Gravity gradiometry

Gravity gradiometry is the study of variations (<a href="/facts/Gravitational_anomaly/sCP5S0Xy">anomalies</a>) in the <a href="/facts/Earth%2527s_gravity/IXe9Bh8k">Earth's gravity</a> field via measurements of the <a href="/facts/Spatial_gradient/2cmoCezd">spatial gradient</a> of <a href="/facts/Gravitational_acceleration/b8IbkkI2">gravitational acceleration</a>. The gravity gradient tensor is a 3x3 <a href="/facts/Tensor/pNjFo5tV">tensor</a>; it is given in coordinates by the <a href="/facts/Jacobian_matrix/0tNv6o8j">Jacobian matrix</a> of the <a href="/facts/Acceleration_vector/HMVvKk5n">acceleration vector</a> (
 
 
 
 g
 =
 [
 
 g
 
 x
 
 
 
 g
 
 y
 
 
 
 g
 
 z
 
 
 
 ]
 
 T
 
 
 
 
 {\displaystyle g=[g_{x}g_{y}g_{z}]^{T}}
 
), totaling 9 <a href="/facts/Scalar_(physics)/05uvvP8N">scalar quantities</a>:

G
        =
        ∇
        g
        =
        
          
            [
            
              
                
                  ∂
                  
                    
                      g
                      
                        x
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    x
                  
                
                
                  ∂
                  
                    
                      g
                      
                        x
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    y
                  
                
                
                  ∂
                  
                    
                      g
                      
                        x
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    z
                  
                
              
              
                
                  ∂
                  
                    
                      g
                      
                        y
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    x
                  
                
                
                  ∂
                  
                    
                      g
                      
                        y
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    y
                  
                
                
                  ∂
                  
                    
                      g
                      
                        y
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    z
                  
                
              
              
                
                  ∂
                  
                    
                      g
                      
                        z
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    x
                  
                
                
                  ∂
                  
                    
                      g
                      
                        z
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    y
                  
                
                
                  ∂
                  
                    
                      g
                      
                        z
                      
                    
                  
                  
                    /
                  
                  ∂
                  
                    z
                  
                
              
            
            ]
          
        
      
    
    {\displaystyle G=\nabla g={\begin{bmatrix}\partial {g_{x}}/\partial {x}&\partial {g_{x}}/\partial {y}&\partial {g_{x}}/\partial {z}\\\partial {g_{y}}/\partial {x}&\partial {g_{y}}/\partial {y}&\partial {g_{y}}/\partial {z}\\\partial {g_{z}}/\partial {x}&\partial {g_{z}}/\partial {y}&\partial {g_{z}}/\partial {z}\end{bmatrix}}}

It has <a href="/facts/Dimension_(physics)/t6UskoCD">dimension</a> of square <a href="/facts/Reciprocal_time/W0Iqf8EL">reciprocal time</a>, in <a href="/facts/Unit_of_measurement/pvTpWbmC">units</a> of s−2 (or m ⋅ m−1 ⋅ s−2).
Gravity gradiometry is used by oil and mineral prospectors to measure the density of the <a href="/facts/Bedrock/mn9WCgtX">subsurface</a>, effectively by measuring the rate of change of gravitational acceleration due to underlying rock properties. From this information it is possible to build a picture of subsurface anomalies which can then be used to more accurately target oil, gas and mineral deposits. It is also used to image <a href="/facts/Water_column/RNQbAVJj">water column</a> density, when locating submerged objects, or determining water depth (<a href="/facts/Bathymetry/vnYgY6qK">bathymetry</a>). Physical scientists use <a href="/facts/Gravimeter/kPrbm8wx">gravimeters</a> to determine the exact size and shape of the earth and they contribute to the gravity compensations applied to <a href="/facts/Inertial_navigation_system/UzUTMhK2">inertial navigation systems</a>.

Gravity gradiometry open-in-new

Gravity gradiometry