Estimating VP/VS ratios using smooth dynamic image warping

Abstract

Multicomponent seismic images are composed of different combinations of downgoing and upgoing wavefields. Each wave mode has different propagation velocity and polarization direction and thus carries unique, directiondependent information about the subsurface. Differences in propagation velocity cause events in converted-wave or PS images to appear at later times than the P-wave or PP image counterparts. Reflectivities are different for each wave mode, and therefore, multicomponent images are not related simply by time shifts. These complications historically required that the alignment, also called registration, of corresponding image features be done manually, which is a tedious process. To register PP and PS images automatically, we used a smooth dynamic image-warping algorithm that can be accurate with respect to problems unrelated to time shifts, such as differences in noise and reflection waveforms. Interval V P ∕V S ratios can be estimated from derivatives of vertical shifts that align reflections in PP and PS images. To optimize accuracy of estimated time shifts and V P ∕V S ratios, we automatically constructed a coarse lattice of points located on reflections with high amplitudes and then estimated time shifts at only those image samples. By adjusting the coarseness of the lattice, we trade off resolution of changes in V P ∕V S with increased accuracy in V P ∕V S estimates. By processing 3D PP and PS images, we learned that our estimates of V P ∕V S cannot be obtained by smoothing time shifts estimated at every image sample.

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

“…One potential problem of the common DTW method (Hale, 2013; is that the estimated shifts are limited to integers, which may not be sufficient to accurately correlate the synthetic and real seismograms. We use the smooth DTW method, proposed by Compton and Hale (2014), to compute smoothly varying shifts, which are often more accurate than those from the common DTW method, as suggested by Muñoz and Hale (2015). As described in detail by Compton and Hale (2014), the smooth DTW method solves the same minimization problem (equation 4) to first compute coarsely sampled shifts and then interpolate back smooth shifts for all samples.…”

“…The number of synthetic seismograms N u f varies with RGT u f because some seismograms may be missing at some u f as shown in Figures 4b and 6a. Because the shifts s u ðu f Þ vary only vertically with u f , we can efficiently perform minimization in equation 11 and obtain s u ðu f Þ using a 1D smooth DTW method (Compton and Hale, 2014).…”

“…We then generate an initial synthetic seismogram by convolving the reflectivity series with the wavelet delayed by the initial time-depth function. We then use smooth DTW (Compton and Hale, 2014) to compute vertical shifts that match the synthetic seismogram with the corresponding real seismogram, and we use these shifts to update the time-depth function. We iteratively update the time-depth function and the synthetic seismogram until the updates are insignificant to finally obtain the single well-seismic tie, as is described by Muñoz and Hale (2015).…”

“…Because the interpolation is guided by the real seismic image as discussed by Hale (2010b), the structures of the interpolated synthetic image laterally conform to the real seismic image. They then match the synthetic image with the real seismic image using smooth dynamic image warping (Compton and Hale, 2014). Cubizolle et al (2015) propose a similar method to compute simultaneous multiple well ties, but they use a relative geologic-time (RGT) volume (Stark, 2004;Wu and Zhong, 2012), computed from the real seismic image, to interpolate a similar synthetic image.…”

Simultaneous multiple well-seismic ties using flattened synthetic and real seismograms

“…As shown in Figure 2a, these synthetic seismograms (red), computed with the initial time-depth functions (equation 2), do not match the real seismograms (black). Next, we will discuss how to update the time-depth functions one by one for better single well-seismic ties using smooth DTW (Compton and Hale, 2014).…”