Statistical analysis of background noise in seismic prospecting

From a conventional viewpoint, seismic‐prospecting background noise is usually regarded as the product of a stationary and Gaussian stochastic process. In this paper, we use statistical methods to investigate the properties of the land‐seismic‐prospecting background noise on stationarity, Gaussianity, power spectral density, and spatial correlation. We use and analyse the passive noise records collected by receiver arrays at different typical geological environments (desert, steppe, and mountainous regions). Differences exist in the statistical properties of the background noise from different geological environments, but we still find some common characteristics. It is shown that the background noise is not strictly stationary and has different stationary properties over different timescales. Most of the noise records appear to be a Gaussian process when examined over a period of about 20 s but are found to be non‐Gaussian when examined over shorter periods of about 1 s. The background noise is a kind of colored noise, and its energy mainly concentrates in the low‐frequency bands. We also find that the spatial correlation of the background noise is weak. The results of this paper provide a scientific understanding about the properties of seismic‐prospecting background noise.     

Univariate modelling of summer-monsoon rainfall time series: Comparison between ARIMA and ARNN

The present article reports studies to develop a univariate model to forecast the summer monsoon (June–August) rainfall over India. Based on the data pertaining to the period 1871–1999, the trend and stationarity within the time series have been investigated. After revealing the randomness and non-stationarity within the time series, the autoregressive integrated moving average (ARIMA) models have been attempted and the ARIMA(0,1,1) has been identified as a suitable representative model. Consequently, an autoregressive neural network (ARNN) model has been attempted and the neural network has been trained as a multilayer perceptron with the extensive variable selection procedure. Sigmoid non-linearity has been used while training the network. Finally, a three-three-one architecture of the ARNN model has been obtained and after thorough statistical analysis the supremacy of ARNN has been established over ARIMA(0,1,1). The usefulness of ARIMA(0,1,1) has also been described.     

Stationarity Scores on Training Images for Multipoint Geostatistics

This research introduces a novel method to assess the validity of training images used as an input for Multipoint Geostatistics, alternatively called Multiple Point Simulation (MPS). MPS are a family of spatial statistical interpolation algorithms that are used to generate conditional simulations of property fields such as geological facies. They are able to honor absolute “hard” constraints (e.g., borehole data) as well as “soft” constraints (e.g., probability fields derived from seismic data, and rotation and scale). These algorithms require 2D or 3D training images or analogs whose textures represent a spatial arrangement of geological properties that is presumed to be similar to that of a target volume to be modeled. To use the current generation of MPS algorithms, statistically valid training image are required as input. In this context, “statistical validity” includes a requirement of stationarity, so that one can derive from the training image an average template pattern. This research focuses on a practical method to assess stationarity requirements for MPS algorithms, i.e., that statistical density or probability distribution of the quantity shown on the image does not change spatially, and that the image shows repetitive shapes whose orientation and scale are spatially constant. This method employs image-processing techniques based on measures of stationarity of the category distribution, the directional (or orientation) property field and the scale property field of those images. It was successfully tested on a set of two-dimensional images representing geological features and its predictions were compared to actual realizations of MPS algorithms. An extension of the algorithms to 3D images is also proposed. As MPS algorithms are being used increasingly in hydrocarbon reservoir modeling, the methods described should facilitate screening and selection of the input training images.