This paper intends to study the dispersion and attenuation characteristics of corrugation, reinforcement, heterogeneity and initial stress on propagation of Love type surface waves in a bedded structure with welded contact, subject to certain boundary conditions. Current composite model is consists of an initially stressed heterogeneous orthotropic layer bonded between fiber-reinforced upper half-space (under hydrostatic stress) and pre-stressed lower porous half-space separated by corrugated boundaries. Exponential variation in elastic parameters of the orthotropic medium is considered in the sandwiched layer. Dispersion equation has been obtained in closed form. Considerable effect of elastic parameters (reinforcement, heterogeneity and initial stress) on the phase velocity of Love type wave has been discussed graphically. Some particular cases have been discussed and it is found that dispersion equation is in well-agreement with the classical Love wave equation. The deduced equations coincide with the classical Love-wave condition for the uniform homogeneous isotropic structure. Numerical computations are carried out for involved parameters and demonstrated with the help of graphs. © 2020, Springer Nature India Private Limited.