Sunday, November 17, 2019

Reducing 3D Seismic Turnaround

There are two main reasons oil and gas producers worry about time spent on 3D seismic acquisition and processing, called turnaround time. First, in the oil and gas business, as in every business, time is money. The more time spent on drilling, logging and well completion, the longer the delay in production and the lower the profit. 

Add the time to acquire and interpret seismic data before drilling, and the delay in bringing reserves to surface may grow beyond the schedules and budgets of many production managers.

Second, and special to the oil and gas business, saving time can make the difference between being able to do business and not. Development contracts worldwide require oil companies to drill within a specified time. The clock starts ticking once acreage is licensed. A 3D seismic survey planned, acquired, processed and interpreted in advance arms developers with tools for intelligent well placement, yielding higher production from fewer wells. 

More 3D seismic surveys are also being commisioned for exploration, in addition to field development, their initial application. Unlike 2D seismic, which grew from the exploration market into development, 3D seismic has grown in the opposite direction. Companies are discovering that early acquisition of 3D data reduces finding costs and overal project costs. Interpreted seismic data are essential for intelligent bidding on acreage. And some exploration contracts now require a 3D survey before drilling. This expansion into exploration, along with decreases in the cost of seismic acquisition and processing, has raised demand for 3D seismic data .

This increased demand has forced service companies to reduce turnaround time- without sacrificing quality. This article looks first at the dramatic improvements in marine turnaround time, then at the steps being takento significantly reduce turnaround in transition zone and land surveys.

The Marine Story

Three years ago, a marine survey of 500 km square took a year or more to be acquired and processed. Today, through a combination of new technologies, turnaround time for similar surveys can be as little as nine weeks. Technolgies responsible for this dramatic reduction vary from faster acquisition capacity to high speed links with shore-based computers for real-time, full-scale processing.

Today seismic vessels can acquire data 12 times faster than they could in the early 1980s, thanks to multielement acquisition- multiple air gun sources, multiple receiver streamers and evel multiple vessels. Prior to 1984, vessels towed one source array and one 3-km streamer. This configuration evolved to two streamers and two sources per vessel by 1986, quadrupling the area covered with each traverse, and decreasing the cost per unit area. In 1990, streamer length started to increase, also decreasing costs. By 1991, there were two sources firing alternately to three streamers, and by 1992, there were four streamers. And, in a continuing quest for greater capacity, contractors are now building or refurbishing seismic vessels to tow 8 to 12 streamers.

A challenge in designing vessels for multi-streamer acquisition is to keep all the streamers uniformly separated while maintaining vessel speed. Streamers are separated with a deflector, which steers outer streamers away from their normal stream lines. Most streamers follow angled slabs-paravenes- which deflect the streamer outward, but also create drag on the vessel. Each 3-km deflected streamer may exert up to 12 tons of drag, forcing the vessel to consume more fuel to maintain speed. Eight to twelve streamers, with paravenes deflecting the outer ones, would act like a sea anchor, creating enough drag to stop an ordinary vessel. One contractor, PGS Exploration , is designing a more powerful vessel to address this problem.

Rather than design a larger, more expensive vessel to tow more streamers, GecoPrakla has designed the monowing deflector. Acting like an airplane wing flying through water, this "lifts" the streamer apart, and result in a 500% increase in lift-to-drag ratio compared to conventional deflectors. The reduced drag increases acquisition efficiency, and also safety. The lower tension in the lead-in, or tow cables, between the vessel and the streamers, reduce the chance of a tow cable snapping and flapping back to hit the vessel. And unlike other deflectors, orientation of the Monowing can be controlled remotoely, to act as a rudder for the streamer. This allows streamer spacing to be controlled from the vessel, and permits individual streamers to be spooled in for repairs.  

The Monowing deflector has already been deployed in the Irish Sea and West Africa, to tow six streamers. It is being tested with five streamers at extra-wide 150-m spacing, making the 600-m swath acquired in a single vessel pass the widest ever. 

Streamers themselves have also been upgrade. In earlier, analog streamers, hydrophones were wired to the streamer cables and the analog signal transmitted up the streamer and then digitized.  

There may have been signal leakage in the streamer, or cross-talk, in which a signal from one hydrophone gets mixed with that from another. With digital streamers, the signal is recorded digitally so cross-talk is eliminated. Digital streamers are also more reliable, resulting in less downtime and better turnaround.

 While multielement acquisition has played the leading role in reducing acquisition time, it has created a new challenge in reducing overall turnaround time. Data can arrive at a staggering 5 MBytes/sec and some of it must be processed before the next shot is fired- about every 10 seconds- if the processing is to keep pace.

Rising to the challenge is concurrent processing, a combination of onboard processing and high-speed communication with onshore computers and decision makers.

To achieve minimum turnaround time, two sets of data- source signature quality and survey position - must be processed between shots. The source is a cluster of different-sized air guns. On Geco-Prakla vessels the air guns are controlled by the integrated acquisition and processing system. This module fires the air guns in a sequence that is tuned to their sizes. As the size of the gun increases, so does the time from firing to maximum pressure. The controller synchronizes the guns' pressure maxima, giving a stronger source signal. 

The hardware also monitors source output to check the quality of each shot.  

The sensors, located within one meter of the air guns, communicate with the vessel through fiber-optic connections, and are packaged based on concepts from Anadrill's measurements-while-drilling (MWD) technology. In this hostile environment, near a high-energy source and sustaining at least 500,000 shocks per year, the rugged construction that ensures reliable MWD also helps reduce seismic turnaround.

To maximize vessel uptime, errors such as a gun going off at the wrong time, or not at all, must be detected immediately. Then processing specialists can determine whether the shot must be retaken, or whether the recorded signal satisfies the geophysical objectives of the survey. If the signal is sufficient, time is saved. If insufficient, time is still saved, because a seismic line can be quickly reshot while the vessel is still over the survey area.

The second set of data that must be processed between shots is survey position coordinates, called navigation data. Navigation data describe the position on the earh of every source and receiver point in the 3D survey. The data come from relative position measurements made with every shot as the vessel is in motion. The position of the vessel relative to satellites is determined using the Global Positioning System (GPS). The in-sea positions of the seismic sources and receivers are computed using directions from compasses mounted on the streamers and distance information-ranges-provided by acoustic sensors and lasers distributed in networks across the ends of the streamers.  

The TRINAV module of the TRILOGY system collects the compass, laer and acoustic signals, detects transit times, processes them for range , computes the network node positions, calculate source and receiver positions and stores the results in a data base before the next shot is fired. 

The number of sensor data measurements- including compass data, laser ranges and bearings , satellite and radio position signals - used in such a calculation has grown from 15 in the days of single source and single streamer, to more than 350 now with dual sources and eight streamers. 

Checking that the positions fall within the project spesifications is a daunting task, and one whose automation has further reduced turnaround time. Until recently, this was done subjectively by navigation analysts, visually checking plots and position listings. Now, computed positions are quality assured using position acceptance criteria (PAC), automating the time-consuming task and slashing weeks of turnaround. The PAC are established by comparing the range in question to the range of the last shot. If the two are within a predefined threshold, the range is accepted. Deviations are flagged by the computer, making them easy to spot.

While navigation data are being collected and processed, the seismic traces are beginning their journey through data processing. Essentially any processing offered by onshore processing centers can be supplied onboard. 

A Turnaround Breakthrough

In the summer of 1994, Statoil, in partnership with Saga and Mobil, conducted a 3D turnaround pilot project  in block 33/6 of the Norwegian North Sea. The area had already been traversed with 2D lines. The acreage covered in the 3D survey was an extension of play concept that had proven prolific to the south - the oil basin contains the Statfjord field, estimated at more than 3.5 billion barrels of recoverable oil, and the Snorre field. 

 The 33/6 area will be part of concession round 15, recently announced by the Norwegian government. With this survey already acquired, processed and interpreted, the oil companies, acting individually, can make better decisions about how to bid for acreage. 

The goal of the pilot project was to turn around the 313-km square survey in seven weeks. With conventional technology, such a survey would take 18 weeks: 6 for acquisition, then at least another 12 for processing. Executing such a tightly constrained survey requires exact planning. Survey design, acquisition parameter selection and choice of processing chain were given special attention by Statoil and Geco-Prakla geophysicists. In addition to these standard steps, during the planning phase it was recognized that to minimize turnaround time, both Statoil and Geco-Prakla would have to reevaluate accepted working practices: Statoil agreed to hold decision-response time to 12 hours, and Geco-Prakla agreed to increase computer and communication resources that would allow more rapid acquisition and processing.

The Geco-Prakla vessel , Geco Gamma, was equipped with the latest technology for the job. Gamma had the TRILOGY system for onboard navigation and seismic data processing, and access to INMARSAT, the international marinet satellite system. Three IBM RISC 6000s were installed to handle the near real-time processing, reproducing the software and hardware of an onshore processing center. The data would travel directly from the acquisition system to the memory of the TRIPRO onboard processing system. The plan called for crucial data to be transmitted via satellite and land lines to the Statoil office in Stavanger, Norway, where a workstation was installed with the same processing and interpretation software. 

The first shot was fired on June, 22, 1994, with the vessel towing two air gun clusters and four 3000-m streamers spaced 75 m apart. The survey was 11 km wide and was completed in 38 vessel passes, making 293 lines. Some of the first lines were shot in bad weather, which created low-frequency swell noise, above the tolerance level set in the presurvey plan. When that level is exceeded, many oil companies choose to shut down acquisition, and the vessel stands by, at up to $30,000 per day, waiting for weather to calm. But onboard processing showed that the noise could be filtered out, though the filtering would have to be done prestack. 

By monitoring signal quality onboard, and processing the acquired, subspecification data in real time, Geco-Prakla geophysicist were able to decide that the processing scheme would tolerate the noisier data. This eliminated the need to reshoot five or six lines, saving $70,000. The savings paid for the added cost of equipping the vessel with the RISC 6000s, and cut two days off the turnaround.

Early in the planning, the team considered undertaking onboard processing of reduced fold data. But test conducted prior to acquisition indicated that the reduced fold would give inadequate imaging of subsurface reflectors, so full, 30-fold data were processed onboard.

One of the crucial phases of the survey was the construction of the earth velocity  model that would be used to stack and later to migrate the data.

Geco-Prakla geophysicist analyzed velocities on 18 seismic lines selected at 500-m intervals, and transmitted their results via satellite to Stavanger.


Statoil geophysicist loaded the data on workstations in their offices and worked weekends to monitor data quality and relay decisions on the quality of the velocity picks back to the vessel. A velocity model for the 3D volume was then built onboard.

The last major step before stacking- 3D dip moveout processing (DMO)- was also completed onboard for the 30-fold data. This process corrects for the reflection point smear that results when events from dipping reflectors are stacked. The final stack volume was being built as soon as the last shot was fired, and inline migration begun while the vessel was steaming back to port.

The computers and processing specialists were flown to Stavanger, where the final processing was completed three weeks later. Data quality was equivalent to that of a normal onshore processing job, and no immediate reprocessing was scheduled. Seven weeks after the first shot was fired, a Charisma workstation-ready tape was produced, waiting to be interpreted .

Fastracks and Quicklooks

Reduced-turnaround surveys are evolving rapidly, and the amount of processing that goes into each survey varies. Specialists divide reduced-turnaround surveys into two categories : fastracks and quicklooks. Fastracks are fast, fully processed surveys, like Statoil's 33/6. Quicklooks are surveys that process a subset of the full data set- called low-fold- or that simplify processing, such as skipping dip moveout processing. 

Quicklooks give interpreters a head start on interpretation, allowing earlier exploration or development decisions and identifing areas that deserve more detailed processing. BP Exploration has conducted four such surveys offshore Vietnam with Geco-Prakla, using onboard processing of navigation, low-fold data and widely spaced streamers to speed turnaround. In one case, BP had farmed into a prospect- taken over a license relinquished by another operator- with only two years remaining. At the time, the planned 3D survey would have taken six months for full-fold processing, compared to 11 weeks for a low-fold interim data cube. By getting the data earlier, BP interpreters were able to spend more time understanding the prospect before the spud date deadline. 

Quicklooks can be considered preliminary or intermediate results, with potential to benefit from later reprocessing. One example is a 700 km square exploration survey shot and processed onbard by Geco Resolution for Mobil in Papua New Guinea. Only portions of the survey were processed with full fold,saving some of the exploration money for drilling and development.  

Today, quicklooks and fasttracks alike are possible only if the onboard processing sequence is nearly set in stone during presurvey planning with tests on prior 2D data. If acquisition conditions require procesing modifications, some, such as noise attenuation, can be accomodated during the survey.

The Onshore Challenge

Today, turnaround for 3D land and TZ surveys can be only unfairly compared with that for marine surveys. The main difference is in acquisition, which in some cases may take 50 times longer on land than that at sea.

There is also litte formal data on the trends in turnaround for land and TZ surveys, because no two surveys can be  compared. In the relatively constant marine environment, where every survey has roughly the same sources, receivers, subsurface and acquisition geometry, surveys of different sizes and from different areas can be scaled up or down for the purposes of keeping statistics. 

However, on and near land, every survey is different, and turnaround comparisons from one area to another may be meaningless. The environment may vary from swamp to arctic tundra, from desert to jungle. Sources, receivers and acquisition geometries come in as many combinations as there are environments. But in spite of the absence of statistics, land and TZ turnaround are improving. 

Paralleling improvements in marine turnaround, TZ and land surveys are seeing more reliable acquisition hardware, faster acquisition through multiple sources and more receivers, and real-time verification of source and receiver positions. The following two sections describe case studies - first transition zone, then land - to demonstrate some of the latest techniques to shorten turnaround.

Transition Zone

The North Freshwater Bayou in southern Louisiana, USA, was the site of a 3D survey demanding exceptional turnaround. The acreage covered leases operated by Unocal and Exxon. Unocal was drilling at the time of the survey, and planned at least one additional well. Drillers, heading for a deep target below 4.0 sec two-way travel time, wanted to confirm the location of the target before reaching total depth. The challenge was to complete acquisition between July 15 end of the alligator breeding season and the October 15 start of duck migration- a 13-week window of opportunity.

Survey planners designed a 200 km square to be processed in two phases. Processing began on an 46 km square priority area, while acquisition continued over surrounding acreage.

The shallow water environment allowed an all-hydrophone acquisition. Some TZ surveys cross the line between water and land, and require a combination of receivers - geophones on land and hydrophones in the water. Processing such surveys takes extra steps to account for the different responses of the various receiver types.

The hydrophones used in the North Freshwater Bayou were attached to the Digiseis FLX system, a new, flexible transition zone acquisition system developed by Geco Prakla. Each Digiseis-FLX data acquisition unit (DAU) is a floating instrumented tube, tethered to an achor and connected to four hydrophone groups. Up to 1536 channels have been recorded in real time without reaching the limit of the system. This large number of channels allows for flexibility in arranging source-receiver combinations, often without moving the DAU. Seismic data are transmitted to the acquisition boat using radio frequencies that can be adapted to avoid conflict with other radio activity. 

The Digiseis-FLX system presents advantages over other TZ equipment, called bay cable. Bay cable consists of a 1/3-in. diameter instrumented cable, two to three miles long, that lies on the sea bottom. 

The cable can shift with currents, and can be damaged by boat propellers and sharp coral. While radiotelemetry avoids these problems, the added flexibility creates a new problem, synchronization: each unit must record at exactly the same time. The Digiseis-FLX system uses a patented synchronization method, achieving an accuracy significantly higher than other radiotelemetry systems. 

Another innovation that contributes to the speed of the survey is the method with which the source explosives and the hydrophones are emplaced. The technique- ramming- is like using a hypodermic needle to inject a source or receiver into the earth. Ramming sources in soft transition zone cuts down on the time required to drill source holes. On land, drilling crews typically drill 100 to 180-ft [30 to 55 m] deep shot holes in advance of the acquisition crew. Equivalent results are obtained with 40 to 50 ft deep ram holes. 

Ramming not only takes less time, but it also costs less. Deep holes cost about $300 per hole to drill, while ramming cost about $75 per hole. Ramming hydrophones to a uniform depth of 20 ft [ 6 m] below sea level results in better receiver coupling and higher quality data. The main limitation of ramming is the restriction to unconsolidated earth.

Not all the North Freshwater Bayou turnaround speed came from fast acquisition. Geometry verification- much like navigation data processing in the marine environment- carried out in the field, cut weeks off the normal processing time. Geometry verification, a feature of the Voyager mobile data processing system, checks that the source and receiver positions attributed to every shot record are correct. Usually this is checked back at the office after acquisition has been completed and the crew has left, but fixing errors after the fact is time-consuming. In some cases, entire land surveys have had to be reshot- a turnaround nightmare.

One error typically encountered in geometry verification is a mistake in the identifcation of shot-point location. This can occur when the source, say a vibrating truck (vibro for short) is at the wrong location, can't get to the right location, or if the location is miss-surveyed. It can also occur if receiver locations are missurveyed, or if the wrong receivers are active.

These mistakes can be detected quickly by applying some simple processing at the base camp, after the day acquisition. The process is called linear moveout , or LMO. LMO compares arrival times recorded for a given source-receiver geometry to those expected for the same geometry, assuming a constant velocity subsurface. If the source and receivers are in the right places, the LMO process yields seismic traces with first arrivals aligned in time. Any other pattern of first arrivals indicates a mistakes in the source-receiver geometry. 

This technique was used in the Unocal survey to quickly verify geometry in the field. Catching errors with the crew still on site permits corrective action. Shot and receiver locations can be resurveyed if necessary to revise the location data base. Without this field verification, errors may be detected weeks or months later. Then, processing specialists would have to test several possible geometries in hopes of discovering what really happened, spending time and adding uncertainty. Verifying the geometry in the field saves up to four weeks in the office. 

With much of the time-consuming work out of the way, the computing center proceeded with the rapid disk-to-disk processing on a Sun SPARCstation 20. The fully processed 3D cube was ready three weeks after acquisition, in time for interpreters to use. 

Interpretation of the seismic volume signaled drillers that their target would be productive. Unocal interpreters were able to use the seismic data to confirm the quality of their next well location and plan at least one additional deep well at greater than 20,000 ft [6090 m].

Reducing Turnaround on Land

Three-dimensional surveys on land encounter many of the same difficulties as in transition zones, with the added problems of access, topography and extreme temperatures. All of these make for longer acquisition campaigns and more difficult processing.  Under fair marine conditions, multielement acquisition can collect more than 75 km square per day. Under extreme land conditions, such as -40 degree C arctic surveys, acquisition may proceed at less than 1 km square per day. Land surveys of 1500 km square have taken up to 4 1/2 years for acquisition. 

In land surveys more than other types, presurvey planning is the key to minimizing turnaround. Time spent planning and designing is more than compensated by time saved acquiring data. With a given set of equipment, say a certain number of geophones and people, one plan might achieve 150 to 200 shots a day, while suboptimal plan with different shot and receiver line spacing may collect only 100 shots a day.

The most time-consuming tasks in acquisition - be they laying out receivers, drilling shot holes, repairing damaged cables or advancing to the next vibro location - must be identified and minimized to reduce turnaround. In the following examples of 3D land surveys in Texas, such bottlenecks were identified during presurvey planning and circumvented in novel ways. 

Rough Terrain Turnaround

The Val Verde basin in Texas, USA is at the edge of the Sierra Madre mountains that extend north from Mexico. The basin is a hot play for gas, with some wells in the region producing more than 7 MMcf/D. The terrain is extremely rough, with steep-edged mesas and incised canyons. Several 3D surveys in the area have contributed to the continuous improvement of field operating procedures.

In one case, Conoco joined forces with Hunt Oil to acquire the Geaslin survey in the summer of 1994. Both companies had a short fuse: they had to evaluate their leases and make decisions for an early 1995 drill date. The survey design specified the number and location of shot points, but the short turnaround and high cost ruled out dynamite as a source, because too much time would be taken to drill shot holes. 

Vibro sources were available- four vibrating trucks at 12.5-m spacing constitute one source - but the terrain presented mind-boggling logistics: in some cases it would take four hours for a vibro trip up and down a mesa.  

The solution was to use two sets of buggy vibros, or eight in all, similar to a dual-source marine survey. While one set was shaking in the valley , the other set would work its way up a mesa. Similar dual-source vibro operations have been extremely successful in desert areas, such as Egypt and Oman, where there are no obstructions. In this case they allowed acquisition of 60 sq miles [153 km square] in 65 days.

As in all land jobs, darkness presents too many hazards, so the crew operates only during daylight hours. Evenings were well spent, though, running geometry verification on the day's acquired data. One of the goals of the next shift was to have that day's geometry checked and attached to the seismic traces, usually by midnight. That way, geometry problems could be fixed the next day, before the receivers were moved. 

Processing the data from the Geaslin survey proved to be a great challenge. Val Verde basin is notorous for bad data. High velocity carbonates near the surface deflect much of the source energy away from deeper layers; receiver and source coupling to the surface varies with location; and the rugged relief introduces high residual statics- differences in seismic travel time through surface topography. After four months of testing and processing, including 3D DMO and migration, the processing was complete. The next step is preparation, in preparation for a possible 1995 drill date. 

In the nearby Brown Basset survey for Mobil, acquisition time was further shortened by the use of helicopters to move cables, recording boxes and geophones up and down the mesa and canyon walls. Three hundred "helibags" - net bags for transporting material- helped the crew complete the 153 km square acquisition in significantly less time than usual. 

What's Coming to Land

Keeping track of all the information pertinent to a land survey is often the most time consuming job, and steps are being taken to shorten it and make fuller use of all the information available. 

The Olympus-IMS information management system, now in use by Geco-Prakla in Germany, is designed to do just that.

The Olympus-IMS system colocates in a single data base the many types of data that must be handled in a land survey. Previously, every type of data had its own data base: the planned survey layout, the actual surveyed receiver and source point locations, shot hole drilling data, shooting schedule data and the recorded seismic trace data were handled by different software. The new integrated system minimizes the number of data handling steps, reducing errors and improving turnaround. The system will also link directly with processing software to allow field processing for geometry verification and further processing steps. 

Further improvements in land turnaround will come from improvements in hardware and communication. In the most adverse conditions, a good crew may spend as little as two to three hours shooting out of ten spent in the field. In these circumstances,a small amount of time spent trouble-shooting equipment faults can have a considerable impact on turnaround. Geco-Prakla engineers are developing more reliable hardware, to reduce the amount of time spent looking for and repairing flaws in geophones, cables and connectors. Today, each receiver point marked on a map consists of up to 72 individual geophones, whose signals are combined to yield a less noisy signal at a central location, or source point. Up to 140,000 geophones will have to be repeatedly picked up, put down and maintained in the course of a 3D survey. Efforts are also underway to find new ways to acquire the same amount and quality of data with fewer receivers, cutting survey time. 

Improved communications will also cut turnaround time. Increased use of GPS is decreasing the time spent  surveying positions for land source and receiver points. Surveying with GPS is faster and easier to check than traditional theodolitic surveying, and leaves less room for human error.  Placing GPS units on vibro sources helps keep track of actual source locations and reduces location error.

For arctic land surveys, snow streamers have been developed in collaboration with Norsk Hydro as substitutes for hand-placed geophones in an effort to increase acquisition efficiency. Geco-Prakla engineers have tested snow streamers in six programs, acquiring 1200 km of 2D data. Efforts are also underway to minimize environmental impact, which in arctic environments must be included as part of turnaround- a single drop of oil spilled must be recovered before the crew moves.

Connecting land crews via satellite to SINet, the Schlumberger Information Network, will give better day-to-day contact with office bases, speeding equipment and supply requests and allowing interaction with processing centers. 

Moving more processing to the field will further reduce turnaround for both land and transition zone surveys. Parameter testing, noise attenuation and velocity picking can be done with today's field processing tools. But full concurrent processing, as performed in marine surveys, is still a dream for land. 

Land acquisition, more so than marine , is a three-dimensional problem: sources are not aligned with receiver lines, and more time is needed to acquire enough seismic traces to process one part of the 3D volume. 

At best, processing through to stacking could lag acquisition by a few weeks, but the difficult task of computing residual statics before stacking cannot begin until all data are in. Advances may come from taking a new view of 3D land surveys- planning, acquiring and processing with a truly three-dimensional view- rather than simply repeating a series of two-dimensional snapshots.

The Role of Integrated Services in Reducing Turnaround

Marine, TZ and land 3D surveys are sure to find further turnaround improvement in the common ground of integrated services. In an integrated-service survey, planning, acquisition, processing and project management are delivered by one service company. Traditionally, the oil company plans the survey, then one contractor acquires the data and another processes it. Time is wasted transferring data and responsibility between parties. 

Geco-Prakla has developed an integrated service for 3D surveys called TQ3D- Total Quality 3D. Larger in area than most surveys, TQ3D projects can cover leased and open blocks. A TQ3D projects may be operated from 100% nonexclusive, or anywhere in between. Data acquired on proprietary basis become the property of the operator.