京津唐张地区速度结构和震源位置联合反演的遗传算法

震源参数和速度结构的联合反演是一个典型的非线性名参数最优化问题，常规的局部线性化反演方法往往易于陷入局部极值，且严重依赖于初始模型的选取。模拟生物界进化的遗传算法则是一种简单而高效的全局性搜索方法。     

AN ALTERNATIVE STRATEGY FOR NON-LINEAR INVERSION OF SEISMIC WAVEFORMS1

A common example of a large-scale non-linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large-scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions. A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process. We propose a new strategy for the non-linear inversion of multi-offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large-scale matrix inversion but pays particular attention to different parameter types in the inversion. We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub-space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well-conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.     

量子遗传算法在大地电磁反演中的应用

量子遗传算法（QGA）以量子理论为基础,通过利用量子位编码代替经典遗传算法的二进制位编码,利用量子旋转门定向更新种群来代替传统方法中种群的选择、交叉和变异过程,使得算法具有一定的内在并行运算能力和量子的隧道效应,从而加快了搜索速度,改善了收敛速度,并具有更强的全局寻优能力.本文针对地球物理反演问题的非线性、多极值特点提出一套实现方案,通过理论模型和实测数据试验对比研究,表明量子遗传方法在大地电磁反演中的寻优质量和效果明显优于传统遗传算法.     

应力张量反演的遗传算法及其在青藏高原东北缘的应用

为准确而快速地求解区域构造应力张量,构建了基于震源机制解反演应力张量的遗传算法策略,详细介绍了计算原理,分析了以断层面上剪应力方向和滑动方向的偏差为约束反演应力张量而忽略剪应力大小偏差对反演结果的影响,表明仅考虑剪应力方向和滑动方向的偏差就可以得到正确结果.利用不同应力状态下人工合成的包含不同噪声水平的震源机制数据对该方法进行检验,并与网格搜索法得到的结果比较.表明本文方法所得结果的拟合差均小于网格搜索法结果的拟合差,并且二者相差较小,体现了本文方法的稳健性.将该方法应用于青藏高原东北缘(103-106°E,34.5-37.5°N)应力张量的估计,结果显示,该区域主要受控于青藏高原近东西向的挤压,从而导致阿拉善块体以及华南块体方向的拉张,并且向华南块体方向的拉张作用强于向阿拉善块体的拉张作用.     

Seismic Event Location: Nonlinear Inversion Using a Neighbourhood Algorithm

—?A recently developed direct search method for inversion, known as a neighbourhood algorithm (NA), is applied to the hypocentre location problem. Like some previous methods the algorithm uses randomised, or stochastic, sampling of a four-dimensional hypocentral parameter space, to search for solutions with acceptable data fit. Considerable flexibility is allowed in the choice of misfit measure.¶At each stage the hypocentral parameter space is partitioned into a series of convex polygons called Voronoi cells. Each cell surrounds a previously generated hypocentre for which the fit to the data has been determined. As the algorithm proceeds new hypocentres are randomly generated in the neighbourhood of those hypocentres with smaller data misfit. In this way all previous hypocentres guide the search, and the more promising regions of parameter space are preferentially sampled.¶The NA procedure makes use of just two tuning parameters. It is possible to choose their values so that the behaviour of the algorithm is similar to that of a contracting irregular grid in 4-D. This is the feature of the algorithm that we exploit for hypocentre location. In experiments with different events and data sources, the NA approach is able to achieve comparable or better levels of data fit than a range of alternative methods; linearised least-squares, genetic algorithms, simulated annealing and a contracting grid scheme. Moreover, convergence was achieved with a substantially reduced number of travel-time/slowness calculations compared with other nonlinear inversion techniques. Even when initial parameter bounds are very loose, the NA procedure produced robust convergence with acceptable levels of data fit.     

三维大地电磁自适应正则化有限内存拟牛顿反演

有别于传统基于梯度信息的反演方法在正则化约束中用总梯度逼近海塞逆矩阵的技术,本文将正则化约束问题的数据拟合项和模型光滑项分开考虑,只利用数据拟合函数的梯度信息对数据拟合项的海塞矩阵进行逼近,通过求解类高斯牛顿下降方向方程得到不依赖前几次迭代正则化因子的更精确下降方向,在求解当前迭代下降方向的过程中,通过保证右端项中两个向量的二范数在同一数量级的原则,实现了正则化因子的自动更新.对理论模型的试算表明这种自适应正则化反演方案可以在拟牛顿反演框架下基本达到OCCAM的算法稳定性,反演结果对初始模型依赖性较小,同时又无需在一次迭代中多次搜索最佳正则化因子.本文还基于此算法讨论了大地电磁各参数对于反演结果的影响,由于本文的反演结果能得到充分的正则化约束,因而在此框架下讨论阻抗和倾子在反演中的作用相对更为客观.     

1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic‐algorithm‐sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis–Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one‐dimensional elastic full‐waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the “genetic drift” effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step.     

Using a hybrid genetic algorithm–simulated annealing algorithm for fuzzy programming of reservoir operation

We present a novel approach for optimizing reservoir operation through fuzzy programming and a hybrid evolution algorithm, i.e. genetic algorithm (GA) with simulated annealing (SA). In the analysis, objectives and constraints of reservoir operation are transformed by fuzzy programming for searching the optimal degree of satisfaction. In the hybrid search procedure, the GA provides a global search and the SA algorithm provides local search. This approach was investigated to search the optimizing operation scheme of Shihmen Reservoir in Taiwan. Monthly inflow data for three years reflecting different hydrological conditions and a consecutive 10‐year period were used. Comparisons were made with the existing M‐5 reservoir operation rules. The results demonstrate that: (1) fuzzy programming could effectively formulate the reservoir operation scheme into degree of satisfaction α among the users and constraints; (2) the hybrid GA‐SA performed much better than the current M‐5 operating rules. Analysis also found the hybrid GA‐SA conducts parallel analyses that increase the probability of finding an optimal solution while reducing computation time for reservoir operation. Copyright © 2007 John Wiley & Sons, Ltd.     

基于GA-BP理论的储层视裂缝密度地震非线性反演方法

基于GA-BP理论,将自适应遗传算法与人工神经网络技术(BP算法)有机地相结合,形成了一种储层裂缝自适应遗传-神经网络反演方法.这种新的方法是由编码、适应度函数、遗传操作及混合智能学习等组成,即在成像测井裂缝密度数据约束下,通过对目标问题进行编码(称染色体),然后对染色体进行选择、交叉和变异等遗传操作,使染色体不断进化,从而快速获得全局最优解.在反演执行过程中,利用地震数据和成像测井裂缝密度数据之间的非线性映射关系建立训练样本,将GA算法与BP算法有机地结合,优化三层前向网络参数;或将GA与ANFIS相结合,优化ANFIS网络参数.并采用GA算法与TS算法(Tabu Search)相结合的自适应混合学习算法,该学习算法自始至终将GA和BP两种算法按一定的概率比例进行,其概率自适应变化,以达到混合算法的均衡.这种混合算法提高了网络的收敛速度和精度.我们分别利用两个研究地区的6井和1井成像测井裂缝密度数据与地震数据之间的非线性映射关系建立训练样本,对过这两口井的测线的地震数据进行反演,获得了视裂缝密度剖面,视裂缝密度剖面上裂缝分布特征符合沉积相分布特征和岩石力学性质的变化特征.这种视裂缝密度剖面含有储层裂缝的定量信息,其误差可为油气勘探开发实际要求所允许.因此,这种新的方法优于只能作裂缝定性分析的常规裂缝地震预测方法,具有广阔的应用前景.     

Inversion of multicomponent seismic time shifts for reservoir pressure and length: a feasibility study

Pressure drops associated with reservoir production generate excess stress and strain that cause travel‐time shifts of reflected waves. Here, we invert time shifts of P‐, S‐, and PS‐waves measured between baseline and monitor surveys for pressure reduction and reservoir length. The inversion results can be used to estimate compaction‐induced stress and strain changes around the reservoir. We implement a hybrid inversion algorithm that incorporates elements of gradient, global/genetic, and nearest neighbour methods and permits exploration of the parameter space while simultaneously following local misfit gradients. Our synthetic examples indicate that optimal estimates of reservoir pressure from P‐wave data can be obtained using the reflections from the reservoir top. For S‐waves, time shifts from the top of the reservoir can be accurately inverted for pressure if the noise level is low. However, if noise contamination is significant, it is preferable to use S‐wave data (or combined shifts of all three modes) from reflectors beneath the reservoir. Joint wave type inversions demonstrate improvements over any single pure mode. Reservoir length can be estimated using the time shifts of any mode from the reservoir top or deeper reflectors. We also evaluate the differences between the actual strain field and those corresponding to the best‐case inversion results obtained using P‐ and S‐wave data. Another series of tests addresses the inversion of the time shifts for the pressure drops in two‐compartment reservoirs, as well as for the associated strain field. Numerical testing shows that a potentially serious source of error in the inversion is a distortion in the strain‐sensitivity coefficients, which govern the magnitude of stiffness changes. This feasibility study suggests which wave types and reflector locations may provide the most accurate estimates of reservoir parameters from compaction‐induced time shifts.     

Assessment of the reliability of 2D inversion of apparent resistivity data

The reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness‐constrained non‐linear least‐squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low‐resistivity fill within a high‐resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least‐squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity.     

Anisotropy from full waveform inversion of multicomponent seismic data using a hybrid optimization method

Seismic waveforms contain valuable information about the media, but the waveform inversion is a non‐linear problem. We present a waveform inversion method that combines a local optimization method with a genetic algorithm to determine the anisotropic parameters of a horizontally stratified medium. Synthetic seismograms for a horizontally stratified anisotropic medium are calculated using the reflectivity technique. In the initial stage of the inversion, the global space‐sampling properties of the genetic algorithm are used to direct the search to the region close to the global solution. This solution is then further improved using a conjugate‐gradient method. The numerical experiments performed with noisy synthetic data show that our hybrid optimization method satisfactorily reconstructs the anisotropic parameters at a reasonable computing cost while the range of slowness is adequate. We found that (i) for small‐angle data neither single‐ nor multiple‐component data are sufficient to determine the anisotropic parameters uniquely; (ii) for medium‐angle data the multiple‐component data are sufficient to determine the anisotropic parameters exactly whereas the single‐component data are not sufficient; and (iii) for wide‐angle data, either single‐ or multiple‐component data are sufficient to determine the anisotropic parameters accurately.     

Non-linear inversion of resistivity profiling data for some regular geometrical bodies1

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting. We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.     

Inversion of controlled‐source electromagnetic data using a model‐based approach

A two‐and‐half dimensional model‐based inversion algorithm for the reconstruction of geometry and conductivity of unknown regions using marine controlled‐source electromagnetic (CSEM) data is presented. In the model‐based inversion, the inversion domain is described by the so‐called regional conductivity model and both geometry and material parameters associated with this model are reconstructed in the inversion process. This method has the advantage of using a priori information such as the background conductivity distribution, structural information extracted from seismic and/or gravity measurements, and/or inversion results a priori derived from a pixel‐based inversion method. By incorporating this a priori information, the number of unknown parameters to be retrieved becomes significantly reduced. The inversion method is the regularized Gauss‐Newton minimization scheme. The robustness of the inversion is enhanced by adopting nonlinear constraints and applying a quadratic line search algorithm to the optimization process. We also introduce the adjoint formulation to calculate the Jacobian matrix with respect to the geometrical parameters. The model‐based inversion method is validated by using several numerical examples including the inversion of the Troll field data. These results show that the model‐based inversion method can quantitatively reconstruct the shapes and conductivities of reservoirs.     

Enforcing smoothness and assessing uncertainty in non-linear one-dimensional prestack seismic inversion

Estimation of elastic properties of rock formations from surface seismic amplitude measurements remains a subject of interest for the exploration and development of hydrocarbon reservoirs. This paper develops a global inversion technique to estimate and appraise 1D distributions of compressional‐wave velocity, shear‐wave velocity and bulk density, from normal‐moveout‐corrected PP prestack surface seismic amplitude measurements. Specific objectives are: (a) to evaluate the efficiency of the minimization algorithm (b) to appraise the impact of various data misfit functions, and (c) to assess the effect of the degree and type of smoothness criterion enforced by the inversion. Numerical experiments show that very fast simulated annealing is the most efficient minimization technique among alternative approaches considered for global inversion. It is also found that an adequate choice of data misfit function is necessary for a reliable and efficient match of noisy and sparse seismic amplitude measurements. Several procedures are considered to enforce smoothness of the estimated 1D distributions of elastic parameters, including predefined quadratic measures of length, flatness and roughness. Based on the general analysis of global inversion techniques, we introduce a new stochastic inversion algorithm that initializes the search for the minimum with constrained random distributions of elastic parameters and enforces predefined autocorrelation functions (semivariograms). This strategy readily lends itself to the assessment of model uncertainty. The new global inversion algorithm is successfully tested on noisy synthetic amplitude data. Moreover, we present a feasibility analysis of the resolution and uncertainty of prestack seismic amplitude data to infer 1D distributions of elastic parameters measured with wireline logs in the deepwater Gulf of Mexico. The new global inversion algorithm is computationally more efficient than the alternative global inversion procedures considered here.     

基于单台加速度记录的混合全局优化HVSR反演场地浅层速度结构

利用水平与竖向谱比（HVSR）方法反演场地速度结构是国际上迅速发展的研究领域.HVSR反演计算实质是一个土层场地模型空间搜索的全局优化问题,当模型搜索空间的复杂程度增大时,目前常用的搜索算法收敛速度慢,计算效率较低.本文实现了一种结合遗传和模拟退火方法优点的混合全局优化HVSR反演算法,通过理论模型和竖向台阵实测数据的检验,表明该算法能获得很好的反演效果,较好地解决了蒙特卡罗方法收敛速度慢,遗传算法收敛早熟和模拟退火算法搜索效率低的问题.本文在此基础上讨论了单台加速度S波记录用于场地速度结构HVSR反演的适用性,为基于单个地震台的地震观测记录反演浅层速度结构提供了一种高效且较为准确的反演方法.     

Soil production and hillslope transport in mid‐latitudes during the last glacial–interglacial cycle: a combined data and modelling approach in northern Ardennes

The relative efficiency of various hillslope processes through Quaternary glacial–interglacial cycles in the mid‐latitudes is not yet well constrained. Based on a unique set of topographic and soil thickness data in the Ardennes (Belgium), we combine the new CLICHE model of climate‐dependent hillslope evolution with an inversion algorithm in order to get deeper insight into the ways and timing of hillslope dynamics under one such climatic cycle. We simulate the evolution of a synthetic hill reproducing the slope, curvature, and contributing area distributions of the hillslopes of a ~ 2500 km² real area under a simple two‐stage 120‐kyr‐long climatic scenario with linear transitions between cold and warm stages. The inversion method samples a misfit function in the model parameter space, based on estimates of the fit of topographic derivative distributions in classes of soil thickness and of the relative frequencies of the predicted soil thickness classes. Though the inversion results show remarkable convergence patterns for most parameters, no unique solution emerges. We obtain five clusters of good fits, whose centroids are taken as acceptable model solutions. Based on the predicted time series of average denudation rate and soil thickness, plus snapshots of the soil distribution at characteristic times, we discuss these solutions and, comparing them with independent data not involved in the misfit function, we identify the most realistic scenario. Beyond providing first‐order estimates of several parameters that compare well with published data, our results show that denudation rates increase dramatically for a short time at both warm–cold and cold–warm transitions, when the mean annual temperature passes through the [0, ?5 °C] range. We also point to the overwhelming importance of solifluction in shaping hillslopes and transporting soil, and the role of depth‐dependent creep (including frost creep) throughout the climatic cycle, whereas the contributions of simple creep and overland flow are minor. Copyright © 2016 John Wiley & Sons, Ltd.     

Inversion of ocean-bottom seismometer (OBS) waveforms for oceanic crust structure: a synthetic study

The waveform inversion method is applied—using synthetic ocean-bottom seismometer(OBS) data—to study oceanic crust structure. A niching genetic algorithm(NGA) is used to implement the inversion for the thickness and P-wave velocity of each layer, and to update the model by minimizing the objective function, which consists of the misfit and cross-correlation of observed and synthetic waveforms. The influence of specific NGA method parameters is discussed, and suitable values are presented.The NGA method works well for various observation systems, such as those with irregular and sparse distribution of receivers as well as single receiver systems. A strategy is proposed to accelerate the convergence rate by a factor of five with no increase in computational complexity; this is achieved using a first inversion with several generations to impose a restriction on the preset range of each parameter and then conducting a second inversion with the new range. Despite the successes of this method,its usage is limited. A shallow water layer is not favored because the direct wave in water will suppress the useful reflection signals from the crust. A more precise calculation of the air-gun source signal should be considered in order to better simulate waveforms generated in realistic situations; further studies are required to investigate this issue.     

Joint facies and rock properties Bayesian amplitude‐versus‐offset inversion using Markov random fields

Seismic reflection pre‐stack angle gathers can be simultaneously inverted within a joint facies and elastic inversion framework using a hierarchical Bayesian model of elastic properties and categorical classes of rock and fluid properties. The Bayesian prior implicitly supplies low frequency information via a set of multivariate compaction trends for each rock and fluid type, combined with a Markov random field model of lithotypes, which carries abundance and continuity preferences. For the likelihood, we use a simultaneous, multi‐angle, convolutional model, which quantifies the data misfit probability using wavelets and noise levels inferred from well ties. Under Gaussian likelihood and facies‐conditional prior models, the posterior has simple analytic form, and the maximum a‐posteriori inversion problem boils down to a joint categorical/continuous non‐convex optimisation problem. To solve this, a set of alternative, increasingly comprehensive optimisation strategies is described: (i) an expectation–maximisation algorithm using belief propagation, (ii) a globalisation of method (i) using homotopy, and (iii) a discrete space approach using simulated annealing. We find that good‐quality inversion results depend on both sensible, elastically separable facies definitions, modest resolution ambitions, reasonably firm abundance and continuity parameters in the Markov random field, and suitable choice of algorithm. We suggest usually two to three, perhaps four, unknown facies per sample, and usage of the more expensive methods (homotopy or annealing) when the rock types are not strongly distinguished in acoustic impedance. Demonstrations of the technique on pre‐stack depth‐migrated field data from the Exmouth basin show promising agreements with lithological well data, including prediction accuracy improvements of 24% in and twofold in density, in comparison to a standard simultaneous inversion. Much clearer and extensive recovery of the thin Pyxis gas field was evident using stronger coupling in the Markov random field model and use of the homotopy or annealing algorithms.     

Iteratively re‐weighted and refined least squares algorithm for robust inversion of geophysical data

A robust metric of data misfit such as the ?₁‐norm is required for geophysical parameter estimation when the data are contaminated by erratic noise. Recently, the iteratively re‐weighted and refined least‐squares algorithm was introduced for efficient solution of geophysical inverse problems in the presence of additive Gaussian noise in the data. We extend the algorithm in two practically important directions to make it applicable to data with non‐Gaussian noise and to make its regularisation parameter tuning more efficient and automatic. The regularisation parameter in iteratively reweighted and refined least‐squares algorithm varies with iteration, allowing the efficient solution of constrained problems. A technique is proposed based on the secant method for root finding to concentrate on finding a solution that satisfies the constraint, either fitting to a target misfit (if a bound on the noise is available) or having a target size (if a bound on the solution is available). This technique leads to an automatic update of the regularisation parameter at each and every iteration. We further propose a simple and efficient scheme that tunes the regularisation parameter without requiring target bounds. This is of great importance for the field data inversion where there is no information about the size of the noise and the solution. Numerical examples from non‐stationary seismic deconvolution and velocity‐stack inversion show that the proposed algorithm is efficient, stable, and robust and outperforms the conventional and state‐of‐the‐art methods.