Porosity is a critical petrophysical property for reservoir characterization. While conventional porosity inversion involves complex processes and factors, deep learning methods offer a more intelligent alternative. However, existing training dataset modeling strategies are inadequate for complex geological formations, whereas seismic facies-controlled modeling method enables fine characterization of underground structures. In order to achieve intelligent and fine porosity prediction, we propose a facies-controlled porosity prediction method constrained by seismic attributes. First, stochastic modeling is used to generate heterogeneous background models, enhancing the spatial variability of the dataset to reduce discomfort. Second, sensitive seismic attributes are selected as facies labels to construct seismogram and porosity training sets with facies-controlled significance. Finally, a designed neural network establishes the intrinsic relationship between seismogram and porosity, enabling petrophysical properties for other seismic sections in the same area. Validation using reservoir model data confirms the method’s feasibility and finer resolution compared to conventional method, offering enhanced accuracy in reservoir prediction. Field data from tight sandstone further demonstrates the superiority in reservoir characterization.

Seismic data reconstruction is a crucial step in seismic data processing, which faces numerous challenges in accurately capturing the complex patterns and structures within the data. Deep learning is revolutionizing the processing of seismic exploration data, enabling more precise imaging of subsurface structures and improving the detection of potential oil and gas reservoirs. We propose a modified least-squares generative adversarial network incorporating the inverse interpolation (LSGAN-II) method for seismic data reconstruction. Our approach integrates inverse interpolation algorithms into a generative adversarial network (GAN) framework to enhance both the accuracy and efficiency of seismic data reconstruction. Initially, a GAN is employed to predict local event slopes in seismic data, where a least-squares loss function is utilized to improve the learning capacity and convergence speed of the deep learning network. Subsequently, the predicted local event slopes are used as regularization operators in inverse interpolation, effectively enhancing the precision of the reconstructed seismic data. A dual-discriminator-based LSGAN-II is developed to implement the seismic data reconstruction process. This network combines the benefits of both GAN and inverse interpolation techniques, utilizing dual discriminator loss functions and a least-squares error loss function to optimize the prediction of local event slopes and the reconstruction of seismic data. The testing of the LSGAN-II method is conducted using two synthetic datasets and one actual dataset, demonstrating its effectiveness and practicality in seismic data reconstruction.

Rock physics and borehole data indicate the presence of directionally aligned fractures with moderate dip angles within the formation. Accurate identification of these fractures is crucial for the efficient exploration and development of unconventional hydrocarbon reservoirs. To enhance the prediction accuracy of fracture parameters in fractured reservoirs, this study derives an approximate reflection coefficient equation for tilted transversely isotropic (TTI) media under the assumption of weak anisotropy. The proposed method is based on the anisotropy parameters (A-parameter) and incorporates linear-slip theory to establish a relationship between the A-parameter and fracture weakness parameters in VTI media. This relationship is further extended to TTI media through coordinate rotation. To achieve stable and reliable estimation of fracture-related parameters, we develop an amplitude-difference-based AVAZ inversion (ADI) workflow within a Bayesian framework. Tests on synthetic models demonstrate that the proposed method is robust to noise and provides accurate inversion results. Furthermore, applying the method to OBN seismic data from a field area in the East China Sea confirms its feasibility and effectiveness, with inverted results showing strong agreement with well log data. This study offers a novel, efficient, and reliable framework for fracture prediction and reservoir characterization in geologically complex settings.

The assumption of transversely isotropic media with a vertical symmetry axis vertically transverse isotropic (VTI) has been widely utilized in the exploration of shale reservoirs, with its reflection response and pre-stack inversion attracting significant attention from geophysicists. However, accurately estimating anisotropic parameters using existing approximate reflection coefficient formulas for VTI media remains challenging. In theory, inversions based on exact reflection coefficients for VTI media could overcome these limitations. Nevertheless, such inversions present a highly nonlinear problem. The simultaneous inversion of five parameters further exacerbates the ill-posed nature of the inversion, making it difficult for conventional linearized algorithms to handle effectively. To address these challenges, this article proposes a nonlinear pre-stack inversion scheme based on the exact reflection coefficient equations for VTI media. Specifically, we establish an inversion objective function within a Bayesian framework and introduce a heuristic Newton-Raphson-based optimization (NRBO) algorithm for solving the nonlinear objective function. This approach mitigates the inaccuracies introduced by conventional linearized algorithms, enhancing the precision of the inversion results. Tests on 1-D single-well synthetic data, 2-D Hess VTI model synthetic data, and field data demonstrate that the proposed inversion scheme can stably and effectively estimate both elastic and anisotropic parameters simultaneously. Moreover, the inversion accuracy of the proposed approach surpasses that of inversions based on an approximate formula.

Fluid factors play an important role in reservoir fluid identification. Current fluid factor inversion methods rely on the exact Zoeppritz equations and their approximations, which neglect seismic wave propagation effects. This necessitates thorough multiple attenuation and amplitude compensation for inversion data. However, complex reservoirs with thin or interbedded strata often do not meet these requirements. The vectorized reflectivity method, based on a 1-D analytical solution of the full elastic wave equation, can accurately describe the true propagation response of seismic waves under the assumption of horizontally layered media. To address the aforementioned challenges, a new nonlinear inversion method for the Russell fluid factor is proposed by combining the reflectivity method with the fluid factor inversion approach. First, we rewrite the traditional reflection coefficient equations of the reflectivity method based on rock physics theory, obtaining new expressions that include the Russell fluid factor. To avoid instability in solving the first-order partial derivatives caused by changes in parameterization, we combine the new equations with a PID-based search algorithm (PSA) featuring global optimization properties, effectively ensuring the stability, accuracy, and convergence speed of the inversion algorithm. Additionally, the edge-preserving smoothing (EPS) operator is introduced into the PSA to enhance the reservoir boundary characterization ability of the fluid factor inversion results. Both synthetic and field data tests show that the proposed method significantly improves the estimation accuracy of the fluid factor in reservoirs with thin or interbedded strata, which is of great significance for advancing seismic fluid discrimination methods.

Prestack seismic data retain the amplitude variation with offset (AVO) characteristics, providing more geophysical information reflecting lateral reservoir variations, thus facilitating the identification of oil and gas reservoirs. However, due to the band-limited nature of seismic data, the precision of forward modeling, and the accuracy of algorithms, traditional prestack approaches suffer from ambiguity and uncertainty. With the development of deep learning and big data, an increasing number of deep learning methods have been proposed. We integrate the extended long short-term memory (xLSTM) modules with the Unet framework, and design a novel neural network architecture, that is, xLSTM-Unet, for elastic parameter inversion ($V_{\text {P}}$,$V_{\text {S}} $, and$\rho $) from prestack seismic gathers. Through testing on synthetic seismic records and field data, the proposed xLSTM-Unet outperforms both the traditional Unet and LSTM-Unet models in predicting elastic parameters from prestack seismic data. The xLSTM-Unet proposed in this article provides a stable and effective approach for predicting prestack elastic parameters, offering new insights for the intelligent development of seismic exploration.

We present a distributed power supply and explore its load transient response and power side-channel security improvements. Typically, countermeasures against power side-channel attacks (PSCAs) are based on specialized dc/dc converters, resulting in large power and area overheads and they are difficult to scale. Moreover, due to limited output voltage range and load regulation, it is not feasible to directly distribute these converters in multicore applications. Targeting those issues, our proposed converter is designed to provide multiple fast-responding voltages and use shared circuits to mitigate PSCAs. The proposed three-output dc/dc converter can deliver 0.33–0.92 V with up to 1 A to each load. Comparing with state-of-the-art power management works, our converter has$2\times $load step response speed and$4\times $reference voltage tracking speed. Furthermore, the converter requires$9\times $less inductance and$3\times $less output capacitance. In terms of PSCA mitigation, this converter reduces the correlation between input power trace and encryption load current by$107\times $, which is$3\times $better than the best standalone work, and it only induces 1.7% area overhead and 2.5% power overhead. The proposed work also increases minimum traces to disclose (MTDs) by$1250\times $. Considering all the above, our work could be a great candidate to be employed in future multicore systems supplying varying voltages and resisting side-channel attacks. It is the first work bridging the gap between on-chip power management and side-channel security.

Deep learning methods have gained widespread popularity for effectively suppressing random noise in seismic data. The recent progress in techniques based on supervised learning for attenuating seismic random noise underscores their potential, particularly when an abundant set of training examples is accessible. Unfortunately, collecting an adequate amount of representative training samples is not always feasible. DIP aims to capture a lot of low-level statistical information by using rich implicit prior knowledge inherent in the structure of the generation network itself. Therefore, it is not essential to provide a training database or uncontaminated data as a truth label, whereas only requires a noisy seismic image. In order to boost the performance, we add an explicit prior, weighted total variation, to the standard DIP, which leverages sparsity-promoting priors and restricts the solutions of DIP to satisfy a prior inherent in the seismic data. The proposed method is tested on synthetic seismic data with random noise that follows different distributions, then is applied to field pre- and post-stack seismic data. Furthermore, a comparison is drawn between the new method and the traditional DIP-based denoising method in terms of signal to noise ratio and local similarity. Our method shows more promising results because prior information from both the structure of the network and the seismic data is considered in the denoising processing.

To increase the accuracy and vertical resolution of seismic inversion for exploratory purposes, a new method was developed for P-wave velocity, S-wave velocity and density inversion using prestack seismic data based on the mayfly optimization algorithm (MA), exact Zoeppritz equations and Bayesian framework. A new form of an accurate Hessian matrix was successfully derived. We innovatively used the MA nonlinear AVA inversion based on the accurate Hessian matrix (MANAI-Hessian) method for prestack seismic inversion and highlighted two main challenges for the first time. The popular and recent whale optimization algorithm (WOA) and a conventional Levenberg–Marquardt (LM) method were introduced to demonstrate the existence of these two challenges. Comprehensive partial derivative tests were well designed to verify the existence of the second-order partial derivatives of the P-wave reflection coefficients. A 3D special wedge model was introduced to test the accuracy and vertical resolution of the new method. Next, we applied the proposed method to the field data of deep carbonate rock from a study area in China. Compared with the conventional LM method and the accurate Jacobian matrix-based nonlinear AVA inversion method, which provides foundational approaches to address the two main challenges, the proposed approach shows superior performance in terms of accuracy and vertical resolution.

In recent years, significant advancements have been achieved in the exploration of oil and gas reserves within carbonate rock formations, particularly with respect to the considerable resources found in deep Ordovician fault-controlled karst fracture-cave reservoirs. Accurately identifying such reservoirs using effective geophysical methods is crucial, but it is often challenging due to low signal-to-noise ratio and strong background reflections shielding of raw seismic data. To fully extract the information of carbonate reservoirs contained in the seismic data and enhance interpretation accuracy, we innovatively employ variational Bayesian principal component analysis (VBPCA) technique to perform background modeling on the raw seismic data, aiming to effectively isolate the bead-like reflections of reservoirs from interfering signals. Subsequently, we conduct attribute analysis on the processed seismic data, and optimize the sweetness attribute to identify cave reservoirs. The identified reservoirs exhibit complete shapes with clear boundaries, providing an intuitive depiction of their locations. In comparison to traditional principal component analysis (PCA) and probabilistic principal component analysis (PPCA), VBPCA offers several advantages, including automatic determination of the number of principal components, eliminating the inconvenience of manual settings, more effective separation of reservoir reflections from interfering reflections, and greater robustness to noise. Testing on synthetic seismic records and actual data from an oilfield in northern China has validated the feasibility and effectiveness of the proposed approach for identifying carbonate karst cave reservoirs.

The geostatistics stimulation method, as an important tool in subsurface modeling, is crucial for hydrocarbon reservoir characterization. Using geostatistical methods to reproduce complex heterogeneous structures is still challenging because of nonstationarity and computational consumption. We develop a stabilized stochastic simulation method by introducing the generative adversarial network based on a single image (SinGAN). It can preserve multiscale features contained in an individual training image by using a multistage training framework. In order to stabilize the training of the discriminator, the spectral normalization is integrated. We also introduce spatial attention and channel attention mechanism into the network to focus on the most significant features in each training stage, so that these features can be reproduced in the realizations. An adaptive strategy is adopted to automatically choose training stages, which balances the diversity and quality of simulation results and decreases the man-made factor on SinGAN. Several experiments are tested on synthetic and actual training images, respectively. We evaluate the simulation results from many perspectives, including variability, connectivity, probability density distribution, and time-consuming. The successful application of the new method on both categorical and continuous variables indicates that it has a strong ability to reproduce complex subsurface models, even for nonstationary geologic phenomena.

Russell’s fluid factor plays a crucial role in predicting hydrocarbon reservoirs. Numerous studies have been conducted on the inversion of Russell’s fluid factor. However, most of these studies exploit the approximate formulas of Zoeppritz as the forward equation. The approximate formulas affect the accuracy of the estimated Russell’s fluid factor, particularly in the moderate to large incidence angle range. To address this issue, we propose a nonlinear inversion scheme for Russell’s fluid factor based on the exact Zoeppritz equation. Initially, we derive a new form of the Zoeppritz equation that incorporates Russell’s fluid factor and Poisson’s ratio. Then, in the Bayesian framework, we establish a joint PP-PS objective function that represents by the Russell’s fluid factor. To solving the nonlinear objective function, we enhance the traditional whale optimization algorithm (WOA) by incorporating the Lévy flight strategy and stochastic learning theory, resulting in an optimized version named LSWOA (Lévy Flight and Stochastic Learning Whale Optimization Algorithm). The Russell’s fluid factor estimated by the new inversion method could provide a theoretical basis for the identification of oil and gas reservoirs, and also provide a new way for unconventional reservoirs prediction and sweet spot identification. To validate the accuracy of our method, we test it using both synthetic and actual field seismic data. Our test results demonstrate that the PP-PS wave joint inversion method of the Russell’s fluid factor based on the LSWOA algorithm exhibits high inversion accuracy and can be effectively applied in production.

This paper presents a scalable single-input-multiple-output DC/DC converter targeting load transient response and security improvement for low-power System-on-Chips (SoCs). A two-stage modular architecture is introduced to enable scalability. The shared switched-capacitor pre-charging circuits are implemented to improve load transient response and decouple correlations between inputs and outputs. The demo version of the converter has three identical outputs, each supporting 0.3V to 0.9V with a maximum load current of 150mA. Based on post-layout simulation results in 32nm CMOS process, the converter output provides 19.3V/$\mu$s reference tracking speed and 27mA/ns workload transitions with negligible voltage droops or spikes. No cross regulation is observed at any outputs with a worst-case voltage ripple of 68mV. Peak efficiency reaches 85.5% for each output. With variable delays added externally, the input-output correlations can change 10 times and for steady-state operation, such correlation factors are always kept below 0.05. The converter is also scaled to support 6 outputs with only 0.56mm2more area and maintains same load transient response performance.

Diffractions in the seismic data are associated with the small-scale subsurface structures, thus their separation and imaging are helpful in characterizing the underground discontinuities with a high resolution that cannot be reached by traditional reflection imaging methods. Traditional seismic slope-based diffraction separation methods are strongly affected by the accuracy and stability of the slope estimation methods, e.g., the plane-wave destruction (PWD) method. When the local seismic slope is not properly estimated, the separated seismic diffraction waves suffer from the mixture between the reflection and diffraction energy due to their coupling in the slope map. We propose an automatic local rank-reduction (LRR) method to separate 3D diffraction waves from zero-offset seismic data, based on which we conduct 3D migration to output the diffraction images. Due to the difficulty in choosing the rank in each local 3D window, we apply an adaptive strategy to obtain the optimal rank. The proposed LRR method with adaptively selected ranks (LRRA) is applied to several 3D synthetic and field data examples and demonstrated to perform better than the traditional PWD, the LRR, and the global rank-reduction (GRR) methods.

The omnidirectional plane-wave destruction (OPWD) algorithm can estimate the large dip by using circle-interpolating plane-wave destruction (PWD) filter but at the expense of causing potential instabilities due to the small values of the denominator in the regularized division problem. To mitigate the instability, one needs to use a relatively larger smoothing radius for a stronger regularization of the element-wise division, which however significantly decreases the resolution of dip estimation. We propose a new OPWD method without compromising the dip resolution for the large dip calculation by applying a nonstationary smoothness constraint to the model. We use a larger smoothing radius for areas that tend to cause instabilities and vice versa. The nonstationary smoothing is carried out in a simple and efficient recursion way. The synthetic and real seismic data examples demonstrate the performance of the proposed algorithm.

Surface wave exploration has been increasingly used in near-surface geophysical investigations. However, the accuracy and efficiency of picking dispersion curves are key to surface wave inversion. Traditional dispersion curve extraction requires manual picking, and the extraction accuracy and efficiency depend on the experience and knowledge of the interpreters. Therefore, developing a fast, high-precision and intelligent dispersion curve extraction method is urgent. This paper improves the structure and output of the U-Net neural network and regards the picking process of dispersion curves as an image classification problem, which quickly and accurately extracts dispersion curves from dispersion energy images. After combining the dispersion energy images of synthetic seismic data with the manually extracted dispersion curve and the theoretical dispersion curve obtained by the Schwab-Knopoff algorithm, the ICM (energy image and dispersion curve extracted manually) training set and the ICS (energy image and dispersion curve calculated by Schwab-Knopoff algorithm) training set are created. The synthetic data tests verify the feasibility of the improved U-Net neural network for automatically picking multimode dispersion curves. The dispersion curve picking results corresponding to two different training sets reveal that the U-Net network model obtained from the ICS training sets exhibits better extraction accuracy. Additionally, we analyze the influence of the sample number of the training set on the dispersion curve picking effect of the improved U-Net and conclude that the improved U-Net network has the advantages of a low training set size requirement and a high dispersion curve extraction accuracy. Finally, the trained network extracts the dispersion curves of two groups of measured surface wave data and obtains plausible extraction results, further proving the proposed method’s effectiveness.

Predictive filtering is one of the most widely used denoising algorithms in the seismic data processing community because of its high efficiency and stability in different situations. The traditional predictive filtering, however, is not able to deal with structurally complex data set unless applied in local windows. We develop a novel noncausal predictive filtering method that is free of the windowing step but is able to denoise complicated data set. We extend the stationary predictive filtering method to its nonstationary version, where the predictive filter coefficients vary across the frequency-space domain. The nonstationary predictive filtering (NPF) model requires solving a highly underdetermined inverse problem using an iterative shaping regularization method. The traditional shaping regularization method solves an inverse problem by applying a constant smoothing operator and thus does not consider the heterogeneity of the filter coefficients in the frequency–space domain. We propose to apply a nonstationary smoothing operator to constrain the model in the shaping regularization framework. The smoothing radius in the nonstationary smoothing operator is chosen based ona prioriinformation of the model, e.g., the nonstationarity of the data in the frequency–space domain. The proposed NPF method offers the flexibility in controlling the smoothness and sharpness of the calculated filter coefficients in both frequency and space dimensions. Several synthetic data sets and complicated real data examples are used to demonstrate the advantages of the new method.

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually misses along various spatial axes and always mix with random noise. In order to obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. Nonsubsampled contourlet transform is an effective transform to obtain multi-scale and multi-direction sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the nonsubsampled contourlet transform framework. First, we use nonsubsampled contourlet transform to convert the seismic missing data with random noise to sparse domain. Then, we apply two-step iterative log thresholding algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse nonsubsampled contourlet transform to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

High-amplitude noise could interfere with useful seismic signals, affecting our ability in processing and interpreting seismic data. Thus, attenuating seismic noise is an important task in seismic processing. Total variation (TV) has played an important role in many steps of seismic data processing but always neglected the seismic structural information. Directional TV (DTV), however, considers the structural direction of seismic events but tends to cause the staircasing effect on seismic records based on the first-order formulation. Here, we develop a high-order DTV (HDTV) method for seismic denoising. It considers the local structural direction of the seismic data and calculates the higher order derivatives of seismic images to avoid the staircasing effect. We design several synthetic models that are contaminated by various types of random noise to test the denoising ability. The denoising performance of our new method is compared with the first-order DTV, conventional high-order TV, and TV regularization methods from two aspects, i.e., the signal-to-noise ratio and the effective signal leakage degree. Then, the advantages of the proposed method are further validated via several field seismic data sets.

Lithofacies classification is an indispensable procedure in well logging and seismic data interpretation. We propose a novel deep classified autoencoder learning approach to identify lithofacies for high-dimensional data and complex problems. Deep autoencoder (DAE) is an unsupervised learning method via layerwise pretraining multiple autoencoders. It can learn deep data features automatically and reconstruct the original data with a small error. Introducing sparse constraint (i.e., sparse autoencoder) potentiates the learning ability of autoencoder. On this foundation, additional regularization terms constructed by labeled samples are considered in the new DAE approach in order to boost the performance. The new method can adaptively preserve the most significant input features and remove insensitive properties to decrease computational complexity. At the same time, we embed the class information into the loss function of autoencoder to measure intraclass similarity and improve the classification accuracy. Several experiments on well data and seismic data show that the proposed method achieves promising results. Compared with the traditional deep autoencoder (DAE), the proposed method is more competitive in terms of classification accuracy and robustness.

Seismic data are usually contaminated by various noises. Noise suppression plays an important role in seismic processing. In this article, we propose a new denoising method based on the nonlocal weighted robust principal component analysis (RPCA). First, seismic data are divided into many patches and grouped based on the nonlocal similarity. For each group, then, we establish a similar block matrix and set up the objective function of the RPCA. Next, we introduce the iterative log-thresholding algorithm into the augmented Lagrangian method to solve the problem. Furthermore, varying weights are specified to different singular values when minimizing the objective function. Finally, aggregating all recovered matrices can obtain the denoised seismic data. The proposed method considers the nonlocal similarity and adaptively sets weights with local noise variance. It performs well also owing to the superiority of the iterative log-thresholding method. The presented method is assessed using a synthetic seismic section with several crossover events. We also apply this novel approach to a real seismic data, which shows good results. Comparison with other approaches reveals the effectiveness of the proposed approach.

A sparse dictionary is more adaptive than a sparse fixed-basis transform since it can learn the features directly from the input data in a data-driven way. However, learning a sparse dictionary is time-consuming because a large number of iterations are required in order to obtain the dictionary atoms that best represent the features of input data. The computational cost becomes unaffordable when it comes to high-dimensional problems, e.g., 3-D or even 5-D applications. We propose an efficient high-dimensional dictionary learning (DL) method by avoiding the singular value decomposition (SVD) calculation in each dictionary update step that is required by the classic$K$-singular value decomposition (KSVD) algorithm. Besides, due to the special structure of the sparse coefficient matrix, it requires a much less expensive sparse coding process. The overall computational efficiency of the new DL method is much higher, while the results are still comparable or event better than those from the traditional KSVD method. We apply the proposed method to both 3-D and 5-D seismic data reconstructions and demonstrate successful and efficient performance.

Facies identification is a powerful means to predict reservoirs. We achieve facies identification using a relevance vector machine (RVM) and develop a facies discriminant method based on a multikernel RVM (MKRVM). An RVM has the same functional form as a support vector machine (SVM) that is widely used in geophysics and shows a promising performance in disposing of small-samples, nonlinear and high-dimensional problems. The RVM inherits these superiorities, and its training is implemented under the Bayesian framework. Thus, it can provide probability information about the classified facies, which is critical to evaluate uncertainty of the result. Besides, the penalty parameter of the RVM does not depend on human experience. Compared with single-kernel learning, multikernel learning (MKL) is more flexible. After mapping the original data into a combined space by MKL, the features can be more accurately expressed in the new space, thereby improving the classification accuracy. Therefore, we introduce the RVM into facies classification and extend it to the MKRVM-based facies identification. The proposed method has advantageous properties such as strong generalization ability and high accuracy. First, we apply the approach to well log facies classification with different input features. Then, it is applied to seismic lithofacies identification with inverted elastic attributes to predict the target reservoirs. All the examples verify the effect and potential of the new method.

We propose a novel two-stage hybrid on-chip DC-DC converter targeting low power applications with multiple supply voltage domains and dynamic workloads. The converter has a nominal input voltage of 1.2V and generates two asymmetrically regulated output voltages simultaneously. The high-power output channel provides voltages ranging from 0.3V to 1.1V and up to 12mA load current; on the other hand, the low power output channel delivers voltages varying from 0.3V to 0.5V with up to 1mA load current. The high-power output is able to respond to load transition requests with a peak voltage slew rate of 16V/µs and maximum voltage ripple of 49mV. During load transitions at the high-power channel, the low-power output voltage with fixed load remains stable with less than 7.6% ripples and a worst case droop of 45 mV. In addition, when load transitions are requested at both output channels simultaneously, there are no observable voltage droops/spikes at the outputs; thus, cross regulations are significantly reduced. Even with input voltage glitches, additional voltage spikes/droops at each output are less than 5%. Peak power efficiency achieved is 73%.