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Terrain correction is an attempt to compensate for irregularities o f topographic surfaces above and below the level o f the Bouguer Plate discussed above. The

gravitational effect o f masses above the Bouguer Plate as well as o f depressions below the level o f the plate {i.e. the station height) is to reduce the value of the observed gravity at the station. Since the Bouguer Plate was assumed to have a flat surface the computed gravitational effect o f these discrepancies must be added to the observed gravity {i.e. terrain corrections are always positive).

The classical method for carrying out terrain corrections is to use a transparent Hammer Chart (Hammer 1939) overlain on a topographic map at a compatible scale and centred on the gravity station under consideration. The difference between the average height o f the terrain and the station height is estimated for each compartment. Software suites are available for carrying out this routine {e.g. Kane 1962, Milsom 1971, Ballina 1990, Ma and Watts 1994) and can to some extent speed-up the

computation but the lack o f digital topographic data at suitable intervals demands the laborious digitisation of the topographic maps in and surrounding the survey areas. Without digital topographic data {i.e. without a Digital Terrain Model), performing terrain corrections is equally time-consuming whether automatic (using a computer) or manually (using the Hammer Chart). As a result, for small scale surveys where no Digital Terrain Models are available, the classic method of using Hammer Chart is still widely and conveniently used.

Although mathematically simple, the computation procedure in terrain

corrections is tedious. In principal, the terrain correction for a gravity station is written in terms o f a gravitational attraction of a cylindrical shell experienced at a gravity station situated at the axial point o f the cylinder; and the overall correction for a station is obtained by summing up all gravitational effects o f each shell surrounding the station extending to a predefined radial distance. The use o f the term shell in this context refers to a particular compartment of a radial zone if the computation is carried out using the Hammer Chart or to an elemental prism o f predefined size and radial distance if computation o f terrain effect is done using computer programs (e.g. Kane 1962, Takin and Talwani 1966, Milsom 1971, Zhou et al. 1990, Ballina 1990, Ma and Watts

1994).

As has already been noted, anomaly Ag due to a cylinder shell at an axial point is given by

Ag = 2jrpG [ (H^+R^) - (h^+R^) * + (h^+R^) ] 3.14

A first requirement to solve this eqiTftion is that the relative magnitudes of the

parameters h, H, r and R should be known. If a cylinder is to be used to approximate to the actual topography, it is known that, in the outer three zones at least, the heights will inevitably be very much smaller than the radii. It is much rarer for the average

topographic level at a given distance from an observation point to differ from the height at that point by more than the distance o f separation (Milsom 1971), i.e. consistent and sustained topographic slopes o f more than 45° are rare. Attention should be paid to the fact that beyond a certain distance from the gravity station, the effect o f the Earth’s curvature should be taken into consideration, i.e. at distances in excess o f about 30 km the zone radii are always much larger than the mean topographic height (Milsom 1971). However, curvature corrections are significant only for stations at siginificant elevation above sea level and are therefore not necessary for stations o f the Sorong Fault Zone survey. Since 'Extended' Bouguer anomalies are obtained by correcting for deviations of the actual land surface from the Bouguer plane, a vast amount of additional topographic information must be used. Use o f this data, whether by approximating contour lines by

polygons or by estimation of the average height o f topographic blocks, is at least partly subjective.

Although the main purpose of the Bouguer and, more particularly, the Extended Bouguer, correction is to reduce the dependence of the contours on station elevation, it must be realised that, because of density variations in the superficial crustal layers, this never be done completely. The reason for this is illustrated in Figure 3.3. The extended Bouguer anomaly relates the gravity observations at A and B after removal o f the effects

of the topography above the geoid. The mass inhomogeneity if not included in these

calculations, represents a source of error. However, masses such as 7, below the

reference level, are not considered in the reduction calculations and their effect forms a valid part of the computed anomaly. Clearly the field due to 7 at ^ will be different

from the field at B, also from the field at on the reference surface (which cannot

certainly be measured). This implies that one can never say that the Extended Bouguer, or any other, anomaly represents a reduction to the reference level. The elevation of the point o f observation cannot be altered by any reduction process, and where this is likely to be an important factor it should be allowed for in interpretation. In the case o f the Sorong Fault Zone surveys (except Irian Jaya), location of virtually all stations close to sea level effectively eliminates this problem.

If either station height varies largely or topographic relief undulates ruggedly, topographic effects may be significant out to distance at which the 'flat earth'

approximation (implicit in the Bouguer assumption) is no longer valid. Corrections for earth curvature are less conceptually simple than might appear at first glance; carried to a logical conclusion terrain corrections would have to be extended around the whole earth and be applied to the theoretical field o f a spherical shell, twice the field of a Bouguer plate o f the same thickness. However a shell with thickness equal to the station height would be a very poor approximation to reality, firstly because the mean elevation o f the Earth's surface is very close to zero and secondly because most

deviations from zero level are compensated by mass change at depth. For distant points the effects o f surface irregularities and their compensation are very nearly equal. Maps of the combined effect of topography and its assumed isostatic compensation at all

points on the globe are published by the Isostatic Institute o f the International

Association of Geodesy (Kârki et a l 1961). These maps ignore all topographic-isostatic effects from sources within 166.7 km o f the observation points {i.e. 1!4° o f latitude, the outer radius of the Hayford zone O) and are based on the assumption that topographic changes are compensated by changes in the depth o f a major density discontinuity at about 30 km below the geoid (the Airy isostatic assumption). For these distant corrections the exact nature o f the isostatic model used is not very important.

3.1.5 Isostatic effects

Isostatic corrections represent attempts to allow for the effect o f compensation of the local as well as the distant topography. The masses being considered are generally within a few tens of kilometres from the point of calculation but even so the vector of their gravitational attraction makes only a small angle with the direction of the earth's main gravitational field. Under these conditions the value of the correction is critically dependent on the nature of the isostatic model used. Two main classes of assumption have been made, the continuous (Pratt model) and the discontinues (Airy model), but the discovery of the Mohorovicic seismic velocity discontinuity (Moho), and its identification as the boundary between the earth's crust and mantle, led to the virtual abandonment o f the Pratt model. Early observations of seismicity showed a strong correlation between topographic height and depth to Moho. Since a significant increase in velocity almost certainly indicates a significant increase in density, the Airy model appeared to be proven correct. More recently, seismic refraction studies have directed attention towards the variations in mantle velocity at the Moho. Woolard (1968) had shown that for the continental o f the United States a simple relation between surface elevation and crustal thickness can be established only where mantle velocity lies in the range between 8.0 and 8.2 km.s"\ In other areas a correlation is observed between thin crust, crustal uplift and low mantle velocity, implying reduction in mantle density. Possibly the transfer o f mass between crust and the upper mantle may be a second important mechanism for maintaining isostatic equilibrium. In some cases the

compensation approaches that proposed by Pratt, with the topographic mass supported by a density deficiency throughout an extended column.

As yet there have been no determinations o f mantle velocity made in the study area and the most recent work on refraction seismic studies near the East Arm Sulawesi and the Banggai Islands regions (McCaffrey et al. 1981) indicated a maximum velocity o f only 6.5 km.s'^ which was interpreted as representing the granitic basement of the region (McCaffrey 1981). However, a number o f measurements made around the Solomon Islands (Furumoto et a l 1970) showed variations from a low o f 7.3 km.s"^ to a high of 8.5 km.s'^ east of the islands. This suggests, by analogy with the North

American observation mentioned above, that isostatic adjustment in this area are not made only by lowering of the Moho.

A further weakness of the conventional isostatic anomaly is that no allowance is made for the compensation o f mass excesses or deficiencies present in the upper crust. The distribution o f such variations is seldom sufficiently understood for corrections of this type to be practicable, even if the computation time involved were not prohibitive, and as a results isostatic anomalies are of very limited use in areas o f strong density contrasts.

As the Sorong Fault Zone occupies a region in which terranes o f various

affinities juxtaposed to eacl% other, implying strong density contrast throughout most of the region. This suggests that isostatic anomalies may not be very useful to use for studying this particular region. Isostatic corrections have therefore not been used, but isostatic effects are critically important consequences o f the models being employed.

3.1.6 Geological correction

The geological correction is an attempt to allow for the effect o f a sub-geoidal mass distribution (usually a sedimentary basin). The geology of an area is seldom well enough understood for the purpose o f this correction to be made with any confidence.

The geology o f the Sorong Fault Zone is at present still a subject of controversy and applying this correction would therefore have been misleading. A variant of the

geological correction may be applied to marine gravity to allow for the thickness o f the water layer, as discussed in the next section.

3.1.7 Correction for shipborne observations

In the discussion above an assumption has been made that the gravity observations are taken on the ground surface. However, a large number of gravity measurements are now made on-board surface ships and some results o f this type (Bowin et al. 1980) have been used in this study. In one respect these data are easier to handle than those obtained on land, since the measurements are all made at sea level and, after instrumental and acceleration corrections have been made, the fi*ee-air

anomaly is obtained directly by the application of the latitude correction. However these ftree-air anomalies are critically affected by sea floor topography and a number o f so called Bouguer reductions have been proposed to eliminate or reduce this effect. Most involve 'replacing' the layer of sea water with that o f an equivalent volume of rock of some specified density, the actual density chosen being the subject of controversy. Perhaps the most common assumption is to use the mean density of upper crustal rock (2.67 Mg.m'^) but in oceanic areas there is much to be said in favour ot the choice of the mean density of the sea floor basalt (2.80 Mg.m'^). Previous gravity work in east of

the East Arm Sulawesi and north of Banggai Islands (Silver et a l 1983) used a density

of 2.80 Mg.m'^ as the mean density for modelling the crustal structure in this area. In the present study, however, a choice o f the standard value o f 2.67 Mg.m'^ has been made for reduction o f the gravity data and modelling o f crustal structures in the Sorong Fault Zone.

Since the mass deficiency in the sea water is compensated entirely or in part by a rise in level o f the Moho, 'infilling' o f the sea with material o f higher density results in Bouguer anomalies which are strongly positive. The characteristics of the marine Bouguer correction have been discussed by Vajk (1964), who proposed a method of

reduction which he refers to as the 'modified free-air anomaly*. Essentially this is an anomaly calculated with reference to sea level for land stations and to a standard sea floor in the ocean. Corrections are made only for deviations from these conditions, assumptions being made as to the bulk density of bathymetric features. The major deviation is represented by the continental margins and in such areas a model

continental margin is to be fitted to the observed bathymetry, removing from this the effect of sea bed relief. However, as has been demonstrated by a multitude of seismic refraction studies {cf. Drake 1966), continental margins are rarely simple structures and the essentially two dimensional app roach used by Vajk (1964) can seldom be

applicable. This is particularly true in tectonically active areas such as the Sorong Fault Zone and the surrounding region.

3.2 Interpretation Techniques

The interpretations of the gravity field in this thesis are based on the technique known as forward modelling, in which a geological model is designed and the

corresponding gravity field is computed. This field is compared with the observed field and the model is adjusted until the computed and observed fields are in close

agreement. At this stage, the computed model may or may not represent the appropriate solution; in other words, a model may or may not be geologically plausible. Ambiguity does exist in the modelling work {e.g. Skeels 1947, Roy 1962), implying that a number of models may satisfy a given observed field, but only a few may be possible

approximations to the geological section under investigation. Other constraints such as bathymetry, depth information from boreholes, isopach maps, sea-bottom morphology and seismic profiles may be used to provide controls on the geometry o f the model. The present study used bathymetry, isopach maps and seismic profiles to provide some control on the geometry o f the models. The forward modelling approach implies that models may be created either using the digitiser, or drawn directly on the screen using the mouse or entered manually using the keyboard; in all cases, the software evaluates the field response due to the models and displays it graphically on the video screen. In

the modelling described here both models and data were entered into the computer manually.

The interpretations in this study used the forward modelling approach as implemented in a potential field modelling software package which is copyrighted as the GM-SYS™. The package is available commercially from Northwest Geophysical Associates, Inc., PO Box 1036 Corvallis - Oregon 97339, USA. This software runs on any MS-DOS machine equipped with a processor or processors capable o f performing floating-point operations, EGA or VGA graphics and a mouse as a pointing device and a plotter.

Many aspects of the implementation in the GM-SYS™ are inherited the principals o f the work by Talwani et a l (1959) although the software makes use o f the algorithms described by Won and Bevis (1987). The Talwani et a l (1959) method is based on the field due to two-dimensional (2-D) bodies, le. bodies which are oriented at right angles to the gravity profile being inspected, have infinite strike length and can be described by cross-sections o f polygonal shape. In detail, the technique relies on the transformation o f the field equation from surface integrals to line integrals so that the field introduced by each polygon is determined by the summation o f terms each of which is associated with a single side. The gravity field of such bodies are reasonable approximations to the fields produced by bodies in which the the along-strike

dimension is at least three times as great as the cross strike dimension. Cady (1980) presented an approach to three-dimensional (3-D) models based on the 2-D models with limited strike length. The strike length may be different on opposite sides o f the profile and the equations even allow for bodies to be completely offset fi*om the profile. This technique, now universally known as the two-and-a-half (2!4-D) modelling, forms the bases o f the Won and Bevis (1987) programs.

Methods proprietary to the Northwest Geophysics Associates Inc. have been used to improve the efficiency and speed of the system so that it is suitable for use in an interactive graphical computing environment. Hardcopy o f models may be obtained

directly when a plotter is connected to the computer. Alternatively, graphics metafiles may be produced and reprocessed for production o f reports.

The GM-SYS™ modelling system accepts both absolute density and relative density values for analysing models. However, absolute density values correspond to absolute gravity fields, quantities which are not of interest in the present study; relative density values {i.e. density contrasts) were therefore used in the analysis and this strategy gives compatible magnitudes of the gravity field in the study area.

The GM-SYS™ program package is capable o f computing both gravity and magnetic fields 'simultaneously' (although the program allows the user to view only either the gravity field or the magnetic field at any one time) and interactively, permitting changes to be made to subsurface geological models whilst the computed fields are displayed graphically on the computer monitor screen and are adjusted in ‘real-time’ as changes are made to the models. The present study only utilised the gravity modelling option, since no magnetic measurements were made during the course of the Sorong Fault Zone Project. It would be desirable in the future to combine gravity with magnetic modelling when on-land or airborne magnetic data become available.

The majority o f the gravity analyses presented in this present study were based on the