Gordon R. J. Cooper

Edge enhancement of potential-field data using normalized statistics

Edge enhancement in potential-field data helps geologic interpretation. There are many methods for enhancing edges, most of which are high-pass filters based on the horizontal or vertical derivatives of the field. Normalized standard deviation (NSTD), a new edge-detection filter, is based on ratios of the windowed standard deviation of derivatives of the field. NSTD is demonstrated using aeromagnetic data from Australia and gravity data from South Africa. Compared with other filters, the NSTD filter produces more detailed results.

Balancing images of potential-field data

Horizontal and vertical gradients, and filters based on them (such as the analytic signal), are used routinely to enhance detail in aeromagnetic data. However, when the data contain anomalies with a large range of amplitudes, the filtered data also will contain large and small amplitude responses, making the latter hard to see. This study suggests balancing the analytic signal amplitude (sometimes called the total gradient) by the use of its orthogonal Hilbert transforms, and shows that the balanced profile curvature can be an effective method of enhancing potential-field data. Source code is available from the author on request.

Sunshading geophysical data using fractional order horizontal gradients

The interpretation of linear features in geophysical imagery is of considerable importance because they can correspond to dykes, faults, or other geologic discontinuities. One popular tool commonly used for their enhancement is sunshading, which considers the data values as if they were a topographic surface that is illuminated by a light source (or “sun”) which has a specified azimuth and elevation. The reflectance of the light by the surface is calculated and imaged. Features whose strike direction is orthogonal to the sun azimuth reflect the light strongly and are consequently enhanced, while those lying parallel to the sun direction do not reflect the light and become less apparent as a result. The reflectance algorithm uses the first horizontal gradients of the data calculated in two orthogonal directions (Horn, 1982).

The detection of circular features in irregularly spaced data

Geophysical potential field data are usually interpolated onto a regular grid before data enhancement and interpretation. Unfortunately the inherent smoothing in the gridding process can be sufficient to distort or even hide small-amplitude anomalies that are nevertheless of economic importance. Circular features may correspond to anomalies from Kimberlite pipes or meteorite impact craters, and are therefore of considerable interest. The Hough transform is a useful tool for the detection of circular features in gridded data, but its sensitivity to the choice of radius means that it performs poorly when applied to ungridded data. A modified version of the Hough transform which works well on ungridded data is described here, and demonstrated on gravity data from South Africa.

Global warming and geothermal profiles: The surface rock‐temperature response in South Africa

Southern hemisphere and South African regional air temperature anomalies for the period 1860–1996 are compared to borehole-derived surface rock-temperature anomalies to assess the extent to which surface rock temperatures reflect possible global warming in South Africa. The warming of the southern hemisphere since the mid-nineteenth century is evident in the regional air temperatures for South Africa. Following a temperature increase to a maximum in the 1920s, the climate cooled until strong warming recommenced in the mid 1970s. Highest temperatures have been experienced in the 1990s. Borehole-derived surface rock temperatures followed a similar pattern, but with a lag of a few decades in the case of the 1920s maximum. The overall warming trend is clearly evident in the rock temperatures. Despite uncertainties in the different data sets, an encouraging degree of agreement exists between the increase in rock temperatures during the twentieth century, the corresponding regional South African air temperature increase and the southern hemisphere counterpart.

Analysing potential field data using visibility

The viewshed of a topographic dataset is the region around a given observation point that is visible from that location. Most GIS packages allow its computation. It has many uses, such as in urban environment planning, or in analysing archaeological site data. The viewshed is used here as a data enhancement tool to aid in the interpretation of geophysical potential field data. The fraction of the area of a moving window visible from each point on the dataset (considered as if it were topography) is computed. Since this area changes if the observer is raised above the surface, its vertical derivative can also be computed. This derivative was found to be a useful method of enhancing subtle features, and is demonstrated on aeromagnetic and gravity datasets from South Africa.

An improved algorithm for the Euler deconvolution of potential field data

Euler deconvolution (Thomson 1982, Reid et al. 1990) is a commonly used semiautomatic interpretation method for magnetic and gravity data. It can be used to indicate locations and depths of anomalous bodies, indicating regions of interest that can be followed up by detailed modeling. Recent work has suggested the usefulness of applying Euler deconvolution to the vertical gradient of the potential field data (Ravat et al. 2002, Hsu 2002). Because the vertical gradient anomaly is narrower than that of the field itself, its use provides improved horizontal resolution of the solutions. However the greater the order of the gradient used, the greater the problems with noise become (because the vertical derivative operator is a high-pass filter). This paper suggests a way around this problem for the first vertical derivative and uses synthetic models of magnetic and gravity data to show the benefits of the approach.

Blocking geophysical borehole log data using the continuous wavelet transform

The interpretation of geophysical log data is frequently difficult due to the noisy downhole environment. Blocking algorithms attempt to smooth the log data while leaving the boundaries between different geological units sharp. This paper introduces a method for the determination of the boundaries based on the zero contour of the continuous wavelet transform (CWT) of the data. The amount of blocking can be controlled by the choice of the scale of the wavelet used. The method is compared with results from the median filter and with discrete wavelet transform (DWT) blocking methods, and is here applied to log data from Australia. The application of the new CWT method overcomes the rounding and shifting of boundaries inherent in median filtering, and provides greater flexibility by overcoming the power of two limitations in the DWT log blocking.

Enhancing ridges in potential field data

The identification of lineaments in potential field data is an important step in many interpretation projects. A method of extracting ridges and valleys based on maxima and minima of a balanced plan curvature dataset is suggested here. The method is compared with other ridge detection algorithms and is applied to aeromagnetic and gravity datasets from South Africa. Source code in Matlab format is available from the author on request.

Optimized inversion of borehole temperature data

A comparison is made between the effectiveness of the inversion of borehole temperature data (for the purpose of climate reconstruction) by the least‐squares (L2) technique and the minimization of the absolute difference between the observed and calculated data (L1) technique. The L1 technique is found to require approximately half the number of iterations to reach the practically achievable minimum error compared to the L2 technique. The choice of which technique to use depends on the statistics of the difference between the observed and calculated data, and it can be advantageous to switch techniques during the inversion process. The inversion damping is also adjusted during the course of the inversion, based on the rate of change of the difference between the observed and calculated data. The aim is to get the best fit of the model to the data while minimising the model size, in the minimum number of iterations. A method of adjusting the damping to achieve this is suggested.