PROBLEM OF SPECIFIC CHARACTERISTICS
OF INTERMEDIARY LAYER DENSITY FOR GRAVITATIONAL SURVEY IN VIỆT NAM

LÊ THANH HẢI, CHU QUỐC KHÁNH, LẠI MẠNH GIÀU, ĐẶNG VĂN HẬU

Division of Geophysics, Thanh Xuân, Hà Nội

Abstract: The most part of gravitational survey projects in Việt Nam have been using the value of medium intermediary layer density of the world, 2.67g/cm³. This value satisfies for gravitational survey in medium and small scales. For large scale and high accuracy gravitational surveys, there is the necessity to determine the specific characteristics of the intermediary layer density of the survey area. The results of determination of specific characteristics of the intermediary layer density by a complex of 4 methods: Netleton, Lucaptrenco, equation system, geologo-geophysical ones satisfy the gravitational survey for large scale and high accuracy as well in the time to come.

I. INTRODUCTION

The gravitational value is the total influence of many material masses with difference density. This density is necessary and important for calculation of terrain correction, Bouguer correction, and intermediary layer correction. The intermediary layer is the layer of rock from observation point to geoid surface. The determination of the average density value of intermediary layer is a necessary problem for gravitational survey. We can use the average density value of intermediary layer of the world (2.67 g/cm³) if the area of gravitational survey is in mountain and 2.30 g/cm³ if the survey area is deltaic area, where the layer is composed of Neogene and Quaternary sediments. The gravitational data of Việt Nam have shown that the use of density value of intermediary layer is very different. Some gravitational survey projects in medium and small scales have been using the value of 2.30 g/cm³ or 2.67g/cm³ [7, 9]. Some others in medium and large scales have been using the value of 2.67 g/cm³ for Bouguer anomaly maps compiling to work out to total. For geological analysis of gravitational survey, some Bouguer anomaly maps have been compiled with several specific characteristics of density values of intermediary layer of survey [5, 6].

According to the definition of in force technical norms of gravitational prospecting, when carrying out gravitational survey in large scale, there is the requirement of absolute necessity to determine specific characteristics of density value of intermediary rock layer in the survey area. Therefore, the determination of specific characteristics of density value of intermediary layer is realized. By methods of Netleton graphics, gravitational point Lucapchenco, to solve the minimum standard deviation of equation system, and geologo-geophysical method, the authors determine the average density value of the land of Việt Nam as 2.58 g/cm³. It is 0.09 g/cm³ smaller than the one of the world.

II. THEORETICAL BASES AND CALCULATION METHOD

1. Theoretical bases

The intermediary layer is the matter layer lying between observed point and geoid surface. The average density value of this layer is called as specific characteristic density value of intermediary layer or intermediary layer density.

The use of cylindrical coordinate system r, j, coordinate origin set in observed point A (Fig. 1), vertical component Dg of gravity force in point A, far from plan layer attract a distance H₁ is calculated by formula:

(1)

To integrate above formula, obtained:

Dg_(A) = 2Õ Gs [(H + H₁) – H₁] = 2ÕGs.H (2)

It is shown that, the vertical component of gravity force does not depend on distance H₁ but only depends on the layer thickness. Replacing the values into formula (2), we obtain:

Dg_(A) = 0.04192s (mGal) (3)

Where: H - height of observation (m); s - density of intermediary layer (g/cm³).

In general, the intermediary layer density is not constant, but varies in vertical and horizontal directions. If the intermediary layer density changes in vertical direction, the calculation is carried out to determine by model of horizontal layers, which have densities s₁, s₂, s₃ …s_n, and the effect is calculated by the formula:

Dg_(A) = 0.0419 (s₁H₁ + s₂H₂ + … s_nH_n) (4)

2. Calculating methods

a. Method of Netleton graphics: Selecting a transversal profile across studied area, where the topography is characteristic; carrying out the measurement of gravitational value in this profile. Calculating the Bouguer anomaly with different intermediary layer densities by formula:

Dg_B = g_qs - g₀ + (0.3086 – 0.0419s) H (5)

Where: Dg_B - Bouguer anomaly (mGal); g_qs - gravitational observation value (mGal); g₀ - normal gravitational value (mGal); H - height of gravitational observation point (m).

for creating the Bouguer anomaly graphics of profile by all used intermediary layer densities. The specified intermediary layer characteristic density is the density of the curve Dg_B, which has the correlation with topographical section is least. The method is simple and easy to be used, the calculation is carried out fast on personal computer.

b. Method of Lucaptrenco gravitational point: The determination of intermediary layer characteristic density is based on the observed gravitational value on area, where the terrain is abrupt or the slope angle of topography is considerable. Selecting the profile to research, carrying out the measurement of the gravitation in two points, one on the lowest area of the mountain; one on the mountain summit, the Bouguer anomaly is calculated by formulae:

For N^o 1 point:

Dg_B1 = g_qs1 - g₀₁ + (0.3086 - 0.0419s). H₁ (6)

For N^o 2 point:

Dg_B2 = g_qs2 - g₀₂ + (0.3086 – 0.0419s). H₂ (7)

The intermediary layer density value is calculated by formula:

(8)

Where: Dg_B1, Dg_B2 - Bouguer anomaly in points N^o 1 and 2; H₁, H₂ - heights of point N^o 1 and 2; g_qs1, g_qs2 - observed gravitational values; g₀₁, g₀₂ - normal gravitational value.

The method is simple and easy to be used, the result is confident.

c. Method of solving equation system: The Bouguer anomaly is represented by an equation system of different degrees.

In an observed point, the Bouguer anomaly value is represented by the formula:

Dg_Bi=g_qs(xi) - g_o(xi) +0.3086 h _(xi) -0.0419s. h _(xi)+Dg_pi =

Dg_f(xi)-0.0419.s.h_(xi)+Dg_pi= (9)

If x = 0 and ignoring the terrain correction, we obtain:

(10)

Sets a_o = Dg_F(0) – bh₍₀₎ , we obtain:

(11)

To simplify, we make sign:

Dg_Fi = Dg_{F (xi)} - Dg_F(o) (12)

Dh_i = h _{( xi)} – h_(o) (13)

The formula is represented in the following form:

(14)

According to minimum square method, b needs to satisfy the requirement:

(15)

Where N: number of observation on profile; m: number of equation.

To carry out derivative of above formula after a_m and b we obtain new equation system. For solving this equation system to look for b value and s (g/cm³) to be calculated.

If the Bouguer anomaly in observed profile varies by linear function, Dg_Bi = a_ix from (15) we obtain the equation system:

(16)

(17)

If the Bouguer anomaly varies by exponentional function, the formula has the form:

Dgbi = a₁x + a₂x² (18)

We have the following equation system:

(19)

(20)

(21)

Basing on the observed data on profiles, we create one from two equation systems, to solve to look for b.

From b = 0.0419 s, looks for s.

d. Geologo-geophysical method: The gravitational profile is on the geological section profile.

The average density of intermediary layer is the arithmetical mean density by section area of all geological formations that are present in the geological section, calculated by the formula:

(g/cm³) (22)

Survey area after geological map or geological schema.

The average density of intermediary layer is the arithmetic mean density by volume of all geological formations that are present in the survey area, calculated by the formula:

(g/cm³) (23)

where S_i: area of numbered geological formation i (23 & 24); s_i: average density of numbered geological formation i; N: number of geological formation; V_i: volume of numbered geological formation i; V_i = S_i x H_i (25); H_i: height of gravitational observation point S_i.

III. OBTAINED RESULTS

1. Graphical Netleton method

By the graphical Netleton method, carried out to calculate 766 points on 79 profiles, consisting of Hà Tiên 6, Southern delta 10, Northern delta 12, Kon Tum 11, Ba Tơ 10, Đà Lạt 6, Quảng Ngãi 6, Nông Sơn 7, Cẩm Thủy 5, Cao Bằng 6. The gravitational Bouguer anomaly on profiles has been calculated with density: s₁ = 2.00, s₂ = 2.10, s₃ = 2.20, s₄ = 2.30, s₅ = 2.40, s₆ = 2.50, s₇ = 2.60, s₈ = 2.70, s₉ = 2.80, s₁₀ = 2.90 và s₁₁ = 3.00 (g/cm³).

The obtained results carried out to analyze statistic by probability method show that: intermediary layer density value of 2.0 g/cm³ is characteristic for Southern and Northern delta regions. Intermediary layer density 2.0 - 2.60 g/cm³ is characteristic for mountain regions such as Kon Tum, Quảng Ngãi, Nông Sơn, Đà Lạt, Cẩm Thủy, Cao Bằng, ....

2. Gravitational Lucaptrenco point method

After this method, it is necessary to determine gravitational anomaly difference (Dg = g_qs - g₀) between two observed points (g_qs1, g_qs2), and their heights (H₁, H₂) far from geoid surface, where the first point (g_qs1) is located near the second point (g_qs2). The second observed point is called as standard basis of survey area. This point always is put on the mountain summit, where the height is greatest (Phan Si Pan, Bạch Mã, Ngọc Linh …). 21 points from the 26 points of standard bases (g_qs2) have the height from 500 to 1600 m. The calculation has been carried out for 1295 points distributed over the whole of our country. The intermediary layer density value obtains by the formula:

Where s: intermediary layer density value for the whole country; s_i: the intermediary layer density value of numbered point I; M: number to calculate.

3. Equation system solving method

To compile the equation system for calculation on 15 gravitational profiles distributed over the whole country. The calculation is performed by personal computer. The result is intermediary layer density value of every profile. The intermediary layer density value is arithmetical mean density value. The intermediary layer density value of every profile is as follows:

1. Profile Rạch Giá - Long Xuyên: 2.35 g/cm³; 2. Profile Long Xuyên - Châu Đốc: 2.38 g/cm³; 3. Profile HồChíMinh City - Bảo Lộc: 2.58 g/cm³; 4. Profile Phan Rang - Đà Lạt : 2.67 g/cm³; 5. Profile A Sầu - A Lưới : 2.56 g/cm³; 6. Profile Đông Hà - Bạch Mã: 2.65 g/cm³; 7. Profile Kon Tum - Khâm Đức: 2.58 g/cm³; 8. Profile Hồ Xá - Bến Hải: 2.58 g/cm³; 9. Profile Phú Nhơn - Krông Búk: 2.56 g/cm³; 10. Profile Mộc Châu - Mường Hét: 2.58 g/cm³; 11. Profile Tuần Giáo - Tây Trang: 2.62 g/cm³; 12. Profile Bắc Ninh - Lạng Sơn: 2.67 g/cm³; 13. Profile Phú Lộc - Nguyên Bình: 2.58 g/cm³; 14. Profile Trà Bồng - Phước Sơn: 2.66 g/cm³; 15. Profile Nguyên Bình - Bảo Lộc: 2.69 g/cm³.

4. Geologo-geophysical method

a. By geological sections: The calculation is performed on 19 sections of 6 geological structural regions, consisting of: Northwest Việt Nam region - 1 section; Northeast Việt Nam region - 1 section; North of Central Việt Nam - 1 section; Huế - Quảng Ngãi region - 5 sections; Kon Tum - Buôn Ma Thuột - 2 sections; Đồng Nai - Bến Khế and South Việt Nam - 6 sections. After the processing of method: - Determining the area of every geological formation on the section; - Density value s_I of every geological formation is specified after gravitational survey projects [5, 6] and synthesized from physical property of rock bed [8]; - The intermediary layer density value is determined on every section, after that the arithmetical mean for every region is calculated; at last the arithmetical mean for the whole country is calculated.

b. By geological map area: To divide the country into cell base areas, which have longitude (l) of 0⁰30’00” and latitude (j) of 0⁰20’00”, made symbol (made code) longitude.latitude.cell name (for example: 0730.1820.01 or 0700.1800.01, studied cell is 01 at position 107⁰30’ or 107⁰00’ E and 18⁰20’ or 18⁰00’ N.

For every cell base area we execute:

- To compile geological section according to request perpendicular or nearly perpendicular to the direction of geological formation; to go through or asymptote nearly the geological works, geological observation point, to go through the whole or nearly the whole geological formation.

- To compile the synthetical stratigraphic column for every cell base area.

- To assign the average density value to correlative geological formation presented in cell base area. Density of geological formation to be used is the value from gravitational survey project [5, 6] and physical property book of rock [8]. After results, the density value can be divided into two characteristic groups, as follows:

- The average density value of intermediary layer is characteristic with value 2.30 g/cm³ for bigger than 115,000 km² in delta region. In there, the area of Red River delta region is about 15,000 km² including the provinces Thái Bình, Nam Định, Hải Dương, Hưng Yên, Hà Nội, Hà Nam and a part of provinces Ninh Bình, Hải Phòng, Quảng Ninh, Bắc Ninh and Hà Tây. The area of Mekong River delta is about 100,000 km² including the provinces Cà Mau, Kiên Giang, An Giang, Bạc Liêu, Sóc Trang, Cần Thơ, Đồng Tháp, Vĩnh Long, Trà Vinh, Bến Tre, Tiền Giang, Long An, Tây Ninh, HồChíMinh City, Bà Rịa - Vũng Tàu, Đồng Nai, Bình Dương, Bình Phước.

- The average density value of intermediary layer is characteristic with value of 2.58 g/cm³ for about 215,000 km² in mountainous region. In there, there are provinces Bình Thuận, Ninh Thuận, Lâm Đồng, Đăk Lắc, Khánh Hòa, Phú Yên, Gia Lai, Bình Định, Quảng Ngãi, Kon Tum, Quảng Nam, Đà Nẵng, Thừa Thiên Huế, Quảng Trị, Quảng Bình, Hà Tĩnh, Nghệ An, Thanh Hóa, Thái Nguyên, Hòa Bình, Phú Thọ, Sơn La, Lai Châu, Yên Bái, Lào Cai, Hà Giang, Tuyên Quang, Vĩnh Phúc, Bắc Cạn, Cao Bằng; in the rest area of the provinces of Red River delta, the density value is characteristic with the value of 2.30 g/cm³.

IV. CONCLUSIONS

The density value of rocks and minerals existing in gravitational survey area is necessary data not only for compiling survey projects, but also for determining intermediary layer correction, terrain correction, compiling Bouguer anomaly map and for quantity analysis of gravitational anomaly related to geological and mineral researching projects. On the world, there are many methods for determining intermediary layer density. Under the present conditions of Việt Nam, the authors applied the following: graphical Netleton, gravitational Lucaptrenco point, solving equation system and geologo-geophysical method. The calculated points are distributed over the whole country of Việt Nam. In there, dominant quantity points are calculated by gravitational Lucaptrenco point and geologo-geophysical method. By gravitational Lucaptrenco point method, 1295 points has been calculated, distributed over the whole country, the characteristic value is 2.58 g/cm³. In calculation process, the authors have been using many types of height difference between the second observation (Hg_qs2) and the first observation (Hg_qs1). 26 points used to act as standard basis, placed on hill summit, mountain summit, top of mountain pass, height of mountain side and mountainous height, have the height varying from 96.45 to 1600.13 m, in average 800 m. The “satellite” points placed around the standard basic point have the height varying from 5.12 to 755.11 m, in average 500 m. The determined mean thickness of intermediary layer varies from 5.12 to 1600.13 m, in average 797.50 m. By geologo-geophysical method, the intermediary layer density is specified from about 30,000 cell base area (20.25 km²) covered over the whole country. The results are as follows:

- Mean density of intermediary layer of 2.30 g/cm³, is characteristic for the Mekong River Delta and the Red River Delta regions.

- Mean density of intermediary layer of 2.58 g/cm³ is characteristic for the mountainous regions, the rest mountain land country.

Like this, one may use the intermediary layer density value of 2.58 g/cm³ for gravitational survey on hilly and mountainous region of Việt Nam, replacing the mean density value of the world.

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