A combined Euler deconvolution and tilt angle method for interpretation of magnetic data in the South region

Introduction: The purpose of this paper is to determinate the position, depth, dip direction and dip angle the faults in the South region of Vietnam from the totalmagnetic intensity anomalies, that reduced to the magnetic pole (RTP).Methods: Based on the Oasis Montaj software, we proposed a new way to compute the positions and the depth to the top of the faults by combining the Tilt angle and the Euler deconvolution methods. In addition, the angle and direction of the dip of theses faults were also determined by considering maximum of the total horizontal derivative of the RTP upward continuation at the different height levels. Results: The results show that there are 12 faults along the longitudinal direction, latitudinal direction, Northwest—Southeast direction and Northeast— Southwest directionwith themazimumdepth is about 3100m and the dip angle changes in the range of 65-82◦ . Conclusion: These indicate that these methods are valuable tools for specifying the characteristics of geology, contribute to give and confirm the useful information on geological structure in the South region of Vietnam.


INTRODUCTION
Determining the dip direction, dip angle and depth of the faults are important steps in the interpretation of magnetic/gravity data. So, there are many methods proposed to solve this problem. To determine the position of the faults, the most commonly method is that using the maximum values of the total horizontal derivatives of the RTP field or the pseudogravity field 1 . In while, the depth of the sources is determined by the statistical methods of Spector and Grant (1970) 2 . Due to the importance of problem, many other methods have been proposed in the past to determine the position of the boundary and the depth of the source individually or the combination of both, such as the Werner method Werner method 3,4 , Euler deconvolution 5,6 ... and a recent method is tilt angle method 7 13 . In which, the studies only determined the position of the fault, did not determine the depth and only a few faults according to the Northwest -Southeast direction are determined the dip angle. Therefore, this paper aims to address the above shortcomings by analyzing the total magnetic intensity anomalies map, that reduced to the magnetic pole (RTP).
For determinating the position and the depth of faults, we proposed a new way by combining the Tilt angle and the Euler deconvolution methods. The tilt angle method was first proposed by Miller and Singh in 1994 14 ; then, was further developed by Verduzco et al. in 2004 15 to determinate the position of faults and the Euler deconvolution method was proposed by Thompson in 1982 5 andReid et al. in 1990 6 to estimate the depth to the top of faults. The combination of the two methods based on the Oasis Montaj software 8.4 16 . Firstly, the tilt angle method was used to delineate the faults (0 contour); then, the Euler deconvolution was applied along the 0 contour of tilt to determine the depth of the faults. This one was intended to overcome the shortcomings of each method. Furthemore, the angle and direction of these faults were also determined by considering maximum of the total horizontal derivative of the RTP upward continuation at the different height levels.

METHODOLOGY Tilt angle method
The tilt angle ( Figure 1) is defined as 14 : first order derivatives of magnetic field T in the x-, yand z -directions. The tilt angle is the ratio of the vertical and horizontal derivatives. Because the horizontal derivative enhances the boundaries (faults) and the vertical derivative narrows the width of the anomaly, so the zero contours (θ = 0 • ) delineate the spatial location of the boundary sources, whilst the depth to the sources are directly identified the contours drawn on the mapthat is the distance between the zero and either the -45 • or the +45 • contours (handwork depth estimation). In this paper, we only use this method to determine the position of the faults.

Standard 3D-Euler Deconvolution method
Recently, using of the Euler deconvolution has become more widespread because it has been automated and rapid interpretation that work with either profile or grid data [17][18][19][20] . This method is based on the homogeneous equation. The 3D form of Euler's equation can be defined 6 : where,x 0 , y 0 , z 0 are the coordinates of the magnetic source whose anomaly ∆T is detected at (x, y, z), ∆T kv is base level (regional anomalies value) and N is a value that describes the anomaly attenuation rate commonly known as the structural index (degree of homogeneity).
In the interpretaion of magnetic data, Thompson (1982) 5 suggested that the index for a magnetic contact was less than 0.5. Reid et al. (1990) 6 said that: This value led to underestimates of depth, even when testing ideal models. They showed that the value for a sloping contact, in fact, zero, provided that an offset A was introduced. The appropriate form of Euler's equation is then: where, A incorporates amplitude, strike, and dip factors which couldn't be separated easily.
In this paper, we only estimated the depth to the top of the contacts by calculating the standard 3D-Euler deconvolution along the position of the structural faults identified from tilt angle.

A combined Euler deconvolution and tilt angle method (Tilt_Euler)
All calculations are made on the Oasis Montaj software version 8.4. The method consists of two parts:

Calculating the 3D-Euler depth using the standard GX Euler3D:
a. Create magnetic grid data for calculation (Euler3D → Grid data) b.Calculate the vertical and horizontal derivatives of the grid data (Euler3D → Process Grid). c. Calculate the Euler depth with input data including magnetic grid map and its horizontal maps (dx, dy) and vertical maps (dz) (Euler3D → Standard Euler Deconvolution).

Determinating the Euler3D depth along the positon of 0 value of the tilt angle:
a.
Calculate the tilt angle using the standard MAGMAP. By default, the Oasis provides both the tilt angle and its horizontal gradient. (Magmap → Tilt Derivative) b. Map the zero contour of the tilt angle without labels. (Map Tools → Contour) c. Export the zero contour layer to a shapefile. (Map → Export) d. Import the shapefile back into a Geosoft database. Specify "New database with shape database(s)". The zero contour will be represented in the shape database as X and Y channels. (Map → Import) e. Determine the value of the standard Euler deconvolution at each x, y coordinate, thereby creating another channel. (Grid Image → Utilities → Sample a Grid) f. Tidy up the database as desired, decimating points based on X and Y and windowing points based on depth. g. Use colored symbols to plot the value of depth at each xy coordinate which is identified by zero values of the tilt angle. (Map tools → Symbols → Colored Range Symbols)

Determination of fault dip angle and direction
In case of a geologic contact (fault surface/trace), the highest upward continuation corresponds to the magnetic response of the deepest part of the contact. If the contact is vertical, then the maxima of total horizontal gradient of upward continued fields are located at the same position. On the other hand, if the maxima systematically shift in horizontal direction, then the dip direction of the contact can be identified. And the fault dip angle (from the horizontal) can be approximated by the method of Chiapkin 21 . Using the anomalous curves upward continuation at the different height levels, we calculated the corresponding total horizontal derivative of them and then determined the angle α by the formula: where, d is the distance on the measuring line from the projection of the fault trace to the projection of the maximum point of the horizontal derivative of curve at the height h.

RESULTS
The data of South  22 . Data was recorded in digitized form (X, Y, Z text file) and was interpolated to grid data sized 178x178, spacing 2 km. In which, the X and Y represent the longitude and latitude of this research area in meters respectively, while the Z represents the magnetic field intensity measured in nanoTesla.

The magnetic anomalies map
After removing the normal magnetic field was calculated by the formula of Nguyen Thi Kim Thoa (1992) 23 , the magnetic anomalies map (Figure 2) showed that the magnetic anomalies were relatively stable, on which the anomalous bands prolonged to the North-South direction with positive -negative zones alternating.
In this paper, we used the RTP operator in Fourier domainat low latitudes of Xiong Li, (2008) 24    had a negative part with large size which was between the two positive ones.
-East of Dam Doi anomalies: the structure is prolonged to Southern Tra Vinh -Soc Trang anomalies; including two anomalies: Gia Rai and Dam Doi anomaly had alternating negative and positive parts.

Interpretation of the South region's magnetic data by Tilt_Euler method
As mentioned in the introduction, the 3D Euler Deconvolution method is used to estimate the depth of the field source with the RTP map, 20x20 window size, flight measured 300 m, 15% maximum depth error.

Determination of the dip angle and dip direction of some faults
On the RTP map, at each fault, we ploted a line perpendicular to the fault and extracted the RTP anomaly values of each line. Then, using that values of each line to perform the upward continuation at the some different height: 3; 4; 5 and 10 km; therefore, determinating the the dip angle and dip direction of faults by considering the location of maximum point of the horizontal derivative of measuring line at the different height levels. Figure 6 is the graph of anomalies at the different height levels and the horizontal derivative of them at the measuring line perpendicular to the Hau river fault. Table 1 showed that maximum positions are determined at positions 33, 37, 39, 46; so, the fault trace shifted from Southwest to Northeast; dip angle was about 74 o . Figure 7 is the graph of anomalies at the different height levels and the horizontal derivative of them at the measuring line perpendicular to the Ca Mau -Chau Doc fault. Table 2 showed that maximum positions are determined at positions 66, 63, 60, 43; so, the fault trace shifted from East to West; dip angle was about 73 o . Similarly, to the remaining faults, the results of determining the dip angle and dip direction of the faults are shown in Table 3.

DISCUSSION
The magnetic anomalies map (Figure 2) showed that the magnetic anomalies were relatively stable, on which the anomalous bands prolonged to the North-South direction with positive -negative zones alternating 25 . According to this map, the research area can be divided into two parts as a straight line from Moc Hoa to Doi Dam: the Eastern part (including Bien Hoa sub-zone, Soc Trang swell bead and coastal hollow in the east) had higher density of anomalies and the length of the anomalies were also greater; in while, the Western part (Dong Thap -Ca Mau hollow of the Can Tho zone) was a larger area, but with fewer anomalies, shorter anomalies length and some magnetic anomalies were isolated 26 . Most of the magnetic anomalies were usually distributed in a particular direction and these often coincided with the major faults in the region. This is even more evident in the RTP map ( Figure 3). Almost strong anomalies are concentrated in the Eastern part. They consisted of the negative and postive ones alternating, the negative are usually larger in size and amplitude than the positive ones, forming the anomalous zones with the    (Figure 4), it can be said that the strong anomalies are aligned with the major directions of the faults in the region because the faults are usually associated with magnetic rock. In Figure 5, there are 12 faults which are divided into 4 groups. And the faults of NW-SE direction and the faults of Longitudinal and Sub-longitudinal direction are faults which developed strongly in the early and late Cenozoic era respectively; and faults NE-SW direction are faults which developed strongly in Mesozoic era, these faults are difficult to detect in the RTP map. The result in Figure 6 and Figure 7 showed that: when elevating the field to different heights, the position of the maximum horizontal derivative depends on the dip direction of the contact (positive or negative angles). With the positive angle, the maxima systematically will shift in horizontal direction to the right (Figure 6b). In contrast, with the negative angle, the maxima systematically will shift in horizontal di-    (Figure 7b). Similarly to the remaining faults, the results of determining the dip angle and dip direction of the faults are shown.
The faults map showed that the faults metioned above matched with rivers and topographical boundaries in the research area 11,27 . There were many faults matching with the announced faults 9,12,22 . These results contributed with the previous studies 9, 13,26,27 to give and confirm the useful information on geological structure in the South region of Vietnam.

CONCLUSION
In this research, the magnetic anomalies map and the RTP were built for the initial evaluation of structure and characteristics of anomalies in the South region of Vietnam. In which, the RTP method at low lattitude is used to reduce some unwanted effects in the interpretation of the magnetic data such as: the peaks are shifted away from the magnetic contact and secondary peaks parallel to the contacts can appear. Based on the Oasis Montaj software, we have developed a method of locating and estimating the depth of the faults by a combined 3D-Euler deconvolution and tilt angle. In addition, building a program to determine dip angle and dip direction of the faults by considering the location of maximum point of the total horizontal derivative of measuring line perpendicular to the faults at the different heights. After that, applying to interpret the magnetic data of the South region, 12 faults and their the angle and the direction of the dip are determinated. This difference is due to the new approach in this article, the resulting faults are determinated on the Tilt_Euler map -the map is built based on the depth results along the the 0 value of the tilt angle. The maximum depth to the top of the faults is about 3100 m. Research results are appropriate and the computing is automatic and quick.