Hagedoorn's plus-minus method: the beauty of simplicity

Hagedoorn developed the plus-minus method with the objective of providing the exploration world with a simple and rapid approximation of Thornburgh's wavefront reconstruction method. Straightforward adding and subtracting produces depths and velocities at all geophones where the refracted waves from a set of reciprocal shots are first arrivals. Even though seismic refraction has not kept up with the revolutionary advance of reflection technology during the past decades, the method still has a lot to offer, especially in shallow engineering, and environmental, groundwater and sea-bed surveying. Its strong points are the ease of application, the low costs, the effectiveness in the shallow zone, the unique ability to provide detailed velocity information on the deepest refractor and the capability for producing parameters for layer and rock characterization.Because of its simplicity, the plus-minus method is ideally suited for real-time processing of refraction data in the field, thus monitoring the data quality and the optimal shot configuration. Today, such field processing is easily performed with a laptop and dedicated software. matlab ^® is a software package that enables tailor-made processing, offering a combination of a programming language, visualization tools and a large library of ready-made functions. This paper presents a plus-minus program developed in matlab and illustrates its application with a case study in Yemen, where seismic refraction was used in a regional groundwater study. Here, refraction provided not only a detailed section across the recharge area of a coastal plain but also the additional information needed to reduce ambiguity in the interpretation of the vertical electrical soundings made in the area.