Calculate adjoint source using GSDF:

Filter the original observed and simulated seismograms ( using f_min = 0.05; f_max = 0.4 Hz) for vx component regarding to source 1 and station D4

 The recursive STA/LTA method is implemented to pick up trigger times on and off for the first arrival component of the observed waveform. The  windowed simulated data based on the arrival time can be used as an isolated filter for GSDF method.

Calculate the cross-correlagram between the isolation filter and the observed seismogram, and auto-correlagram between the isolation filter and the complete simulated seismogram:

Select Gaussian windows for cross-correlagram and auto-correlagram

Windowed signals as input for GSDF measurements

Apply narrow-band filter to decompose the correlagrams (Cross-correlagram or observed and auto-correlagram or simulated) in frequency domain corresponding to 4 central frequencies: 0.05 Hz, 0.1 Hz, 0.15 Hz and 0.2 Hz.

Reconstruction of the windowed correlagrams from the decomposed phases

Waveform perturbation kernels

Seismogram perturbation kernels Jpq (time samples) for the given isolation filter at four different narrowband filtering frequencies

Adjoint source selected in broad band of frequency (sum of the Jpq function scaled by the corresponding TauP value)

Inversion of the true model using 16 sources and 49 stations

Adjoint sources at different stations for source 16

Kernels calculated for source 1