Spatial interpolation methods for nonstationary plume data

Plume interpolation consists of estimating contaminant concentrations at unsampled locations using the available contaminant data surrounding those locations. The goal of ground water plume interpolation is to maximize the accuracy in estimating the spatial distribution of the contaminant plume given the data limitations associated with sparse monitoring networks with irregular geometries. Beyond data limitations, contaminant plume interpolation is a difficult task because contaminant concentration fields are highly heterogeneous, anisotropic, and nonstationary phenomena. This study provides a comprehensive performance analysis of six interpolation methods for scatter-point concentration data, ranging in complexity from intrinsic kriging based on intrinsic random function theory to a traditional implementation of inverse-distance weighting. High resolution simulation data of perchloroethylene (PCE) contamination in a highly heterogeneous alluvial aquifer were used to generate three test cases, which vary in the size and complexity of their contaminant plumes as well as the number of data available to support interpolation. Overall, the variability of PCE samples and preferential sampling controlled how well each of the interpolation schemes performed. Quantile kriging was the most robust of the interpolation methods, showing the least bias from both of these factors. This study provides guidance to practitioners balancing opposing theoretical perspectives, ease-of-implementation, and effectiveness when choosing a plume interpolation method.     

位场数据网格化的反插值法

位场不规则分布数据的网格化是位场数据分析处理的首要问题.本文借鉴反插值法的原理,提出利用基于预条件共轭梯度的反插值法实现位场数据的网格化.其中,插值算子采用高斯权系数,滤波算子采用Laplacian算子,预条件算子采用滤波算子的逆.通过理论模型和实际航磁数据的网格化试验分析,验证了本文的反插值法适合地球物理位场特征,网格化速度快,精度高,效果好.     

Directional interpolation of multicomponent data

A method for interpolation of multicomponent streamer data based on using the local directionality structure is presented. The derivative components are used to estimate a vector field that locally describes the direction with the least variability. Given this vector field, the interpolation can be phrased in terms of the solution of a partial differential equation that describes how energy is transported between regions of missing data. The approach can be efficiently implemented using readily available routines for computer graphics. The method is robust to noise in the measurements and particularly towards high levels of low‐frequent noise that is present in the derivative components of the multicomponent streamer data.     

混采数据分离中插值与去噪的同步处理

近年来,由于新兴的混合采集观测系统在很大程度上提高了采集效率,因此得到了很多学者和石油公司的青睐.但在实际应用中,这种特殊观测系统的采集质量却受到很多因素的影响.一方面,该观测系统采集到的炮记录会受到相邻炮记录的干扰;另一方面,复杂的采集环境使得地震记录中包含部分空道;另外,采集过程中的场地环境干扰会不可避免地带入随机噪音,它们都会影响采集质量.虽然已有一些学者对这些因素做了相关研究,但都是单独分析,未能综合考虑各种干扰因素.本文基于稀疏约束反演的基本原理,将混合炮数据的分离、缺失道集的插值以及对随机噪音的压制问题整合在一起,通过一步处理同时减小如上三方面因素的不利影响,在改善信噪比的同时极大地提高了地震资料的处理效率.文章利用模拟数据和实际数据对这种新方法进行了验证,均得到了比较满意的效果.     

Suitable gravity interpolation technique for large data gaps in Africa

Studia Geophysica et Geodaetica - The gravity database for the IAG African Geoid Project contains significantly large data gaps. These large data gaps affect the interpolation precision of the...     

Interferometric interpolation of sparse marine data

We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green's function and a model‐based Green's function for a water‐layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up‐ and downgoing separation of both recorded and model‐based Green's functions can help in minimizing artefacts in a virtual shot gather. If the up‐ and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non‐stationary 1D multi‐channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f‐k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method.     

Performance of detrending models of crop yield risk assessment: evaluation on real and hypothetical yield data

Detrending is a widely used technique for obtaining stationary time series data in residual analysis and risk assessment. The technique is frequently applied in crop yield risk assessment and insurance ratings. Although several trend models have been proposed in the literature, whether these models achieve consistent detrending results and successfully extract the true yield trends is rarely discussed. In the present article, crop insurance pricing is evaluated by different trend models using real and historical yield data, and hypothetical yield data generated by Monte Carlo simulations. Applied to real historical data, the linear, loglinear, autoregressive integrated moving average trend models produce different risk assessment results. The differences among the model outputs are statistically significant. The largest deviation in the county crop assessment reaches 6–8 %, substantially larger than the present countrywide gross premium rate of 5–7 %. In performance tests on simulated yield trends, popular detrending methods based on smoothing techniques proved overall superior to linear, loglinear, and integrated autoregression models. The best performances were yielded by the moving average and robust locally weighted regression models.     

基于匹配追踪算法的OVT域五维插值技术研究

为提高宽方位地震数据的成像质量,改善面元属性之间的不均匀性,发展了宽方位OVT域数据五维插值技术.正交匹配追踪傅立叶插值技术是OVT域五维数据插值的有效技术,该技术以傅立叶变换作为算子,将数据变换到频率空间域,产生若干个频率切片,从若干个频率切片中选取一个傅立叶分量系数,同时综合利用地震数据的"纵向、横向、时间、偏移距、方位角"五个维度信息计算插值算子,为了避免选中假频成份,在每一步迭代中通过引入滤波算子对所选取的傅立叶分量的系数进行重新计算,实现反假频的目的 .与常规三维数据插值相比,OVT域五维插值更精确,振幅保真性更好.     

反插值法实现地球物理数据快速网格化

本文借鉴反演理论，采用反插值法实现地球物理数据的快速网格化.首先由已知点与未知网格点的反距离拓扑关系建立反演方程，用已知点值直接计算出其所在网格的未知网格点值，再利用Laplacian算子滤波，使得模型光滑，且能量最小化.利用预条件共轭梯度法求解网格化方程组，并结合螺旋坐标系思想和Wilson\|Burg谱分解法，将二维数据的滤波处理转换到一维空间进行处理，实现二维数据快速滤波.另外，引入了阻尼约束，保证求解稳定、迭代收敛.最后，应用该方法对合成数据和实际资料进行了试验.     

Performance of geostatistical interpolation methods for modeling sampled data with non-stationary mean

The measured ozone pollution peak in the atmosphere of Mexico City region was considered in order to study the effect of a non-stationary mean of the sampled data in geostatistics interpolation methods. With this objective the local mean value of the sampled data was estimated through a linear regression analysis of their values on the monitoring station’s coordinates. The residuals obtained by removing the data trend are considered as a set of stationary random variables. Several interpolation methods used in geostatistics, such as inverse distance weighted, kriging, and artificial neural networks techniques were considered. In an effort to optimize and evaluate its performance, we fit interpolated values to sampled data, obtaining optimal values for the parameters defining the used model, that means, the values of the parameters that give the lowest mean RMSE between the interpolated value and measured data at 20 stations at 1500 hours for a set of 21 days of December 2001, which was chosen as the training set. The training set is conformed by all the days in December 2001 excepting the days (3,6,9,12,...,27,30) which were considered as the testing set. Once the optimal model is obtained, it is used to interpolate the values at the stations at 1500 hours for the testing days. The RMSE between interpolated and measured values at monitoring stations was also evaluated for these testing values and is shown as a percentage in Table 2. These values and the defined generalization parameter G, can be used to evaluate the performance and the ability of the models to predict and reproduce the peak of ozone concentrations. Scatter plots for testing data are presented for each interpolation method. An interpretation of the ozone pollution levels obtained at 1500 hours at December 21 was given using the wind field that prevailed in the region 1 h before the same day.     

基于频率-结构双重加权阈值的地震数据插值

地震数据的插值是地震数据处理的关键环节,插值效果的优劣关系到后续反演、去噪、反褶积、偏移等工作的进行.基于稀疏反演的常规频率-波数（FK）域插值方法往往使用广义阈值,而由于缺失地震数据仅沿波数方向呈稀疏态,在沿频率方向呈类子波频谱形态分布的非稀疏态,直接应用基于Lp范数的广义阈值会难以补全缺失数据的高低频信息,不利于后续依赖低频信息的反演及依赖高频的高分辨率处理工作的开展;基于该问题,本文设计沿频率方向类子波频谱形态变化的频率加权阈值,同时考虑完整地震数据在波数域的聚集分布,引入沿波数方向的结构加权阈值,提出基于频率-结构的双重加权阈值,在补全缺失地震道的同时,保证其高低频信息的有效恢复.模型和实际数据表明,相比于广义阈值,基于频率-结构的双重加权阈值可以减少插值误差,最大限度保证缺失地震道位置插值结果高低频信息的完整性.

     

强剩磁强退磁条件下的二维井中磁测反演

强剩磁、强退磁改变了总磁化强度的大小和方向,给磁测资料解释带来困难.为此,本文利用二维井中磁测数据反演磁化强度矢量的二维分布.首先利用井中磁测的磁异常模量反演磁化强度大小的分布.然后,在已知磁化强度大小分布的前提下,拟合磁场分量,反演磁化强度方向的分布.其中,磁化强度大小和方向均用共轭梯度法求解,并通过预优矩阵改善磁化强度大小的反演效果.理论模拟说明,该方法能准确获得磁化强度矢量分布.磁化强度矢量反演结果包括感磁、剩磁及退磁的影响,这为研究强剩磁、高磁化率矿床提供了一种有效方法.     

改进的正交多项式变换在地震资料去噪中的应用

水平叠加虽然在很大程度上压制了噪声,提高了地震剖面的信噪比,但CMP遭集上还存在不少不是一次波的规则干扰和随机噪声,不利于叠前资料的岩性反演和叠后资料的波阻抗反演.本文提出了基于改进的正交多项式变换压制地震资料中随机噪声的方法,其优势在于:通过对不同时间信号的奇异值分解,确定有效信号正交多项式系数谱的阶数;再利用小波变换,改善有效信号和噪声在低阶上的混叠.文中给出了具体处理的过程,数据试验和实际资料的处理结果表明该方法不仅能有效地压制噪声,而且还能较好地保护地震数据中AVO变化特征.     

A new approach for high fidelity seismic data recovery by fractal interpolation

Recovering accurate data is important for both earthquake and exploration seismology studies, when data are sparsely sampled or partially missing. We present a method that allows for precise and accurate recovery of seismic data using a localized fractal recovery method. This method requires that the data are selfsimilar on local and global spatial scales. We present examples that show that the intrinsic structure associated with seismic data can be easily and accurately recovered by using this approach. This result, in turn, indicates that seismic data are indeed self-similar on local and global scales. This method is applicable not only for seismic studies, but also for any field studies that require accurate recovery of data from sparsely sampled datasets with partially missing data. Our ability to recover the missing data with high fidelity and accuracy will qualitatively improve the images of seismic tomography.     

Non-parametric seismic hazard analysis in the presence of incomplete data

The distribution of earthquake magnitudes plays a crucial role in the estimation of seismic hazard parameters. Due to the complexity of earthquake magnitude distribution, non-parametric approaches are recommended over classical parametric methods. The main deficiency of the non-parametric approach is the lack of complete magnitude data in almost all cases. This study aims to introduce an imputation procedure for completing earthquake catalog data that will allow the catalog to be used for non-parametric density estimation. Using a Monte Carlo simulation, the efficiency of introduced approach is investigated. This study indicates that when a magnitude catalog is incomplete, the imputation procedure can provide an appropriate tool for seismic hazard assessment. As an illustration, the imputation procedure was applied to estimate earthquake magnitude distribution in Tehran, the capital city of Iran.     

Mapping mesoscale currents by optimal interpolation of satellite radiometer and altimeter data

 Mapping the mesoscale surface velocity stream function by combining estimates of surface height from satellite altimetry and surface currents from sequential infrared (sea-surface temperature) imagery using optimal interpolation is described. Surface currents are computed from infrared images by the method of maximum cross-correlations (MCC) and are combined with altimeter sea-level anomaly data from the TOPEX/Poseidon and ERS satellites. The analysis method was applied to 6 years of data from the East Australian Current region. The covariance of velocity and sea-level data is consistent with the statistical assumptions of homogeneous, isotropic turbulence, with typical length scales of order 220 km and time scales of 10 days in this region. Augmenting the analysis of altimeter data with MCC velocity observations improves the resolution of the surface currents, especially near the Australian coast, and demonstrates that the two data sources provide consistent and complementary observations of the surface mesoscale circulation. The volume of MCC data is comparable to that from a satellite altimeter, but with a more variable distribution of spatial and temporal resolution. In concert with altimetry, satellite radiometer velocimetry represents a technique useful for retrospective analysis of currents from high-resolution satellite radiometer data-sets. Received: 3 July 2001 / Accepted: 16 November 2001     

Inversion of magnetotelluric data in the presence of strong bathymetry/topography

We describe an algorithm for inverting magnetotelluric (MT) data in the presence of strong bathymetry or topography. Instead of correcting distortions due to bathymetry or topography we incorporate them directly into the inversion. To achieve a high accuracy in computing MT responses we use finite‐difference approximations that permit sloping discrete boundaries inside model elements. The same approach is applicable to any seafloor electromagnetic calculation and can also be used to incorporate steep topography on land. We test our approach on various topographic features and compare our results to that of a finite element approach. Finally, we present inversion examples that illustrate the effectiveness of our inversion algorithm in recovering true subsurface structures in the presence of strong bathymetry and topography.     

分形插值法在地电场干扰数据处理中的应用

当地电场和地电阻率同场地观测时,地电场观测会受到地电阻率观测的供电干扰,这类干扰时间短、干扰形态和出现时间固定,影响了地电场观测数据的正常变化形态,给数据分析和地震科学研究造成困难.为解决这一干扰问题,本文在比较分形插值方法与传统插值方法优劣的基础上,采用分形插值方法对受干扰的地电场观测数据进行重建,以提高信号重建的精...     

Calendar time interpolation of amplitude maps from 4D seismic data

A calendar time interpolation method for 2D seismic amplitude maps, done in two steps, is presented. The contour interpolation part is formulated as a quadratic programming problem, whereas the amplitude value interpolation is based on a conditional probability formulation. The method is applied on field data from the Sleipner CO₂ storage project. The output is a continuous image (movie) of the CO₂ plume. Besides visualization, the output can be used to better couple 4D seismic to other types of data acquired. The interpolation uncertainty increases with the time gap between consecutive seismic surveys and is estimated by leaving a survey out (blind test). Errors from such tests can be used to identify problems in understanding the flow and possibly improve the interpolation scheme for a given case. Field‐life cost of various acquisition systems and repeat frequencies are linked to the time‐lapse interpolation errors. The error in interpolated amplitudes increased by 3%‐4% per year of interpolation gap for the Sleipner case. Interpolation can never fully replace measurements.