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Maps of apparent electrical conductivity (ECa) of the soil profile are widely used in precision agriculture. A number of ECa sensors are commercially available, each with a unique response function (i.e., the relative contribution of soil at each depth to the integrated ECa reading). Our past research estimated depth to an argillic horizon (i.e., topsoil depth, TD) on claypan soils by fitting empirical equations to ECa sensor data. The objective of this research was to determine if TD estimates could be improved by combining data from multiple ECa sensors and by solving for TD by inverting a two-layer soil model incorporating instrument response functions. Data were obtained with three sensors having five different ECa depth-response functions (Veris 3150*, Geonics EM38 vertical dipole mode, and DUALEM-2S) on two Missouri claypan-soil fields. Soil cores obtained in each field provided measured TD data for calibration and validation. Using a numerical optimization approach, response-function models were developed for ECa variables individually and in combination. Similarly, linear regression was applied to single and multiple variables. Root mean square error of validation (RMSEv) of single-variable TD estimates was 22 to 25 cm, with better results for those variables with moderately deep ECa response functions. Results from the model-based approach were very similar to those obtained by regressing TD on ECa−1. The best calibrations using multiple variables in model inversion or regression were somewhat better than those using single variables, with RMSEv of 22 cm and 20 cm, respectively. For all approaches, highest TD errors were localized to one area of one field, possibly because soils in this area violated the model assumption of spatially homogeneous soil layer conductivity. Although these calibrations are sufficiently accurate to be useful in TD mapping, a model solution allowing layer conductivities to vary spatially should be investigated for possible improvements.