Seismic Waveform Inversion by Stochastic Optimization

Algorithm 2

Stochastic descent.

While not converged do

 draw 𝑤 from a pre-scribed distribution

 𝑠←−∇𝜙[𝑚_𝑖,𝑤]/‖∇𝜙[𝑚_𝑖,𝑤]‖₂

 find 𝜆 s.t. 𝜙[𝑚_𝑖+𝜆𝑠,𝑤]≤𝜙[𝑚_𝑖,𝑤]+𝑐𝜆∇𝜙[𝑚_𝑖,𝑤]^𝑇𝑠

 𝑚_𝑖+1←(1/(𝑛+1))(∑^𝑖_𝑖−𝑛𝑚_𝑖+𝜆𝑠)

 𝑖←𝑖+1

end while