Patent ID: 11940531
Assignee: THE TRUSTEES OF PRINCETON UNIVERSITY
Field: Measurement (Instruments)
Classification: CPC A  G | IPC A  G

Claim 3:
4. The system of claim 3, wherein the processor is further configured to:
(i) evaluate the gradient of the cost function for the bulk modulus κ, as defined by, K
      κ
    
    ⁡
    
      (
      x
      )
    
  
  =
  
    
      -
      
        2
        
          Δ
          ⁢
          τ
        
      
    
    ⁢
    
      
        ∫
        
          T
          
            s
            ⁢
            s
          
        
        
          
            T
            
              s
              ⁢
              s
            
          
          +
          
            Δ
            ⁢
            τ
          
        
      
      ⁢
      
        
          
            κ
            
              -
              1
            
          
          ⁡
          
            (
            x
            )
          
        
        ⁢
        
          
            ∂
            
              t
              2
            
          
          ⁢
          
            
              P
              syn
              †
            
            ⁡
            
              (
              
                x
                ,
                
                  
                    T
                    
                      s
                      ⁢
                      s
                    
                  
                  +
                  
                    Δ
                    ⁢
                    τ
                  
                  -
                  t
                
              
              )
            
          
        
        ⁢
        
          
            P
            
              s
              ⁢
              y
              ⁢
              n
            
          
          ⁡
          
            (
            
              x
              ,
              t
            
            )
          
        
        ⁢
        dt
      
    
  

where Psyn† is an encoded adjoint wavefield, and ∂t2 is a second order partial derivative in time, operator.