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\begin{document}
\title{Reservoir monitoring with permanent encoded seismic arrays} 
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\author{Gboyega Ayeni\footnotemark[1], Stanford University.}
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\footer{4D seismic with permanent encoded seismic arrays}
\lefthead{Ayeni, Tang \& Biondi}   
\righthead{4D seismic with permanent encoded seismic arrays}
\maketitle
%:abstract
\begin{abstract}
	Hydrocarbon reservoirs can be monitored with encoded data from permanent seismic arrays.
	Permanently installed arrays can yield a vast amount of data that may be used for near real-time monitoring.
	Because these vast data volumes pose operation, storage and processing challenges, an encoding approach is desirable.
	Although data encoding introduces cross-talk artifacts, permanent arrays for high-repeatability of such artifacts, making time-lapse cross-equalization easy.
	Furthermore, stacking data from several encoded low-energy intermittent seismic sources improve the signal-to-noise ratio.
	Direct migration of the recorded data is efficient and gives good-quality seismic images.
	Using a 2D numerical model, we show that this method can give reliable time-lapse images that are comparable to those from conventional single-source data sets.
\end{abstract}
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\section*{Seismic reservoir monitoring with encoded data}
	Time-lapse seismic reservoir monitoring is an established technology.
	By repeating the seismic experiment over an evolving reservoir, changes in reservoir properties can be estimated from seismic amplitude and travel-time changes.
	Many successful case studies demonstrate the technical considerations and business impact of time-lapse seismic \cite[]{rickett:2001,whitcombe:2251,ebaid:holstein}.
\par
	By enabling seismic recordings at small time intervals, permanent seismic arrays can make near real-time monitoring possible.
	Several authors have discussed seismic reservoir monitoring with permanent seismic arrays.
	\cite{lumley:instru,lumley:perm} discuss important business and technical drivers, 
	\cite{meunier:perm} discusses a field experiment at the C\'er\'e-la-Ronde test-site, 
	\cite{smit:perm} discuss a sparse field implementation at the Valhall field, and 
	\cite{forgues:perm} discuss a field experiment at the Steam-Assisted Gravity Drainage (SAGD) project.
	Because permanent monitoring systems do not suffer from positioning errors, seismic experiments can be repeated with high accuracy.
\par
	In addition to the high operation and storage costs of the recorded data volumes, conventional processing cost of the recorded data can be high.
	Although, under certain conditions, simple (e.g. Normal moveout) processing can give satisfactory results  \cite[]{forgues:perm}, such methods are inadequate in many geological environments.
	In this paper, we show that direct wave-equation migration of encoded data-sets from such permanent recording systems can provide high-quality time-lapse images at relatively low cost.
\par
	Encoded seismic data recording with permeant seismic arrays straddles conventional and passive data recording.
	Although our understanding of passive data imaging has improved over the past decade, several limitations exist.
	Direct imaging of passive data suffers several pitfalls \cite[]{artman:pass}, and the cost of high-quality Green's function retrieval by interferometry is non-trivial \cite[]{ridder:pass}.
	In many scenarios, seismic reservoir monitoring with interferometric Green's function from surface passive seismic arrays is difficult \cite[]{lu:interf}.
	However, reservoir monitoring with active-source (virtual-source) and ambient-noise interferometric Green's functions have been shown for borehole sensors \cite[]{bakulin:virt,lu:interf}.
	Although borehole systems may give satisfactory time-lapse response in the vicinity of the well, surface or seabed systems provide better coverage and are easier to manage.
\par
	Although encoded seismic data recording is not new \cite[]{womack:1389}, recent acquisition and processing technology advances have increased interest in the subject \cite[]{hampson:2816,beasley:2796,berkhout:2831,howe:simu}.
	Direct imaging of such encoded data is possible but suffer from {\it cross-talk} between data sets \cite[]{romero:426,artman:pass}.
	These imaging artifacts can be attenuated by linearized least-squares migration/inversion \cite[]{tang:seg09}.
	To directly image field-encoded time-lapse data sets from non-permanent arrays, a linearized inversion method can be used to attenuate artifacts caused by non-repeatable geometry and relative shot delays \cite[]{gboyega:seg1}.
	Because permanent seismic arrays enable excellent repeatability of the geometry and encoding function, cross-term artifacts are similar between consecutive surveys, and linearized inversion is unnecessary.
\par
	To ensure good repeatability at the source-position over the monitoring period, and to limit operation cost, low-energy, low-footprint seismic sources are desirable.
	The source waveform may be a long-duration sweep \cite[]{meunier:perm,forgues:perm}, or an idealized seismic source that can emit intermittent pulses.
	By stacking data from several low-energy sources, the signal-to-noise (S/N) ratio is increased and sufficiently high-quality data and images can be obtained.
	Direct imaging of encoded data from several weak, intermittent seismic sources can also give high-quality seismic images.
	Data-encoding is important because it reduces the total recording time for several shots, each requiring long recording duration.
	In this paper, it is assumed that these conceptual low-energy sources are randomly and intermittently ignited over a long time period.
\par
	Using a phase-encoding migration operator and the relative time-delays between sources, the encoded data are imaged directly without any separation or Green's function retrieval by interferometry.
	Because all the data are migrated with a baseline velocity model, images from different vintages are not aligned and must be cross-equalized.
	Migrated monitor images are aligned to the baseline using an iterative 1D correlation algorithm \cite[]{hale:V99}. 
	Apparent displacements from this process contain velocity and geomechanical information. 
	The aligned images are then matched using a variant of the the optimized local-matching method \cite[]{gboyega:seg3}.
\par
	First, we give a conceptual description of the data recording and imaging.
	Next, we summarize the cross-equalization methodology that is applied.
	Finally, using five data sets from a 2D numerical model, we show that the proposed method gives good-quality time-lapse images.

\section {Data recording and imaging}
	From the linearized Born approximation of the acoustic wave equation, the seismic data ${d}$ recorded by a receiver at ${\bf x_{r}}$ due to a shot at ${\bf x_{s}}$ is given by
	\begin{equation}
		{ d}{(\bf x_{s}, x_{r},\omega})=\omega^{2}  \sum_{\bf x}f_{\bf s}(\omega)G ({\bf x_{s}, x,\omega}) G ({\bf x},{\bf x_{r}},\omega)   m({\bf x}),
		\label{eqn:one}
	\end{equation}
	where $\omega$ is frequency, ${m({\bf x})}$ is the \emph{reflectivity} at image points ${\bf x}$, $f_{s}(\omega)$ is the source wavelet, 
	and $G ({\bf x_{s}, x,\omega})$ and $G ({\bf x, x_{r},\omega})$ are the GreenÕ's functions from ${\bf x_{s}}$ to ${\bf x}$ and from ${\bf x}$ to ${\bf x_{r}}$, respectively.
	When there are multiple seismic sources, the recorded seismic data is due to a concatenation of phase-shifted sources. 
	For example, the recorded data due to shots starting from ${\bf s=q}$ to ${\bf s=p}$, is given by 
	\begin{equation}
		{d}{(\bf x_{s_{pq}}, x_{r},\omega})=\sum_{s=p}^{q} a(\gamma_{\bf s}) \omega^{2} \sum_{\bf x} f_{\bf s}(\omega)  G ({\bf x}_{\bf s}{\bf, x,\omega}) G ({\bf x}, {\bf x}_{\bf r},\omega)   m({\bf x}),
		\label{eqn:two} 
	\end{equation} 
	where $a(\gamma_{\bf s})$ is given by
	\begin{equation}	 
		a(\gamma_{\bf s})=e^{i\gamma_{\bf s}}=e^{i \omega t_{\bf s}},
		\label{eqn:three}
	\end{equation} 
%:
	and $\gamma_{s}$, the time-delay function, depends on the delay time $t_{s}$ at shot ${\bf s}$.
\par
	Intermittent shooting of each shot is equivalent to repetition of equation~\ref{eqn:two}, with the different encoding function.
	Data from intermittent seismic sources are similar to passive seismic data, except that all shot positions and timings are known.
	Therefore, the recording experiment can be regarded as a controlled-source passive experiment.
	Figure~\ref{fig:perm-source,perm-source-big} shows examples of the idealized source waveform from four intermittent seismic sources.
	It is assumed that these sources are orders of magnitude weaker than conventional seismic sources and that data from a single pulse is insufficient to create a good-quality image. 
	
\multiplot{2}{perm-source,perm-source-big}{width=0.85\columnwidth}{Source waveforms for four intermittent seismic sources (a) and the same waveforms showing the first 12 s. Note the relative delays between pulses from different source.}
 
\par	 
	Direct imaging of the recorded data, the adjoint to equation~\ref{eqn:two}, is a linear phase-encoding migration operator \cite[]{romero:426,artman:pass}.
	This is equivalent to a single shot-profile migration of the recorded data with a single source-function derived from concatenating delayed intermittent source waveforms from all shot positions.

\section {Cross-equalization}
	Cross-equalization processing removes unwanted differences between the imaged data sets.
	Such differences may be caused by uncorrelated noise or geomechanical changes. 
	The post-imaging procedure can be divided into two steps.
\subsection {Image alignment:}
	Because direct velocity analysis with the recorded data is difficult, we assume that a baseline velocity model built from conventional seismic data will be used to image all data sets.
	This leads to misalignment due to reservoir compaction and velocity changes. 
	To align the monitor and baseline images, an iterative 1D correlation method is used to estimate vertical and horizontal displacement components \cite[]{hale:V99}. 
	For each iteration, and each correlation direction, inputs are the shifted images from the previous step and updated accumulated displacements in all directions. 
	Starting with large correlation gates and lags, low-frequency high-amplitude components are first estimated, then with gradually decreased gates and lags, high frequency low-amplitude components are estimated.
	This process is repeated until a satisfactory alignment is obtained.

\subsection {Match filtering:} 
	This trace-by-trace procedure involves estimation of a match filter that equalizes a non-reservoir segment of each monitor trace to the corresponding baseline trace and application of such a filter to the whole trace.
	For each trace, the estimation window and parameters are optimized with an evolutionary programming algorithm \cite[]{gboyega:seg3}.
	For each iteration, spatial consistency between the local filters is ensured by applying a smoothing operator to the optimized filter-estimation parameters and repeating this process with the new parameters as the starting guesses.

\section {Numerical example} 
	Five data sets were modeled over a modified section of the 2D Marmousi model (Figure~\ref{fig:vel-0}).
	The objective is to image seismic amplitude and geomechanical changes around the reservoir using encoded data sets from permanent arrays.
	The non-linear discontinuous changes in the reservoir were modeled by changes in velocity within the reservoir.
	Geomechanical changes due to reservoir compaction were modeled by a morphed expanding gaussian anomaly above the reservoir.
\par
\plot{vel-0}{width=1.01\columnwidth}{2D Marmousi velocity model.}
	Each surface seismic source generates an intermittent pulse within a $6$s window with unique random $0-3$ s delays between sources. 
	Five minutes of data from ${388}$ seismic sources were recorded by surface receivers (Figure~\ref{fig:perm-data}).
	The data were imaged directly with a phase-encoding one-way shot-profile wave equation algorithm (Figure~\ref{fig:perm-mig0-15}).
	Each data set was migrated with a smooth version of the baseline modeling velocity (not shown).
	For comparison, images from conventional data and processing are shown in Figure~\ref{fig:perm-mign-15}. 
\par 
	Time-lapse images computed from the migrated images show significant misalignments (Figures~\ref{fig:perm-mig0}).
	Prior to match-filtering, the estimated displacements (Figure~\ref{fig:perm-ts-z,perm-ts-x}) were used to align the monitor images to the baseline.
	The final time-lapse images from the proposed method and conventional data are shown in Figure~\ref{fig:perm-mig2,perm-mign}.

	
\plot{perm-data}{width=.9\columnwidth}{Five seismic data sets from intermittent seismic sources over the model in Figure~\ref{fig:vel-0}. 
The blue intersecting lines indicate positions of slices through the data volume that shown on the three faces.}
 
\section {Discussion} 
	Data from several permanent intermittent low-energy seismic sources have the form of passive data recording (Figure~\ref{fig:perm-data}).
	However, because the shot locations and the shot times are known, a strong limitation of passive data is eliminated.
	Direct imaging of data from these randomly encoded seismic sources can give images of comparable quality to conventional data recording and processing (Figure~\ref{fig:perm-mig0-15,perm-mign-15}).
	This is because, during migration, cross-talk artifacts from different seismic pulses destructively interfere, whereas the true reflections constructively interfere.
	It is important that the time-lapse images obtained from these type of recording can provide similar information to that provided by conventional recordings.
	The time-lapse images computed prior to cross-equalization (Figure~\ref{fig:perm-mig0}) are similar to those from conventional data recording and processing (not shown).
\par
	Note that there is significant cost-savings in both the acquisition and data processing.
	Encoding eliminates the need for long waiting periods that would be otherwise required for low-energy seismic sources that require data stacking.
	Furthermore, because permanent arrays enable frequent data recording, encoding reduces the data storage requirements.
	In addition, independent of the number of encoded sources, direct imaging is a single phase-encoding shot-profile migration.
\par	
	Even when all data are imaged with a strongly smoothed baseline velocity model, interpretable geomechanical information can still be obtained (Figure~\ref{fig:perm-ts-z,perm-ts-x}).
	These apparent displacement components are similar to those from conventional time-lapse seismic data (not shown).
	After cross-equalization, time-lapse images from the proposed method and from time-lapse seismic data are similar (Figure~\ref{fig:perm-mig2,perm-mign}).

\section {Conclusions}
	A method for reservoir monitoring with encoded data from permanent seismic arrays has been proposed.
	Encoding randomly delayed intermittent pulses from low-energy sources reduces the total recording time for each seismic experiment.
	Direct imaging of such data give good-quality images that can be used for near-continuous reservoir monitoring.
	From the numerical experiment, it was shown that geomechanical and seismic amplitude changes from the proposed method are similar to those from conventional seismic data.
	Therefore, with this encoding approach, no useful time-lapse information is lost.
	
\section {Acknowledgements}
	The author thanks sponsors of the Stanford Exploration Project for their financial support.

\multiplot{2}{perm-mig0-15,perm-mign-15}{width=0.8\columnwidth}{Images from direct migration of a baseline and one monitor data (Figure~\ref{fig:perm-data}) (a), 
													and from shot-profile imaging of conventional data over the same set of models (b). 
													Note that the two sets of images comparable.}
%\multiplot{2}{perm-mig0,perm-mig1}{width=0.88\columnwidth}{Downgoing source wavefields for (a) the baseline and (b) monitor data sets. Note the difference in shot-timing.}

\plot{perm-mig0}{width=0.8\columnwidth}{Time-lapse images from direct imaging of encoded intermittent source data (Figure~\ref{fig:perm-data}). 
Note that the seismic amplitude changes at the reservoir are masked by the strong misalignment of the images.
Reservoir change increases non-linearly from top to bottom.}
\multiplot{2}{perm-ts-z,perm-ts-x}{width=0.8\columnwidth}{Estimated vertical (a) and lateral (b) apparent displacement components between the baseline and monitor images.}
\multiplot{2}{perm-mig2,perm-mign}{width=0.8\columnwidth}{Time-lapse images from direct imaging of encoded intermittent source data (a) and from conventional seismic data (b).
Note that as in the conventional data (b), discontinuities in the seismic amplitude change are accurately imaged by the proposed method (a).
The two sets of images are comparable.}
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\end{document}
