Noise in FTG Data and its Comparison With Conventional Gravity Surveys

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1 Noise in FTG Data and its Comparison With Conventional Gravity Surveys G. Barnes, J. umley, P. Houghton, R. Gleave ARKeX td. Cambridge, U.K. Summary Employing various assumptions and approximations, we propose a simple method to compare the performance of gravity gradiometer and gravity surveys in the land, marine and airborne environments. Derived relations estimate the noise on the final grid as a function of the spatial filtering applied by an interpreter. The analysis takes into account the resolution of the measurement system and survey parameters such as line spacing, speed and bandwidth. After mapping the measurements onto a grid it is straightforward to implement component transformations and apply upward continuation; both necessary for fair comparisons between the different acquisition systems. Such analysis is believed to be a useful preliminary guide for survey selection and planning. Introduction Interpreters of gravity and gravity gradient data invariably study gridded forms of survey measurements so that a variety of filtering can be easily applied to emphasize anomalies of different sizes and depths. In general, it is known that filtering to longer wavelengths improves the detectability of anomalies, but sacrifices overall resolution. If data is over-filtered, then due to the loss of resolution, positional accuracy is compromised and multiple isolated anomalies can even be mistaken as a single entity. On the other hand; without adequate filtering, the noise level can be too intrusive and mask the signal completely. The noise therefore dictates the useable resolution for interpretation and consequently ultimately determines the positional accuracies of any identifiable anomalies. Knowledge of the expected noise on gridded data is therefore crucial when planning a survey to ensure that the geological features of interest can be detected and resolved. Methodology To facilitate the analysis, for both gradiometer and conventional gravimeter surveys, the survey data is assumed to be sufficiently well leveled / corrected so that the noise is uncorrelated and can be specified by a Root Mean Square (RMS) value. We have estimated the noise in Full Tensor Gradiometer (FTG) surveys by considering the sum of the three inline components of the differential curvature outputs. In this construction, the signals cancel leaving a residual that can be used to assess the overall noise in the FTG channels. Figure 1 shows the Power Spectral Density (PSD) of these noise levels from a real survey where the 9 quality accepted lines were partitioned into three equally sized groups according to their turbulence level. The black line represents an empirical fit which is used in the subsequent analysis as the typical survey noise model. During the processing of FTG data, the multiple channels are combined together in a compatible way to produce enhanced gravity gradient components that have effectively reduced noise levels compared to the individual measurement

2 channels. To simplify the analysis we model the FTG noise as though it were an equivalent Gzz instrument with a noise level reduced by a factor.1. This factor is achieved in practice by equivalent source methods that essentially average together multiple measurements of the same potential field in a tensorially and harmonically consistent way. The RMS noise level on each measurement sample is estimated by integrating the PSD up to the measurement bandwidth (typically Hz). Figure 1. Averaged output channel noise from FTG survey data for 3 levels of turbulence as shown in the legend quantified as (mean level, median level). Turbulence defined as z acceleration power over a 5 second window. Black line shows an empirical noise model fitted to the data. The equivalent noise on a Gzz measurement can be modeled as the average channel noise divided by.1. A convenient noise model for airborne gravity, is provided by assuming the GPS acceleration correction being the limiting factor (van Kann 00). To estimate the noise in a marine gravity survey, we have performed statistical analysis of leveled mis-tie data from a survey that had ample survey line tie line intersections resulting in a noise as a function of filter time constant, T c, of T c noise( T c ) = e (1). The noise is obviously dependent on sea-state, but the data behind this model seems representative of a typical survey and can be used for time constants of ~ 180 seconds and above. and gravity noise is harder to quantify because of the large range of quality. Although standard land gravimeters are capable of microgravity measurements, this is rarely achieved in a large scale survey because the accuracy is more dominated by the error bounds on height, latitude and the terrain correction. We therefore split up land gravity noise into three categories representing legacy (pre- GPS), terrain limited, and carefully acquired / corrected modern surveys. Attributed accuracies are respectively 0.5, 0.1 and 0.05 mgal. To translate the noise estimates in the survey measurements to noise values on a grid, we define a grid with a pitch such that, on average, one measurement point contributes to one grid cell. This clearly

3 under-samples in areas between survey lines, but over-samples where survey tie lines cross; it only makes sense on average. The grid pitch, Δ, that meets this condition is given by Δ = v F s Sx S y 1 where S x and S y are the line and tie-line spacings, v is the acquisition speed and F s is the sampling frequency of the data commensurable with the bandwidth imposed by the system or any time domain filtering (F s = bandwidth). With the assumption of uncorrelated noise, the noise distribution on this grid will be white having a power spectral density, P, that can be easily deduced, P = nδ (3) π where n is the RMS noise on each band limited measurement. By employing Fourier analysis, one can now estimate the noise power on the grid as a function of spatial radial bandwidth which is implied by the filtering performed during standard interpretation. Further to this, Fourier methods make the transformations between gz and Gzz grids and also upward continuation by a distance z straightforward. The following equations give the filtered grid noise levels n g defined over a spatial bandwidth to representing the longest to shortest Fourier wavelengths of interest. These equations apply to Gzz and gz grids deriving from either noise in gravity or gravity gradient measurements. (). Gzz grid noise from Gzz measurements, or gz grid noise from gz measurements: 1 ng (, ) = ( Pe ) πz / x n Δ e = z x ( x + πz ) () Gzz grid noise from gz 1 measurements: ng (, = 10 ( P k e ) ) 10 = z nδ π e πz / x ( 3x + 1zx + π z x + 3 z ) x 3 (5) gz grid noise from Gzz measurements: 1 1 ng (, ) = P e k nδ πz = Γ 0, 10 x In conjunction with the survey parameters specified in Table 1, these equations are plotted to compare five different systems resulting in the curves of Figure showing how the noise level for Gzz grids varies with. For the marine FTG, the raw noise level was pessimistically assumed to be the same as (6)

4 the airborne case analysed above. The biggest effect here is due to the vastly different acquisition speeds making the marine survey noise statistics considerably lower. Speed ms -1 ine spacing, m Tie-line spacing, m noise, (RMS) Measurement Bandwidth Upward cont, m Air FTG E 0. Hz 0 Air gravity mgal (GPS limit) 70 seconds 0 Marine gravity mgal 00 seconds 00 Marine FTG E 0. Hz 00 and gravity x 500 grid - 0.5, 0.1, 0.05 mgal - 00 Table 1. Survey parameters used for the comparison example. 100 Gzz Noise Comparison 10 Airborne FTG Airborne Gravity Marine Gravity Marine FTG and Gravity 0.5 mgal and Gravity 0.1 mgal and Gravity 0.05 mgal Gzz Noise (Eotvos RMS) Filtering, Radial Wavelength (Km) Figure. Comparison example of gridded Gzz noise for different survey scenarios as a function of bandwidth. Maximum wavelength of interest, = 80 km. Although unrealistic, land and marine surveys are presented on the same graph. Conclusions When comparing one survey system with another, it is some times useful to identify the wavelength,, of the grid filter at which the two perform equally well. The example parameters used above were taken from a real consideration where poor land gravity data (0.5 mgal) was already available (albeit sporadically) over a prospect area and the question was whether commissioning an airborne FTG survey would offer extra useful information. Referring to Figure, these two curves cross at 1 km indicating that if the targets of interest have significant Gzz signals contributing Fourier wavelengths shorter than 1 km, then the FTG survey will offer more useful resolution than the existing gravity data. However, if the targets are lower bandwidth, for example deeper structures, then the FTG survey will not offer substantially more information. When considering grids of gz, the curves (not shown) cross at 5.5 km and the gravity data appears superior over a wider bandwidth. However, when employing stronger high pass filtering, to remove more regional field (equivalent to decreasing ), the gz cross-over point increases since the higher frequency information in the gradiometry data becomes relatively more important. Viewing Gzz grids essentially suppresses the regional field automatically.

5 References Van Kann, F. 00. Requirements and general principles of airborne gravity gradiometers for mineral exploration, Airborne Gravity 00 - Abstracts from the ASEG-PESA Airborne Gravity Workshop: Geoscience, Australia Record , 1 5.