A Synthetic from a Well Log

Part 2, Part 2: The Convolutional Model

Learning objectives

Trace the pipeline: velocity and density to impedance to reflectivity to trace
Build a synthetic seismogram from measured logs
Identify a soft gas sand as a strong trough on the trace
See the synthetic as the seismogram used to tie a well

The Whole Model on One Well

Everything in this part so far, impedance, reflectivity, convolution, tuning, comes together in the one product interpreters actually make: a synthetic seismogram from a well. The four tracks below are the pipeline in order.

The velocity and density logs are measured in the borehole by the sonic and density tools.
Their product is the acoustic impedance, $Z = \rho v$ .
The impedance contrast at every bed is the reflectivity, $R = (Z_2 - Z_1)/(Z_2 + Z_1)$ .
Reflectivity convolved with a wavelet is the synthetic trace.

Reading the Well

A soft gas sand sits in the middle of this well. Because its impedance drops below the surrounding shale, its top is a strong soft reflection, a trough, and you can see it stand out on both the reflectivity and the trace. That is the calibration use of synthetics from Part 0 made concrete: this trace is exactly what an interpreter slides against the recorded seismic at the well until the events line up, which ties the well to the survey and confirms the velocities and picks.

Change the wavelet frequency and the resolution changes with it. At low frequency the thin limestone stringer and the sand blur into their neighbours, exactly the tuning of the last section; at high frequency they separate. Nothing here is new physics. It is the convolutional model, scale-shift-and-sum, applied to real rock, and it is the everyday bridge between a well and a seismic line. The last two sections of this part add noise to this trace and then ask, honestly, when this cheap model is enough.