Investigation of Crystalline Basement-Surface Topography Using Aeromagnetic Data

Information on the topography of the crystalline basement surface of ancient platforms is highly important for diverse regional and exploration problems, including oil and gas exploration within the basement itself and in inherited structures of the sedimentary cover.

Basement-surface topographic maps are usually constructed from drilling and seismic data, sometimes supplemented by electrical soundings. Nevertheless, the number of points with reasonably reliable basement-depth information generally remains very limited, and their distribution is extremely uneven. Formal interpolation produces highly unreliable results in these circumstances, and gaps are often filled using regional gravity-field data. However, basement structures determine the gravity field only partly; a substantial portion arises from the sedimentary cover, naturally introducing errors into the resulting maps. Thus, where several researchers have compiled such maps, their basement elevations usually differ by 100–300 m, and often considerably more.

Mapping of the crystalline basement surface can be significantly improved by incorporating additional aeromagnetic information, as was recognized almost immediately after the method appeared. A substantial share of anomalous magnetic-field energy—usually more than 99%—is associated specifically with the upper crystalline basement, and aeromagnetic surveying is effectively a direct mapping method in most platform regions. The problem lies only in developing effective means of extracting the required information, an endeavour that has attracted considerable effort over a long period.

The principal approaches currently used in practice to determine basement-surface depths analyse singular points of functions describing anomalous fields. In 1956, V. K. Ivanov first proposed determining the depth of the uppermost singularity from the amplitude spectrum [2]. He showed theoretically that at high frequencies the amplitude spectrum asymptotically approaches an exponential whose decrement equals the depth of the uppermost singularity. Several computer programs were developed and actively used on this basis [4]. Abroad, essentially the same idea was proposed in 1970 by A. Spector and F. Grant [12] for multiblock models and has since been widely applied to diverse practical problems. In the 1990s, several studies showed that the combined effects of heterogeneous blocks in real media can generate anomalous fields with other spectral types. On the one hand, in 1994 J. Garcia-Abdeslem and J. Ness demonstrated [7] that media with uniform and normal block distributions can systematically underestimate depths determined by the Spector–Grant method. On the other hand, in 1997 M. Fedi, T. Quarta and A. De Santis noted that a fractal medium may instead systematically overestimate depths determined by such a method [6]. These determinations are usually made from a field reduced to the pole, without accounting for measurement-height variations.

Another widely used approach is Euler deconvolution, based on Euler’s equation for homogeneous functions. D. Thompson in the United States first proposed it in profile form in 1982 [13]. In 1990, British geophysicists led by A. Reid extended it to three dimensions [11], after which it was incorporated into all major interpretation systems. Within a moving window, a linear inverse problem for Euler’s equation is solved to determine the coordinates of a single singularity of a specified type accounting for most of the field energy in that window. The results are point clouds generally associated in plan view with gradient zones of the anomalous field. Manuals for modern interpretation systems estimate the accuracy of singularity-depth determination by Euler deconvolution at 15%. Although its application leaves vast areas of the maps entirely devoid of singular points, Euler deconvolution is often recommended as the principal method for rapid estimation of anomaly-source parameters [3].

Werner deconvolution is in some respects related to this approach. S. Werner first proposed it in 1953 to determine thin-sheet parameters [14], and many researchers subsequently modified it. It also effectively solves a linear inverse problem by approximating the field in a moving window with rational-fraction expressions. Recently, M. Nabighian and R. Hansen indicated the possibility of unifying these two methods for three-dimensional models [10].
This article discusses ROMGAS, which consolidates previous advances in this field and forms part of the SIGMA-3D interpretation package. It determines singular points of functions describing magnetic anomalies from the amplitude spectrum calculated in a moving window, and has the following principal features:

1. The singularity depth is determined in a square moving window whose dimensions should be approximately an order of magnitude greater than the expected basement depths. Calculations use the anomalous field directly, without prior reduction to the pole. The interpreter obtains singularity-elevation estimates on a regular grid. Together, they characterize the envelope of the singularity set, often called the Main Magnetically Active Surface (MMAS). The MMAS most often coincides with the crystalline basement surface, although deviations are naturally possible. If the upper basement consists of virtually non-magnetic rocks, the MMAS lies deeper and indicates the depths of magnetized basement rocks. Conversely, if the sedimentary cover contains highly magnetized intrusions or thick volcanic–sedimentary successions, the MMAS lies shallower than the basement surface. Another limitation is the inability to determine depths in narrow aulacogens. In a moving window whose plan dimensions often greatly exceed those of the aulacogen, the uppermost singularities located clearly lie on its flanks rather than its floor. Despite these limitations, ROMGAS has proved highly effective under diverse geological conditions.
2. If the original field is specified on a square grid in plan, the two-dimensional spectrum is calculated conventionally using the fast Fourier transform.
3. If the original field is specified on an irregular grid with observation-point heights above the geoid, the two-dimensional spectrum is calculated approximately using truncated corresponding two-dimensional Fourier series.
The idea of approximately calculating spectra from observations on an irregular three-dimensional grid apparently first appeared in widely accessible literature in R. Henderson and L. Cordell’s 1971 paper [8]. They cited their approach as an extension of W. James’s earlier 1966 work [9]. Since then, various geophysicists have used the idea in different programs, including one of the present authors in the integrated Singular system [1]. V. N. Strakhov and I. A. Kerimov are currently developing an original modification of approximation-based spectral analysis using the integral-representation method [5].
The number of harmonics calculated approximately by ROMGAS is naturally much smaller than the number of observations. A 30×30 km moving window usually contains several tens of thousands of points from a 1:50,000 aeromagnetic survey, whereas stable determination of the depth of the singularity characterizing the MMAS requires only about one thousand initial harmonics. The linear inverse problem for their determination is solved by regularization.

Fig. 1. Determination of the depth of the Main Magnetically Active Surface above a borehole in a 30×30 km window: а) anomalous magnetic field DT; б) ground-surface topography; в) cross-plot of the logarithm of the amplitude-spectrum modulus of the field reduced to the mean observation height against spatial frequency, with a regression line whose slope characterizes depth.

4. The depth of the singularity characterizing the MMAS can be determined in two ways. In the first, the calculated two-dimensional spectrum is radially averaged and logarithmically transformed, then approximated over a segment automatically selected by the program by a straight line whose slope estimates the required depth. This approach is widely used, including in the well-known integrated Geosoft system.
In the second, the logarithms of the amplitude-spectrum modulus and their corresponding spatial frequencies are fitted directly, with a regression line constructed over all low frequencies. A real example illustrates this approach. Figs. 1а and 1б show the anomalous magnetic field DT within a 30×30 km window and ground-surface topography above a borehole in the southern Moscow Syneclise. Drilling gives a crystalline basement-surface elevation of -586 m. Fig. 1в plots the logarithm of the amplitude-spectrum modulus of the field reduced to mean observation height against spatial frequency. A total of 900 harmonics (30×30) were used. The regression-line slope corresponds to a singularity elevation of -599 m. Note that the lowest-frequency part of the spectrum contains relatively few points, which do not significantly impede depth determination, as they would in the first approach with prior radial averaging.
Information obtained by either approach is usually treated as a depth correlate rather than the actual depth, since neither the combined effects of heterogeneous blocks in the area nor the fractal dimension of basement magnetization is generally known beforehand. Nevertheless, where no a priori information on the surface is available, depths calculated in this way can themselves serve as an estimate of basement-surface morphology.
4. After determinations over the entire study area, excluding naturally the boundary strips half a moving-window width across, the results are tied by linear regression to available a priori surface information, principally from drilling, to correct for the combined ensemble effect of blocks. This provides final calibration to the specific area, including the fractal dimension of the basement model.

Fig. 2. Comparison of basement-surface elevations from ROMGAS and drilling within the Moscow Syneclise: а) cross-plot of data from 394 wells and ROMGAS; б) histogram of differences between depths determined by drilling and ROMGAS.

ROMGAS has been applied in diverse geological settings and has proved highly effective. It has already been used to investigate crystalline basement topography over approximately 20% of the Russian Federation. MMAS determination accuracy is usually no worse than 10%, and significantly better under favourable conditions.
Fig. 2а compares drilling data from 394 wells in the Moscow Syneclise with ROMGAS results, while Fig. 2б shows a histogram of the corresponding depth differences. These indicate reliable results everywhere except in areas containing aulacogens. There, the uppermost singularities within a 50×50 km moving window lie on the flanks and therefore do not represent the true depth of the aulacogen floor. Nevertheless, the overall root-mean-square error in crystalline basement-surface depths within the Moscow Syneclise was 267.5 m, with a correlation coefficient of 0.940 between drilling and ROMGAS depths. Most of the syneclise where this technology was applied is covered by aeromagnetic surveys at 1:200,000 scale. Modern detailed, high-precision survey data provide still greater accuracy in MMAS depths.

Fig. 3. Crystalline basement-surface topography determined from 1:25,000 aeromagnetic data in the Pre-Volga region of Tatarstan: а) DT isodynamic map showing deep-well locations; б) Main Magnetically Active Surface map from ROMGAS; в) map of singular points found by Euler deconvolution in Geosoft using structural index 0; г) cross-plot of basement-surface elevations from drilling and ROMGAS.

As an example, consider the MMAS study in the Pre-Volga region of Tatarstan using 1:25,000 aeromagnetic data. Fig. 3а shows the original DT isodynamic map with deep-well locations, and Fig. 3б shows the resulting MMAS map from ROMGAS. The root-mean-square error in basement-surface depth was 26.4 m at an average depth of approximately 2 km. Fig. 3г compares ROMGAS results with drilling data; the correlation coefficient was 0.805. For comparison, Fig. 3в presents Euler deconvolution results for the same area using structural index 0, targeting rock contacts, calculated in Geosoft. The singular points obtained by Euler deconvolution occupy a depth range from 300 m to 2.5 km, making it very difficult to infer the actual basement-surface morphology. In this example, Euler deconvolution produced incomparably poorer results than ROMGAS.
Thus, ROMGAS has proved effective under diverse geological conditions and can be recommended as a basic method for interpolating drilling and seismic data when mapping basement-surface topography. Even without a priori information, ROMGAS can provide sufficiently accurate estimates of the required depths.

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