Christopher V. Kimball

Semblance processing of borehole acoustic array data

A new method of processing borehole acoustic array data is described. The method detects arrivals by computing the scalar semblance for a large number of possible arrival times and slownesses. Maxima of semblance are interpreted as arrivals. Their associated slownesses are plotted on a graph whose axes are slowness and depth. The processing makes few prior assumptions about data and the algorithm is uncomplicated. Results of the processing applied to data from a 12-receiver device are presented for both open and cased holes.--Modified journal abstract.

Shear slowness measurement by dispersive processing of the borehole flexural mode

In sonic well logging, the flexural mode generated by a dipole transducer allows measurement of shear slowness in slow formations, that is, formations in which the shear slowness is slower than the borehole fluid speed. The flexural mode is a dispersive borehole mode, but many current processing methods do not account for this dispersion. The approximate semblance equation is derived to explain what happens when a dispersive wave is processed nondispersively. The processing described here is a dispersive analog of the slowness‐time coherence (STC) processing used commonly for array sonic waveforms. It back‐propagates waveforms according to model dispersion curves and calculates semblance. It is a specialized version of the maximum likelihood (ML) and least‐mean‐squared‐error (LMSE) estimator for formation shear slowness. The dispersive analog of STC is too slow for depth‐by‐depth logging but may be a helpful analytic tool. A high‐speed variant, dispersive STC (DSTC), eliminates this difficulty by a new wi...

Error bars for sonic slowness measurements

Semblance provides a quality indicator for beam‐former array processing methods such as slowness/time coherence (STC) and dispersive STC (DSTC). Semblance does not indicate the slowness variance because the array design, the processing time‐bandwidth parameters, and the signal spectral content are not taken into account. For the classical case of a single propagating wave with added Gaussian noise, semblance is distributed according to the noncentral beta distribution. This distribution is parameterized by the number of receivers, M, the processing time‐bandwidth product, BT, and signal‐to‐noise ratio. Given M and BT, the measured semblance can be inverted to give a high‐quality estimate of the signal‐to‐noise ratio. The Cramer‐Rao lower bounds on slowness variance for the classical case of signals in added Gaussian noise depend on the array dimensions, the signal power spectrum, and the signal‐to‐noise ratio. Estimates of the Cramer‐Rao bounds can be calculated from the estimated signal‐to‐noise ratio an...

Dispersive Wave Processing of the Borehole Flexural Mode

Current Array Sonic processing techniques, such as Slowness-Time Coherence (STC), were designed for nondispersive waves, i.e., monopole compressional and shear arrivals [l]. Monopole sources do not allow the measurement of shear slowness in slow formations, that is, formations having shear slownesses greater than the fluid slowness. Dipole sources allow the measurement of shear slowness in slow formations by means of the flexural ‘mode [4]; however, the flexural mode is dispersive and contradicts the assumptions of STC. Fortunately, an analog of STC suitable for processing dispersive waves can be defined. The dispersive analog of STC backpropagates waveforms according to model dispersion curves parameterized by the formation shear slowness S and computes semblance. Backpropagation is performed in the frequency domain. The value of S that maximizes semblance is taken as the estimate of formation shear slowness. A general and valuable equation approximates the semblance when data containing a dispersive wave are backpropagated according to a specified dispersion curve. This equation is critical in understanding dispersive wave processing and explains the results of processing a dispersive wave with nondispersive processing such as STC. “Dispersive STC” (DSTC) is a faster version of the dispersive analog of STC. DSTC starts with a specified, linearly moved-out window and then performs a one-dimensional semblance maximization over shear slowness.