Prior Probability

Prior Probability

We set prior probability of each model parameter as follows.

Model parameter	Distribution type	Tuning parameter
# of layer interfaces	Truncated uniform	k_min, k_max
Interface depth	Truncated uniform	z_min, z_max
S wave velocity perturbation (prior_mode=1)	Laplacian	sig_dVs_prior
P wave velocity perturbation (prior_mode=1)	Laplacian	sigma_dVp_prior
S wave velocity perturbation (prior_mode=2)	Gaussian	sig_dVs_prior
P wave velocity perturbation (prior_mode=2)	Gaussian	sigma_dVp_prior
Data noise standard deviation	Truncated Uniform	sig_min, sig_max

Note

There are two chocies for velocity perturbation: (1) Laplacian and (2) Gaussian. The fomer prior tries to produce zero amount perturbation for as many layers as possible, analogous to L1 norm regularization.

Related parameters

For the following notations, please refer to Input files.

• k_min, k_max
• z_min, z_max
• prior_mode
• sig_dVs_prior
• sigma_dVp_prior
• sig_min, sig_max