We propose a new method to determine source parameters and attenuation structure of a three-dimensional medium based on first P rise time and total pulse width measurements from microearthquake data. The effects of fault finiteness on seismic radiation are taken into account by assuming the rupture model for a circular crack of Sato and Hirasawa (1973). Ray theory synthetic seismograms in a constant Q anelastic medium are computed to derive a set of nonlinear equations which relate the source and attenuation parameters (fault radius, orientation of the fault plane, and quality factor) to the pulse width data (half and total duration of the P waveforms). The numerically built relationships are used to compute the direct problem in the framework of a nonlinear inversion scheme, based on the modified downhill Simplex method. The validity and robustness of the inversion method are tested by synthetic simulations by assuming the sources and receivers configuration of the seismic passive experiment conducted in the Campi Flegrei caldera (southern Italy) during the last microearthquake crisis (1982--1984). Different heterogeneous Q models have been considered in order to assess the uncertainty and resolution of source and attenuation parameters for the given acquisition layout. The results of this simulation study indicate that first pulse width data from a local network permit retrieval with sufficient accuracy of the heterogeneous Q structure and fault radii. A rather dense azimuthal coverage of the sources is instead needed to recover the angles (in particular, the fault strike) which define the fault orientation. ¿ 2001 American Geophysical Union