The pioneer researchers of West Siberia empirically found that the main oil deposits of the region are related to the system of Triassic rifts (   and other) and located predominately in such places in the basement, where Precambrian complexes had been developed. The conducted analysis has shown that two groups of reasons cause this: 1) Rifts destroy continental crust and are regional penetrable zones draining the upper mantle and it is in these zones that deep fluids easy penetrate in the sedimentary cover; 2) Deformations and structures of the sedimentary cover are defined by the basement. Thickness of the basement of West Siberia plate in average 14 times exceeds thickness of the cover. Taking into account average strength of basement rocks (153 ± 10 MPa) and other factors one may conclude that its strength of two orders of magnitude is greater than the strength of the sedimentary cover. Sialic blocks (considered earlier as Precambrian) are composed of middle-low crust rocks, predominantly granitoids and metamorphic schists, with density deficiency 0.07 - 0.1 g/cm3 (relatively to the mean earth crust density 2.67 g/cm3). These blocks come to the level of the upper crust in time of Triassic rifting and continue isostatically “floating” after Triassic time. As a result, antiforms in sedimentary cover were created above them. Later the antiforms were filled with oil.
A modeling area is the central part of Danilov graben-rift that situated in Khanty-Mansi autonomous district (KhMAD) of the central part of the West Siberia oil and gas basin. KhMAD is the main oil region of the country―about half of Russian oil is produced here. The modeling area may be considered as a standard for the entire West Siberia taking into consideration that Danilov and North-Danilov oilfields are here and there are representative geophysical and wellsite data. Besides, vast majority of wells encountered only the uppermost parts of the basement not only in the modeling area but also throughout West Siberia that make it difficult to study graben-rift structures and as well as to detect and classify faults. Therefore, it is of importance to clarify the structure of the standard area utilizing potential field information and geophysical approach in computer modeling. It should be said that such modeling was done for the first time in the study area as scientists worldwide constantly address the potential field interpretation for graben and rift studies  -  .
Magnetic anomalies allow us to trace earth crust faults, borders of blocks and structures   . In particular, the relatively magnetic serpentinites are able to make chain anomalies along graben borders. On the other hand, the fact that an intense magnetic anomaly is observed in the limits of Danilov graben-rift of West Siberia but numerous wells encountered only weakly magnetized Triassic graben basalts and liparites, leads us to conclusion that magnetic rocks are situated at great depth. In addition, we suppose that the liparites joint together in a single body. In fact, the wells penetrated only the first tens meters of the basement that covered everywhere by loose sediments of Jurassic and younger age with thickness of 1.5 - 2.5 km.
Besides, geomagnetic data themselves do not give a guaranty of single-valued interpretation because of potential character of the field. Therefore, fitting of magnetic characteristic having in mind reasonable geological constraints, allows not only testing geological hypotheses but also refining existing structural maps. Thus, validity of geological conceptions on graben-rift structure can be proved or denied with the help of computer modeling.
The purpose of the present study is to build magnetic model of the central part of Triassic Danilov graben situated within Khanty-Mansi autonomous district (KhMAD) of central part of the West Siberia oil and gas basin.
2. Geological Background
West Siberia basement has been studied for more than fifty years    -  . The efforts have resulted in detecting many grabens originated in rift formation process that supposedly are responsible for forming oil and gas deposits   . It is generally recognized that all West Siberia was subjected to rifting that leaves traces in the form of branching graben system covered by Mesozoic and Cenozoic sediments  . In the central part of West Siberia, in the limits of junction zone of the eastern slope of the Urals and Tyumen region of KhMAD, two Triassic graben-rifts were singled out   : northern Sosva (at the east slope of the Urals) and Danilov (in the western part of KhMAD). Danilov graben-rift geology (Figure 1) can be considered as a standard for such structures.
3D magnetic model was built with a trial-and-error procedure when repeatedly solving a direct problem. The method was realized in software program complex “3D Interpretation of potential fields”   . Our fitting methodology takes into account the a priori geological information    as well as ideas on graben-rift formation processes. Thus, in the given method an interpreter specifies initial conditions that include geometry of the basement, magnetizing field, magnetic susceptibility and remanent magnetization distributions and obtains at the end total force anomalous magnetic field (AMF), which is compared with observed AMF. Then model is changed and procedure is repeated unless satisfactory fitting is obtained. In doing so in the fitting, many times the following equation for magnetic field is solved  :
where , ―the radius-vector of a source point , r―the radius vector of an observation point , in which we calculate the field, ―magnetic susceptibility. An observation point may be inside or outside of a source body. The equation can be obtained from anomalous field definition  or from Maxwell equations by standard procedure involving Green’s theorem application     . The equation is solved by a numerical method based on   .
The magnetic model was based on our previously constructed density model  . The density model of the Danilov graben has shown that rocks with a significantly excess density of 0.3 g/cm3 and higher, which probably represent the Triassic mantle diapir, should be located under the axial part of the graben.
Figure 1. Geological map of Danilov graben-rift of West Siberia. The black rectangle shows a modeling area. Yellow straight lines inside the model area are vertical cross-section profiles.
Rhyolites, forming small irregular bodies on the geological map of the basement, are combined into the common lopolith-like subvolcanic body at depths. The graben is flattened toward the north, which explains the previously unclear presence of Carboniferous shales among the Triassic rocks in the northern part of the structure. In the course of modeling we achieved good correspondence of magnetic and density geometry. The correctness of the gravitation model was checked by the magnetic model of the graben-rift. Actually, we have a single graben-rift model, in which we fitted different parameters (density, magnetic susceptibility, natural remanent magnetization) and geometry of the bodies.
4. Technical Characteristic of the Model
In modeling, we used a rectangular system of coordinates with the vertical axis pointed upwards, the abscissa directed eastward and the ordinate directed to the north. Gauss-Krüger projection for the 11 zone was used to transfer geological formation contours to the “Complex…”. The final model contains 222,301 elementary cells located in 22 horizontal layers. In horizontal plane, an elementary cell has a dimension of 1.5 × 1.5 km. A layer contains 10,100 elementary cells. Each elementary cell is assigned magnetic susceptibility and remanent magnetization. Basement relief begins with a depth of 1.25 km and continues to a depth of 2.5 km. In this range, a layer thickness of 0.25 km was used. Deeper, from a depth from 2.5 to 12.5 km, we define thickness of a layer equal to 1 km. The grids of the basement and observed AMF coincide and have a dimension of 74 × 76 nodes. The source AMF is presented for epoch of 1965 (Figure 2, the upper part), which is determined calculation of the magnetizing field in IGRF model  . The magnetizing field was calculated at each node of the observed AMF grid and considered constant up to half distance to a next node. The data on magnetic susceptibility were taken typical for the rocks of the area.
5. Accuracy of Fitting
An accuracy is characterized by residual field (Figure 2, bottom part) obtained as difference between observed and model AMF. As one can see from the bottom part of Figure 2, the residual field isolines have mosaic structure with fine details in a range of ±30 nT that is about 5% of the range of the observed AMF (changing from −242 to 1053 nT) excluding boundaries of the model area.
6. Results and Discussion
Our initial supposition that AMF in the area is due to only induced magnetization failed because we cannot model satisfactorily some local negative anomalies above almost nonmagnetic bodies. Another assumption that AMP above the study area contains significant regional component does not confirm. Any filtering of the observed AMF with a purpose to separate regional and local components leads to wide negative anomalies in the local field (taking more than 90% of the area) that requires remanent magnetization opposite to present
Figure 2. Magnetic field of the model: observed AMF (the upper part) and residual AMF (the bottom part). Contours of geological formations (Figure 1) are shown in red lines. The cross-section profiles are shown as black straight lines.
geomagnetic field for all bodies. In the long run, we decide to fit source observed AMF and compensate negative anomalies after taking into account induced magnetization.
As one can see on Figure 3, blocks with opposite to the present geomagnetic field magnetization were inserted at depths from 8.5 to 12.5 km. Other model cells have all components of remanent magnetization equal to zero. We assign values only to z-component of remanent magnetization. Reverse magnetization rocks can be explained by tectonic movement, metasomatosis, or inversion of the main geomagnetic field when rock to form. An analysis of the initial fitting reveals big variety of magnetic susceptibility values that can be grouped in several classes in the ranges of 0 - 0.00072, 0.005 - 0.007, 0.02 - 0.04, and 0.07 - 0.1 SI units. In some cases, it was useful to get average value for a class and alter body geometry that rather improve quality of the fit. The result is shown on Figure 4, where magnetic susceptibility structure. On the Figure 4 magnetic susceptibility in SI units are shown in every horizontal layer of the model where magnetic susceptibility is not equal to zero. The magnetic susceptibility scale is shown to the right. Subscriptions under each graph is a layer range in vertical direction (z-coordinates) beginning from a depth of 1.25 km to the bottom of the model (12.5 km). In the central part of the area, one can trace liparite magnetic susceptibility change with a depth (shown in light blue colors) as well as magnetic
Figure 3. Natural remanent magnetization of the model. Contours of geological formations (Figure 1) are shown in black lines. On the bottom, right part (Layer from −12.5 to 11.5 km) reverse remanent magnetization zones are marked by blue arrow with number.
Figure 4. Layer by layer model of magnetic susceptibility of the study area in SI units. On the upper left part, contours of geological formations (Figure 1) are show in black lines. The scale is shown to the right.
susceptibility of graben-rift basalts (shown in orange colors). At a depth range 1.75 - 2.5 km the liparites have worm-like structure that encountered by wells, below a depth of 2.5 km the liparites form lopolithlike body. Highly magnetic (having big magnetic susceptibility) areas (shown in red colors) are at the bottom of the model.
Let us consider vertical cross-sections of the magnetic susceptibility along profiles (AB, CD, MN, RS and OP) presented on Figure 1. The cross-sections are shown on Figure 5, vertical and horizontal scales coincide.
The profile MN from the southwest to the northeast (center of Figure 5) begins in a serpentinite zone (Figure 1) bounding the graben-rift from the west. Rocks model the periphery of serpentinites have magnetic susceptibility 0.02 - 0.04 SI units and reach a depth of 5.5 km. There are practically nonmagnetic blocks underneath. Further, the profile intersect effusive rocks with tuffs, a
Figure 5. Cross-sections of the model along profiles (shown on Figure 1). Each cross-section begins with local zero coordinate. The scale is shown below. The vertical and horizontal scale are the same.
negative anomaly under which partly taken into account by bodies with reversed magnetization (Figure 3, zone 5). Further on the cross-section clear seen basalts of the graben-rift with magnetic susceptibility 0.025 SI units and less magnetic liparites (0.007 SI units). At a mark of 40 km, the profile intersect intense magnetic anomaly (Figure 2, the upper part) above weakly magnetized graben-rift basalts and liparites (Figure 1). The given anomaly can be explained by very magnetic rocks under the graben-rift. On the given cross-section this rocks come from a depth of 12.5 km to a depth of 5.5 km. Further along the cross-section one can observe graben-rift bottom rising from the southwest to the northeast. Gabbro-dolerites massif (Figure 1) are marked by intense magnetic anomaly (about 600 nT in the maximum) (Figure 2, bottom part), which can be seen at 100 km of the profile. An irregular body (Figure 4), which cross-section along the profile reaches a depth of 11.5 km, models the anomaly. Further, there is a long low intensity anomaly (170 nT at the maximum). However, according to the geological map (Figure 1) here graben basalts are situated and to model the anomaly we entered magnetic body at a depth of 12.5 - 6.5 km (Figure 4 and Figure 5, profile MN). Further, effusive rocks with tuffs have near zero magnetic susceptibility.
The profile RS (Figure 5, cross-section RS), coming from the northwest to the southeast (Figure 1, Figure 2 upper part), gives us an insight into the transversal graben-rift structure. The graben-rift at this cross-section begins 100 km from the profile beginning (magnetic susceptibility 0.025 SI units). To the west of this point, magnetic bodies model Triassic liparites (Figure 1) with susceptibility 0.007 SI units. The cross-section comes through a circumference of serpentinites limiting graben-rift from the west. To the northwest Carboniferous terrigenous-schist formation has magnetic susceptibility near zero (0.00005 SI units) and give nothing to the anomaly. Surrounding magnetic rocks compensate only a half of intensity of the negative magnetic anomaly (about −130 nT in the minimum) and other half is given by deep seated (from 12.5 to 9.5 km depth) rocks (Figure 3, zone 2) with remanent magnetization opposite to the present main geomagnetic field. Above granitoids (from 20 to 40 km along profile), an intense magnetic anomaly (492 nT in the maximum) is modelled by rock underneath.
Coming back to magnetic structure of the graben-rift (110 km along the profile and further) it should be noted its lopolith-like form manifested in magnetic properties and the bottom at a depth of about 5.5 km.
Profiles AB and CD (Figure 5) come from the west to the east. At 40 km from the beginning, the profile AB intersects Late Devonian―Early Carboniferous effusives represented by practically nonmagnetic rocks. The profile CD, situated 30 km to the south, intersects magnetic serpentinites, magnetic susceptibility of which changes from 0.06 to 0.1 SI units in the center and from 0.02 to 0.04 SI units at the periphery. They give an anomaly by order of 1000 nT in the maximum and bound the graben-rift at the west.
Nonmagnetic effusive rocks with tuffs adjoin to them. A negative anomaly (−260 nT) above them are mainly due to magnetic serpentinites at the west, but requires reversely magnetized rock at a deps from 12.5 to 8.5 km (Figure 3, zone 5) for full fitting.
The graben-rift is clearly seen in the plane (Figure 4) and on these cross-sections as rocks with magnetic susceptibility ranging from 0.02 to 0.04 SI units and deepening in some places to 5 km depth. At the end of AB cross-section, further from 120 km and to the end, lowering of AMF (to −170 nT) is observed. This part of the profiles comes through nonmagnetic Carboniferous terrigenous-schist formation. Negative AMF above it cannot be explained by induction of strongly magnetized rocks and require a deep-seated reversely magnetized body (Figure 3, zone 5). As can be seen from AB cross-section, under relatively weakly magnetized rocks of the graben-rift (basalts and liparites) there is a strongly magnetized block of rocks with magnetic susceptibility varying from 0.06 to 0.1 SI units at a depth from 8.5 to 12.5 km. Magnetic susceptibility of graben-rift rocks (changing from 0.02 to 0.04 SI units) gives a wide positive AMF.
Profile OP demonstrates transversal cross-section of magnetic structure of the rock at the northeast (Figure 1), where the bottom of the graben-rift rises to the erosional truncation of the crystal basement. The profile begins from peripheral fragment of serpentinites, the most part of which are situated beyond the modeling area. This is reflected in magnetic susceptibility structure first 5 km along profile. Further, the profile intersects Late Devonian-Early Carboniferous effusives, basalts of the graben-rift (the thin stripe in the upper part of the cross-section with magnetic susceptibility 0.02 - 0.04 SI units) and gabbro-dolerites (0.06 - 0.1 SI units). Negative AMF around 70 km mark of the profile has engaged our attention because it is formed by strongly magnetized bodies (0.06 - 0.1 SI units) situated beyond its outline at a depth of 7.5 km at the northwest and rising up to a depth of 4.5 km at the southeast.
About magnetic susceptibility structure of granitoids and bordering sialic gneiss and schists laying to the west from the graben-rift on the basis of the RS and AB cross-sections (Figure 5) and layer by layer structure (Figure 4) it is possible to say that their magnetic susceptibility (0.005 - 0.007 SI units first 40 km along RS and about zero the first 20 km along AB) is not big enough to generate the observed anomaly. To model the anomaly we enter highly magnetized rocks (0.06 - 0.1 SI units) underneath.
At modeling, we supposed that observed AMF does not have significant regional component above the modeling area.
The presented magnetic modeling confirms the results of gravimetric modeling that, in the first place, the studied structure is not a graben but a rift because continental light crust is absent in the structure (it pulled apart).
The modeling of magnetic susceptibility and natural remanent magnetization of the rocks in the limits of Danilov graben-rift of West Siberia reveals the presence of continuous magnetic rocks coming from a depth of 12.5 km with magnetic susceptibility of 0.06 - 0.1 SI units, which can be interpreted as manifestation of a mantle diapir.
The modeling shows that some local zones of nonmagnetic (according to the geological map) rocks require entering at a depth of 7.5 - 12.5 km reversely magnetized bodies that can be explained if their formation took place in a period of geomagnetic field reversals or recursion. However, the hypotheses about obtaining reverse remanent magnetization in the course of metasomatosis and tectonic movement cannot be excluded.
The graben-rift structure traced by magnetic susceptibility points to that 1) the bottom of the graben-rift rises from the southwest to the northeast; 2) from the northwest to the southeast the graben-rift has lopolith-like structure with eastern fall of western borders marked by serpentinites and western fall of eastern borders.
In total, the modeling results allow confirming and refining geological assumptions on structure of Danilov graben-rift of West Siberia.
Potential field modeling limitation is well known ambiguity: infinitely many models can fit the observed field. The limitation may be overcome by taking into account geological considerations, drilling data and knowledge of genesis of the area. Further development of graben rock property modeling may lay in direction of creating a complex geophysical model incorporating density, magnetic and heat flow parameters.
The work was supported by Russian Science Foundation (Project 16-17-10201).