The most common way to estimate lithology, porosity and fluid content from seismic data is through inversion for acoustic and shear impedances. If properly computed, these impedances can be compared to impedance logs computed by combining sonic, dipole sonic and density logs measured in the well. Crossplotting the well impedance logs with gamma ray, porosity and mineralogy logs provides a rock physics template that can then be applied to the seismically derived impedances, thereby providing 3-D estimates of the desired property.

Seismic data are bandlimited, with frequencies commonly ranging from 8-80 hertz. Impedances computed from such data are also bandlimited (to the same 8-80 hertz range, for example) and lack the low-frequency trends and biases needed to map the seismically derived impedances onto our rock physics template. A general workflow to construct “absolute” impedance measures is to pick horizons from the seismic data, use the impedances measured in the wells, interpolate them to honor structure and any geologic processes (such as changes of impedance with depth or interpreted lithologies) and then low pass filter the “modeled” result to 0-8 hertz. This low-frequency impedance model is then added to the seismic-derived bandlimited impedance to produce the absolute impedances needed for our crossplots.

If we could acquire more low frequencies during seismic acquisition, we would be able to measure and then invert for the spatially detailed low-frequency response of the subsurface on a 25-by-2-meter grid, thereby obviating the need to interpolate these components with our spatially smooth low-frequency model. In the absence of acquiring new data, we need to improve the data we have in hand.

## Bandwidth Determination, Spectral Balancing

A key part of seismic processing is to determine its bandwidth; to do so, the seismic processor applies a suite of bandpass filters to the data and subjectively decides (despite their love of arithmetic!) which frequency bands contain some signal (specifically, show some geology), and which frequency bands are mostly noise. With an estimate of these values, the processor then applies a (perhaps time-variant) bandpass filter to the data volume, where the edges of the bandpass are tapered smoothly to reduce artifacts.

One way to enhance both the low- and high-frequency components of the seismic data is through spectral balancing, which we addressed in our October 2023 installment of Geophysical Corner. We therefore apply spectral balancing to the data shown in figure 1a and obtain the result in figure 1b. The results are unsatisfying, where we have increased the noise in our data. Unfortunately, structure-oriented filtering using the normal 3-trace by 3-trace (50×50-meter) analysis window is too short to filter the longer wavelength low-frequency noise. Applying a much larger 400-meter-diameter circular filter suppresses the noise but overly smooths the data.

## Application

At this point, we recognized two earlier contributions in this area that we had previously overlooked, and which have not made their way into mainstream seismic processing and interpretation workflows. While one suggested frequency slice filtering technique that targets precise parts of the frequency spectrum, the other introduced the idea of dividing the frequency spectrum into bands, applying structure-oriented filters, and recombining for improved frequency content. In this application, we apply a suite of bandpass filters to the data shown in figure 2. We then follow standard seismic processing best practices and visually examine each of the bandpass filtered data volumes. Filter banks 5 and 6 had only moderate noise, so were left alone. Filter bank 1 centered about 0 hertz had no geologic signal so was rejected. Figure 3a shows filter bank 2, centered about 5 hertz. Following the previous work cited above, we designed the filters shown in table 1. The filtered 5-hertz component is shown in figure 3b and the rejected noise in figure 3c where we see little geologic signal has been rejected. Because of the strong vertical noise, edge preservation would sharpen the signal-noise boundaries. Although the edges in figure 3b may now be smeared, the stratigraphic reflectors are now conditioned for impedance inversion. We repeat the process to filterbanks 3 and 4, add the filtered results to the unfiltered filterbanks 5 and 6 and apply spectral balancing to obtain the seismic data shown in figure 4.

Figure 5 shows the time-frequency spectra of the original data and after the workflow described here. Note that the spectra are both flatter and extend to both higher and lower frequencies. With these data we can proceed to model-driven impedance inversion.

For the original data, we needed to provide a very smooth low-frequency impedance model ranging from 0-15 hertz. For the filtered data volumes, this low-frequency smooth impedance model only needed to cover the 0-2.5 hertz range, with the 2.5-15 hertz frequency band being defined by the measured high spatial resolution 25×25-meter seismic data.

Acknowledgement: We thank Ritesh Kumar Sharma for generating the images shown in figure 6.

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