geology

How to Calculate and Solve for Total Anomalous Mass | Gravity

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The image above represents total anomalous mass.

To compute for total anomalous mass, one essential parameter is needed and this parameter is Number of Area Segments (n).

The formula for calculating total anomalous mass:

ME = 23.9 Σ(ΔgδA)

Where:

ME = Total Anomalous Mass
Δg = Change in Gravity
δA = Area Segment

Let’s solve an example;
Find the total anomalous mass when the number of area of segments is 2 (change of gravity (Δg1) is 5, area segment (δA1) is 12, change of gravity (Δg2) is 8 and area segment (δA2) is 10).

This implies that;

δA1 = Area Segment = 12
Δg1 = Change in Gravity = 5
δA2 = Area Segment = 10
Δg2 = Change in Gravity = 8

Δg δA ΔgδA
5 12 60
8 10 80

Σ(ΔgδA) = 60 + 80
Σ(ΔgδA) = 140

Therefore,

ME = 23.9 Σ(ΔgδA)
ME = 23.9 (140)
ME = 3346

Therefore, the total anomalous mass is 3346 g.

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How to Calculate and Solve for Actual Mass of Geological Body | Gravity

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The image above represents actual mass of geological body.

To compute for actual mass of geological body three essential parameters are needed and these parameters are Total Anomalous Mass (ME), Anomalous Density of the Body (ρ1) and Host Rock Density (ρ0).

The formula for calculating actual mass of geological body:

M = ME (ρ1 / ρ1 – ρ0)

Where:

M = Actual Mass of Geological Body
ME = Total Anomalous Mass
ρ1 = Anomalous Density of the Body
ρ0 = Host Rock Density

Let’s solve an example;
Find the actual mass of geological body when the total anomalous mass is 12, anomalous density of the body is 21 and the host rock density is 13.

This implies that;

ME = Total Anomalous Mass = 12
ρ1 = Anomalous Density of the Body = 21
ρ0 = Host Rock Density = 13

M = ME (ρ1 / ρ1 – ρ0)
M = 12 (21 / 21 – 13)
M = 12 (21 / 8)
M = 12 (2.625)
M = 31.5

Therefore, the actual mass of geological body is 31.5 kg.

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How to Calculate and Solve for Total Mass Determination | Gravity

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The image above represents total mass determination.

To compute for total mass determination, two essential parameters are needed and these parameters are Maximum Gravity (Δgmax) and Half Width (x1/2).

The formula for calculating total mass determination:

M ≃ 255Δgmax(x1/2)²

Where:

M = Total Mass
Δgmax = Maximum Gravity
x1/2 = Half Width

Let’s solve an example;
Find the total mass determination when the maximum gravity is 10 and the half width is 6.

This implies that;

Δgmax = Maximum Gravity = 10
x1/2 = Half Width = 6

M ≃ 255Δgmax(x1/2)²
M ≃ 255(10)(6)²
M ≃ 255(10)(36)
M ≃ 91800

Therefore, the total mass determination is 91800 kg.

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How to Calculate and Solve for Theoretical Value of g | Standard Formula | Gravity

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The image above represents theoretical value of g.

To compute for theoretical value of g, one essential parameter is needed and this parameter is Latitude (φ).

The formula for calculating theoretical value of g:

g = (-172 + 136sin²φ)

Where:

g = Theoretical Value of g | Standard Formula
φ = Latitude

Let’s solve an example;
Find the theoretical value of g when the latitude is 18.

This implies that;

φ = Latitude = 18

g = (-172 + 136sin²φ)
g = (-172 + 136sin²(18))
g = (-172 + 136(0.309)²)
g = (-172 + 136(0.0954))
g = (-172 + (12.986))
g = -159.01

Therefore, the theoretical value of g is -159.01 mGal.

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