We have developed a lateral constraint to the inversion of 1D seismic impedance models to suppress the effect of data noise and improve the fidelity of formation boundaries in 2D models for situations with dips of less than 20°. Typical inversion frameworks rely on a 1D forward model with each 1D trace being inverted independently. Adjacent inversion models are combined together to form a 2D impedance model. Adding a lateral constraint improves the fidelity of the 2D impedance models while retaining much of the advantage of the low-computational cost associated with typical 1D inversion schemes. Solving the 1D lateral constraint inversion (1D-LCI) problem involves the simultaneous inversion of multiple 1D traces producing layered sections with lateral smoothed transition. In addition to enforcing lateral continuity in the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We determined the effectiveness of this algorithm on two synthetic models, as well as a field seismic data set. One-dimensional-LCI inversion results produced well-defined horizontal boundaries, while suppressing noise.