Broadband wavelet estimation For Hampson-Russell software Menne

Menne Schakel

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Table of contents

1 Background and introductory remarks ............................................................................................................................... 3

2 Broadband wavelet estimation method .............................................................................................................................. 4

3 Illustrations broadband wavelet estimation ........................................................................................................................ 5

4 References ...................................................................................................................................................................... 8

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1 Background and introductory remarks

Broadband seismic has energy at lower frequencies than what is called “conventional” seismic. For example, broadband seismic may have energy down to 2.5 Hz, while conventional seismic doesn’t contain energy at frequencies below say (typically) 6 Hz. For seismic inversion the gap between 0 Hz (or DC component) and the lowest frequency that still contains significant seismic energy is filled by a low frequency model. A seismic inversion can be regarded as the merge between this low frequency model and the inverted seismic, where the merging occurs around the lowest frequency that contains significant energy in the seismic. The low frequency model determines the absolute values of elastic properties computed from a seismic inversion. Elastic properties generally correlate well with reservoir properties. Therefore the low frequency model is required for most workflows that derive quantitative estimates of reservoir properties.

The low frequency model often consists of interpolated well values. This interpolation can be regarded as arbitrary, for instance when a simple mathematical interpolation is performed. Such an arbitrary interpolation may bias the inversion. An alternative is to use processing velocities that are readily available to guide the low frequency model trend. Since these velocities are derived from the seismic data itself, they are more likely to correlate with geology. However, their (meaningful) energy content may be limited, for instance 0 – 2 Hz. Therefore it is customary to use the low frequency model trend from processing velocities for the lowest frequencies and to use the interpolated well values for frequencies above it. It must be noted that the useful energy content of processing velocities depends on how they were derived. For instance NMO-derived velocities may have a smaller useful bandwidth than velocities that were obtained from tomography. Therefore it is up to the geoscientist to make sensible choices regarding the highest frequency to use for low frequency model building from processing velocities. In a similar fashion it is up to the geoscientist to decide on the lowest broadband seismic frequency to use. For example, a geoscientist may decide to invert broadband seismic energy down to 3 Hz (requiring a 1/3 s length wavelet), and to use the low frequency model up to 3 Hz (either from the velocity trend, the well logs, or both). Several case studies have shown that broadband seismic inversions can be performed by using a low-frequency model derived from processing velocities up to a frequency close to those used for conventional inversions (e.g., 5 Hz, see Michel et al., 2012; Kneller et al., 2013). The wavelet estimation procedure then becomes similar to a conventional inversion wavelet estimation. The workflow below is about estimating longer wavelets (say > 200 ms) than wavelets used for conventional seismic inversions.

Given current practice as described above, one of the natural advantages of broadband seismic is to invert the low frequencies in the broadband seismic, rather than having to model them by interpolated wells. The ultra-low frequencies (< 2.5 Hz), are then obtained from the seismic data-driven processing velocities. Thus fully data-driven inversions are obtained, allowing fully data-driven quantitative reservoir characterization.

However, inverting low frequencies requires a long wavelet. For instance if a 2 Hz signal in seismic is to be inverted, it will require a wavelet with a minimum length of 500 ms. Conventional wavelet estimation is performed by relating well log reflectivity to seismic. It is generally advised to use an estimation time window that is several times larger than the length of the wavelet. For seismic data having frequency content potentially down to 2 Hz, this would mean that the well log length over which the wavelet is estimated should be, say, 1500 ms in length in order to properly catch the low frequency content of the data. This poses several issues: well logs often are not of this length, estimated wavelet error is introduced because the seismic and well logs are less likely to match consistently over a long interval, and the seismic may suffer from vertical (amplitude) variability. Here we outline a broadband wavelet estimation procedure to overcome these issues.

The enhanced higher frequency content of broadband seismic, which reduces with depth, can be inverted consistently using time-variant wavelets. A pragmatic approach using a single (non time-variant) wavelet suitable for inversion at the target interval may be preferred for timing constraints. Inverting the higher frequencies of broadband seismic will not further be discussed here.

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2 Broadband wavelet estimation method

The steps are (for full stack and simultaneous inversions):

1. Estimate a short “conventional” wavelet from a preferred workflow

2. Estimate a broadband constant phase wavelet from the seismic. Decide on the desired broadband wavelet length

3. Match the phase and amplitude spectrum of the conventional and broadband wavelet within the frequency range of the conventional wavelet. Extrapolate the phase spectrum of the broadband wavelet to the lowest frequency to invert for and (if applicable) to the highest frequency to invert for

4. Validate the broadband wavelet and modify it when desired

In case of a simultaneous inversion, these steps are performed per angle/offset stack.

ad 1. Wavelet estimation and well-tying is a key task during an inversion project. Much insight is gained on how the well logs (and reservoir properties) relate to the seismic during wavelet estimation. The conventional wavelet estimation can be performed on the broadband seismic data directly. Another option is to use the bandpassed (e.g. 6 -60 Hz) or low-cut filtered broadband seismic (e.g. at 6 Hz)

ad 2. Use the Wavelets > Extract Statistical Wavelet process to estimate a spectrum from the seismic using a fixed phase spectrum for a fixed wavelet length. Test several time intervals. The geoscientist has to make a choice on the lowest seismic frequency/wavelet length to use for the inversion. Low-frequency energy coherency can be investigated by examining filter panels in several frequency ranges (e.g., 2 – 3 Hz, 3 – 4 Hz, 4 – 5 Hz) along a key event. Background information from processing is another valuable resource to establish the lowest meaningful frequency.

ad 3. Use Data Explorer > Wavelet Data Explorer > Options > Edit to edit wavelets. Matching and extrapolation of the phase is done. For extrapolation of the phase spectrum (at low and high frequencies) several scenarios can be tested, such as constant, linear, and curved

ad 4. Use the Log processing > Log Correlation process and the Inversion > Inversion Analysis process for test-inversions. The following tests can be done (non-exhaustive): judge the quality of the well-tie, perform test-inversions to judge the validity of the broadband wavelet(s) and look at the QC’s (for instance a crossplot of well-log and inverted elastic property at the well location). From this validation the suitability of a broadband wavelet for inversion can be assessed. In case there are several plausible broadband wavelets, the preferred wavelet and the extent to which the inversion results will differ can also be determined.

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3 Illustrations broadband wavelet estimation

Figure 1 shows the wavelets corresponding to each of the steps. The “conventional” wavelet (top left) was estimated from bandpassed broadband seismic using a conventional workflow. Note that the wavelet could also have been obtained from the un-bandpassed broadband seismic when estimated over the target interval (also note that the high frequency content of broadband seismic reduces with depth). A zero degree statistical wavelet was estimated from the broadband seismic (top right). A 1000 ms window centered on the target was used. Frequency spectra estimated from the broadband seismic indicated energy presence down to 2 – 3 Hz, and it was decided to use a 500 ms wavelet. The proposed broadband wavelet (bottom left) was obtained by matching the conventional and zero-phase statistical wavelet within the conventional wavelet range and extrapolating the phase trend at low and high frequencies. In order to validate it, individual well-ties and wavelet extractions were performed and the wavelet was updated resulting in the final broadband wavelet (bottom right).

Figure 1: Conventional wavelet (top left), estimated zero-phase statistical wavelet (top right), initially proposed broadband wavelet (bottom left) and final broadband wavelet (bottom right).

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Figure 2 (left) shows a comparison of a direct broadband wavelet estimation (gray) (Extract Wavelet Using Wells) and the proposed broadband wavelet (blue). The direct estimation of the wavelet is very noisy, however it does validate the amplitude spectrum. Also it suggests that a linear slope from a negative phase value rather than remaining constant is another possible scenario for the broadband wavelet, which is shown in the right panel.

Figure 2: Left panel: Proposed wavelet (blue) and a direct broadband wavelet estimation (gray). Right panel: Final broadband wavelet (blue) and the direct broadband wavelet estimation (gray). The gray wavelet phase spectrum can also be approximated by a linear slope towards a negative phase value.

Whether the blue broadband wavelet of the left panel or the blue broadband wavelet of the right panel should be used can be tested by comparing the well-ties and real log versus inversion result correlations in the Inversion Analysis process. The inversion result using the blue broadband wavelet of the left panel is shown in the left panel of Figure 3 (red curve). Also shown is the starting model (black curve) and the real log (blue curve). The inversion result using the blue broadband wavelet of the right panel is shown in the right panel of Figure 3.

Figure 3: Real P-impedance (kg/m^3*m/s) log (blue), starting model (black), and inversion at well location (red) for an inversion using the blue broadband wavelet of the left panel in Figure 2 (left) and for an inversion using the blue broadband wavelet of the right panel in Figure 2 (right).

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Some differences in the inversion results of Figure 3 can be observed. Figure 4 quantifies the match between actual well logs and inverted logs for the two possible broadband wavelets. This shows that the final broadband wavelet (blue broadband wavelet of the right panel in Figure 2) is the optimal wavelet in terms of this QC.

Figure 4: Crossplot of the well log P-impedance and the inversion result at the well location for an inversion using the blue broadband wavelet of the left panel in Figure 2 (left) and for an inversion using the blue broadband wavelet of the right panel in Figure 2 (right). Time interval corresponds to the time interval over which the inversion was computed as shown in Figure 2. Sample interval is 2 ms.

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4 References

- Kneller, E., A. Ferrer, and J. Langlois, 2013, Benefits of broadband seismic data for reservoir characterization, Santos Basin, Brasil: Thirteen International Congress of the Brazilian Geophysical Society, 966–970.

- Lafet, Y., L. Michel, R. Sablon, D. Russier, and R. Hanumantha, 2012, Variable depth streamer — Benefits for rock property inversion: 74th EAGE Conference & Exhibition, J07.

- Schakel, M.D., P.R. Mesdag, 2014, Fully data-driven quantitative reservoir characterization by broadband seismic, SEG 84th Annual International Meeting, Expanded Abstracts, 2502-2506.