data obtained from multiple measurement points. In particular, this study investigates multiple scattering and multipath effect suppression (MES) to reduce artefacts in the reconstructions. MES is necessary since the high-contrast and complex-shaped target and, especially, its back wall in high curvature regions cause intense reflections that deteriorate the reconstruction quality if not treated correctly. We considered the following two approaches to obtain MES: (i) geometrical optics-based pathlength thresholding and (ii) a peak detection method to investigate whether a data-driven approach could be used. At the inversion stage, we investigated marginalisation of random effects due to modelling by splitting a larger point set into several sparse sets of measurements.Results.Based on the results, MES is crucial to localise a void inside the complex analogue target. A reconstruction can be found when the maximum signal propagation time approximately matches that of the first back-wall echo for each measurement point. The marginalisation approach allows us to find a reconstruction that is comparable in quality to the case of full data, while reducing the computation effort per subsystem, which is advantageous when inverting a large data set.

Efficient estimation of groundwater contaminant source and hydraulic conductivity by an ILUES framework combining GAN and CNN

In the inverse estimation of groundwater model parameters (e.g., contaminant source parameters and hydraulic conductivity fields), data assimilation is the most commonly used method for solving the inverse problem. However, data assimilation requires iterative calculation, which tends to increase the computational costs. This is particularly problematic when dealing with high-dimensional problems. In this study, we propose a hybrid inversion framework, which combines a generative adversarial network (GAN) and a convolutional neural network (CNN) for groundwater model parameter estimation. The GAN is equipped with gradient penalties (WGAN-GP) to achieve fast characterization of high-dimensional aquifer structures with low-dimensional vectors (200 dimensions). Meanwhile, this study proposes an enhanced convolutional neural network (OANW), which introduces two-layer weights near the contamination source to achieve an effective surrogate of the process-based groundwater model. Moreover, an iterative local update ensemble smoother (ILUES) is applied for simultaneous identification of the contaminant source parameters and hydraulic conductivity fields in the inversion stage. The results demonstrate that by integrating WGAN-GP and OANW, the ILUES framework accurately characterizes the aquifer parameters and significantly improves the efficiency of the computational process.

Two-stage broad learning inversion framework for shear-wave velocity estimation

Shear-wave (S-wave) velocity is considered an essential parameter for the study of the earth, and Rayleigh wave inversion has been widely accepted and used to determine it. Given high-quality measured dispersion curves, the inversion performance depends on the applied optimization algorithm inside the inversion process. We propose a novel inversion framework to promote efficient and accurate inversion, i.e., a two-stage broad learning inversion framework (TS-BL). The proposed TS-BL not only inherits the powerful mapping capability and simple configured structure of broad learning (BL) network but also makes two significant improvements to better acclimatize itself to Rayleigh wave inversion. First, TS-BL adopts a two-stage inversion strategy to perform optimizing two times. It does not yield the same search space in the two inversion stages. In the first stage, because the inversion aims to find an approximation rather than the accurate value of model parameters, the difficulty in constructing the mapping model is reduced by sacrificing accuracy. Then, an effective BL network can be established using smaller sample sizes. In the second stage, the search space becomes much narrower, commencing with the approximation results obtained in the prior stage. This helps the final BL network to easily and quickly model the actual relationship between measured dispersion curves and unknown model parameters. After that, the forward modeling of measurements rather than the validation data set is exploited for tuning the network’s hyperparameters. The physical model is superior to the validation data set for selecting a suitable network complexity to adapt to the measured dispersion curves because the latter only describes an overall relationship. As a result, accurate S-wave velocities can be efficiently acquired by using the proposed TS-BL with a low cost of training samples. The efficiency and reliability of TS-BL have been demonstrated in numerical and field data examples.

Petrochemical and geochronological data of Permian-Lower Triassic clastic sedimentary rocks in the northwestern Junggar basin, NW China: Implications for provenance, tectonism and paleoclimate

The Permian clastic sediments in the Mahu sag offer outstanding conditions to test the control of tectonism and paleoclimate on sedimentation in a rift basin. A synthesis of petrological and geochemical analyses of sandstones, zircon U–Pb geochronology of granitic conglomerates, and principal component analysis have been used to investigate the source composition and chemical weathering indices. The rare earth and trace element compositions of 16 sandstone samples are consistent with first cycle sources from the Carboniferous–Lower Permian mafic and felsic igneous rocks in West Junggar. Lower Permian sandstones contain abundant volcanic lithic clasts and plagioclase grains, and have high Na2O, CaO, Sr and V, suggesting a coeval proximal volcanic source in Central West Junggar during the syn-rift stage. Middle Permian sandstones consist of trachyte and rhyolite clasts, and quartz and albite grains, and show a gradual increase of Th, U and SiO2, indicating an expansion of source areas to more distant Southern and Northern West Junggar during the post-rift stage. In the Lower Triassic, an abrupt increase in the percentages of quartz and K-feldspar, as well as the zircon U–Pb geochronology of granite-clast conglomerates (290–330 Ma), all indicate regional uplift and unroofing of Carboniferous–Permian granitic plutons in West Junggar during the tectonic inversion stage at the Permian-Triassic boundary. Various chemical weathering indices indicate cold and arid climate conditions during the early Permian, followed by a transition to warm and humid climatic conditions. Comprehensive analysis of petrography and geochemistry sheds a new light for studying the source-to-sink evolution of a rift basin, and has further implication for paleoclimate fluctuation and change.

Fuzzy Fractional-Order PID Control for PMSG Based Wind Energy Conversion System with Sparse Matrix Converter Topology

Sparse matrix converter (SMC) is an indirect AC-to-AC power electronic converter that has a fictitious DC link between rectification and inversion stages in which neither a capacitor nor an inductor, as the storage element, is utilized. Due to this advantage, SMC is used in AC drives, marine thrust systems, aerospace industry, as well as in wind energy applications. On the other hand, permanent magnet synchronous generator (PMSG) is competitive in wind turbine applications due to their prominent features. In this work, a fuzzy fractional-order PID (FFOPID) controller is designed for a PMSG based wind energy conversion system (WECS) which employs a three-phase three-level SMC. The FFOPID controller is chosen to combine the salient features of the fractional-order calculus and fuzzy logic operations to enhance the dynamic response of classical PID controller with fixed gains. The simulation results taken under different case studies are analyzed in detail, which demonstrate the superiority of the designed FFOPID controller over classical PID control approach in tracking d- and q-axis current references of the SMC at the output. With the designed control approach, the smooth control of the real and reactive power injections into the grid from the WECS are ensured with acceptable transient response.

An Efficient MPPT Technique-Based Single-Stage Incremental Conductance for Integrated PV Systems Considering Flyback Central-Type PV Inverter

Central-type photovoltaic (PV) inverters are used in most large-scale standalone and grid-tied PV applications due to the inverter’s high efficiency and low-cost per kW generated. The perturbation and observation (P&O) and incremental conductance (IncCond) have become the most common techniques for maximum power point tracking (MPPT) strategies of PV/wind generation systems. Typically, the MPPT technique is applied in a two-stage operation; the first stage tracks the MPP and boosts the PV voltage to a certain level that complies with grid voltage, whereas the second stage represents the inversion stage that ties the PV system to the grid. Therefore, these common configurations increase the system size and cost as well as reduce its overall footprint. As a result, this paper applies two IncCond MPPT techniques on a proposed single-stage three-phase differential-flyback inverter (DFI). In addition, the three-phase DFI is analyzed for grid current negative-sequence harmonic compensation (NSHC). The proposed system efficiently provides a MPPT of the PV system and voltage boosting property of the DC-AC inverter in a single-stage operation. Moreover, the MPPT technique has been applied through the DFI using the conventional and modified IncCond tracking strategies. Furthermore, the system is validated for the grid-tied operation with the negative-sequence harmonic compensation strategy using computer-based simulation and is tested under uniform, step-change, as well as fast-changing irradiance profiles. The average efficiencies of the proposed system, considering the conventional and modified IncCond MPPT techniques, are 94.16% and 96.4% with tracking responses of 0.062 and 0.035 s and maximum overshoot of 46.15% and 15.38%, respectively.

Evaluation of the Main Control Strategies for Grid-Connected PV Systems

The present study aims at analyzing and assessing the performance of grid-connected photovoltaic (PV) systems, where the considered arrangement is the two-stage PV system. Normally, the maximum power point tracking (MPPT) process is utilized in the first stage of this topology (DC-DC). Furthermore, the active and reactive power control procedure is accomplished in the second stage (DC-AC). Different control strategies have been discussed in the literature for grid integration of the PV systems. However, we present the main techniques, which are considered the commonly utilized and effective methods to control such system. In this regard, and for MPPT, popularly the perturb and observe (P&O) and incremental conductance (INC) are employed to extract the maximum power from the PV source. Moreover, and to improve the performance of the aforementioned methods, an adaptive step can be utilized to enhance the steady-state response. For the inversion stage, the well-known and benchmarking technique voltage-oriented control, the dead-beat method, and the model predictive control algorithms will be discussed and evaluated using experimental tests. The robustness against parameters variation is considered and an extended Kalman filter (EKF) is used to estimate the system’s parameters. Future scope and directions for the research in this area are also addressed.

A novel step‐up topology for multilevel power conversion

AbstractRenewable energy sources employ a power conditioning unit for injecting power into the grid. Such resources of small capacity are characterized by low generated voltage and thus require a high voltage boost at the inversion stage. This paper proposes a novel transformer‐less, single‐phase grid‐connected, 13‐level inverter to yield the voltage boost. The presented topology is realized through 12 unidirectional switches, 2 diodes, and 3 capacitors. A single‐stage circuit synthesizes 13 levels with a single input source and yielding an overall voltage gain of six. The adapted modulation technique is robust enough to keep the capacitors self‐balanced for all values of the modulation index. The proposed topology is modular and cost‐effective in comparison to other similar typologies due to reduced device count and space requirement. The presented topology is validated experimentally with satisfactory operation in yielding input voltage boost by a factor of six.

Pliocene transverse shortening in the southern central Andes recorded in the Iglesia basin

The Iglesia basin is a ∼3.5 km thick depocenter that holds an outstanding record of the late Cenozoic tectosedimentary evolution of the southern Central Andes. Previous studies have indicated an initial tectonic stage associated with NNE-striking basin-bounding faults, formed by extension in the Late Oligocene (?)-early Miocene, and a subsequent basin inversion stage in the middle-Late Miocene. We conducted a multi-disciplinary study that allowed us to unravel a conspicuous structural system orthogonal to the previous basin-bounding faults. The analysis of seismic reflection lines, satellite and local gravimetry, and field data allowed the recognition of WNW-striking thrust fault zones involving the basement and Cenozoic sedimentary cover of the Iglesia basin. Also, we document Pliocene growth strata in seismic reflection lines and intra-Pliocene thrust faults at the surface that inform the timing of transverse fault activity. Therefore, we propose new tectonic stage during the Pliocene associated with the onset of a transitory NNE-trending contractional stress field, which triggered the reactivation of inherited basement structures transverse to the main Andean strike. This indicates a transient shifting in the stress field at ∼5 Ma that we associate with a major upper-plate reconfiguration caused by the full development of the Pampean flat-slab and major plate coupling.

Onset of Iberian-European plate convergence: Late Cretaceous flexural response of a hot lithosphere (Aquitaine Basin, France)

The Aquitaine Basin is closely linked to the evolution of the Pyrenees, providing precious evidence of the early stages of the Pyrenean orogeny in the Late Cretaceous. Although the timing and geometry of the Early Cretaceous rifting stage is well constrained in the Pyrenees and surrounding north Pyrenean basins, the subsequent early inversion stage has resisted characterization. In this study, we used well log correlations and interpretation of seismic reflection profiles to determine the Late Cretaceous evolution of the sedimentary record in the Aquitaine Basin, spanning the transition from the postrift stage to the beginning of convergence. We identified two main deformation stages during the Late Cretaceous with radically different basin geometries in the western and eastern portions of the Aquitaine Basin. The western part appears to remain under a thermal subsidence regime, inherited from the postrift stage initiated in the Turonian, with little to no deformation. In contrast, the eastern part records early inversion, as indicated by the presence of a well-defined Campanian flexural basin. Between them, Coniacian and Santonian strata indicate a sharply increasing distinction between a very slowly subsiding North Aquitaine Domain (condensed sedimentation) and a strongly subsiding South Aquitaine Domain. We interpret this development as a consequence of lithospheric buckling resulting from far-field compressive strain between the Eurasia and Africa plates. During the Campanian, northward convergence of the Iberia plate led to the formation of a flexural basin with a narrower, steeper geometry than the subsequent Eocene basin that formed in nearly the same region during the Pyrenean orogeny. We attribute this difference to the development of the foreland over a lithosphere that was not thermally reequilibrated in Campanian time, roughly 10 Myr after rifting. This thermal inheritance resulted in lithosphere of very low rigidity. Sedimentary basins formed during both the Coniacian-Santonian and Campanian to early Maastrichtian were thus accommodated by short-wavelength flexural deformation of the lithosphere, a distinctive deformation pattern that represents an immediate response to the onset of compressive strain.

A time-domain multisource Bayesian/Markov chain Monte Carlo formulation of time-lapse seismic waveform inversion

Seismic waveform inversion has been shown to be well-suited for identification and characterization of time-lapse changes in a reservoir. However, the subtle medium variations associated with enhanced oil recovery and/or [Formula: see text] storage problems give uncertainty quantification within such inverse approaches a heightened importance. To analyze both of these features of the time-lapse inverse problem, we formulate a Bayesian full-waveform inversion (FWI) procedure, based on a Markov chain Monte Carlo (MCMC) algorithm. The formulation uses several existing strategies, such as the use of a double-difference time-lapse FWI (DDFWI), incorporation of time-domain multisource data, and application of a local-updating target-oriented inversion. However, it incorporates these within a stochastic framework, involving computation of model covariance with an adaptive Metropolis algorithm, and a method to estimate data error statistics based on the features of time-lapse difference data that is incorporated. A random walk Metropolis-Hastings MCMC is adopted for optimization. In conventional, i.e., deterministic, DDFWI, inversions are carried out for the baseline and monitoring models; in the MCMC approach, a deterministic FWI procedure is carried out for the baseline model, and the MCMC algorithm is applied in the monitoring inversion stage; and the final time-lapse model is the difference between these. A feasibility study is carried out using synthetic 2D acoustic models and data, including time-lapse model estimation and uncertainty quantification. We compare the MCMC approach with conventional deterministic optimization DDFWI and remark on benefits derived, which appear to justify the expanded complexity and cost of a global approach. In addition to the availability of posterior distributions, which are critical for the assessment of the estimations, we observe that the MCMC approach tends to produce monitoring images with clearer edges and fewer coherent errors.